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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Putting the "Rule of Thumb" to test
#5401331 - 09/03/12 03:49 PM

While the Dawes and Rayleigh limits are quite useful but limited to doubles in the range of +6mag and about 1 delta-m the Lord Rating is more versatile considering parameters like delta-m and seeing but the same time more wishy-washy with indications like "extremely difficult" etc. (reminds me to Clive Coates with his Burgundy reviews - very well indeed). The fuzzy Difficulty Index is a seemingly exact number but without any referencing parameters ignoring even aperture - and is to my feeling of no real value.
What I like is the from Bruce and Fred in another thread on this forum suggested rule of thumb for the required aperture for splitting a double: Required aperture in mm = 116/(sep/delta-m) with delta-m set to 1 if less than 1 - seems quite useful to me and some testing should prove the validity of this formula.
I started with Eps Lyr as entry point near the Dawes limit:
116/(2.2/1)=~50mm. Starting with 140mm this was an easy one with x140. Reducing the aperture with a mask down to 100/90/80/70/60mm did not change very much besides a better saturation of colours. At 50mm there was no longer a clear split but still a clear elongation indicating the position of the companion. Test result positive I would say.
Now comes the interesting part - how will the RoT (rule of thumb) perform with magnitude values and deltas beyond the Dawes limit range? The next clear sky should allow the next step with a larger delta-m. Participation in this test topic is welcome.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5410072 - 09/08/12 01:04 PM

Next object: 23 Aql 3.2"DS +5.3/8.3mag giving a delta-m of 3.
116/3.2*3=108,75~110mm aperture according to rule of thumb.
Splitting with a 140mm refractor at x140 was easy, the image was stable and the faint companion was in the correct position. Using aperture masks I reduced to 130/120/110/100/90mm without any significant changes but the companion got fainter each step and was therefore increasingly harder to see. With 80mm things got worse and the companion needed moments of stable seeing for resolution but I still was positive so see it. With 70mm I had only short moments of recognizing the companion as faint fuzzy little spot but that could be interpreted as bad seeing without the knowledge of having it seen before. With 60mm I could not see the companion any more even with long waiting for moments of good seeing. Conclusion: Resolution of 23 Aql with 80mm refractor is possible and this is much better than the 110mm according to the mentioned rule of thumb. But Fred had already explained that this rule is for reflectors with obstruction and his calculation for refractors is 2/3 of this value - this gives a required aperture between 70 and 80mm.
Tests of the rule of thumb will be continued when further candidates of dobules with larger delta-m values pop up in the next observing sessions.
Wilfried

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drollere
Pooh-Bah

Reged: 02/02/10

Loc: sebastopol, california
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5410108 - 09/08/12 01:36 PM

point of experimental procedure, wilfried ... start with the smallest aperture and work up. detecting an object when you already know its location is a different task from detecting an object when you don't know where to look.

the interesting issue is that "rules" similar to the ones that fred or i use (or as calculated with chris lord's nomograph) are really a type of personal guidance, not a fixed statement about optics. (at least, that's how i think of them, along with rules about limiting magnitude, system resolution, etc., etc.) the point isn't that the rule i use is correct or incorrect in your experience, but that you discover a rule that is optimal for you.

rules are easily misapplied or misinterpreted. robert aitken compiled a double star catalog, and as part of that process wanted to incorporate the double stars listed in the catalog compiled by sherburne burnham. "too many stars!" aitken declared. so he developed an editorial rule -- a rule to edit a manuscript -- that stars with a separation and primary magnitude (m) of rho > 10^(2.8-0.2m) "could to advantage be omitted". yet many people assume (incorrectly) that aitken was claiming that stars above that limit could not be (or are not) actual double stars. in other words, they mistook an editorial procedure for an astrophysical hypothesis.

we live in human cultures in which rules are assumed to apply to everyone and prescriptions from authority should be followed. and i grudgingly concede that helps to reduce traffic accidents and contractual disputes. but astronomy is really a personal enterprise, a solitary endeavor when most of our peers are asleep, and the key is to find the rule (assuming that a rule would be useful) that works for you.

i've enjoyed your reports. keep at it!

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: drollere]
#5411881 - 09/09/12 04:03 PM

Good idea to start with the smaller apertures - this way I have better threshold control.
My interst in this rule of thumb is strong because it could be a very good tool for selecting doubles from the WDS catalogue appropriate for a specific scope. The results from the Sissy Haas project will be of high interest for me in this regard.
But as JNW mentioned in another thread magnitude of the primary also plays a role as the Dawes limit may work perfect around +6mag but less so for brighter or fainter stars. So I am looking not for some optical theory but only for a formular useful for session planning.
Wilfried

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Bonco
Post Laureate

Reged: 04/17/06

Loc: Florida
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5411955 - 09/09/12 04:58 PM

I'm considering cutting out cardboard optical masks of different apertures to be placed at the front of the dew shield on my 80mm f/15 refractor. Is there any optical problem having the mask several inches in front of the objective? Or, should it be adjacent to the objective? My guess is that it doesn't matter. I ask because its much easier to install/remove the mask at the end of the dew shield.
Thanks Bill

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: Putting the "Rule of Thumb" to test [Re: Bonco]
#5412010 - 09/09/12 05:36 PM

Doesnt matter.

Pete

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Sasa
professor emeritus

Reged: 11/03/10

Loc: Ricany, Czech Republic
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5412768 - 09/10/12 04:17 AM

Hello Wilfried,

I can confirm your observation of 23 Aql. I was looking at it at the end of August with 80mm refractor (AS80/1200). With strong concentration, I could glimpse at 200x the secondary at PA~20deg and hold it steady for a few seconds. It was a little bit further from the primary than the 1st diffraction ring.
Last year, I accidentally run on this double with my 100mm refractor (ED100). Without knowing what to expect, I noticed with some effort the faint secondary.

Alexander

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: Sasa]
#5412783 - 09/10/12 05:17 AM

Wow - two owner of a 80mm f15 refractor, I would like to have such a scope.
To Bill: I had the same question and to minimize any side effects I retract the dew shield when using the aperture masks but as Pete mentioned I think also that the visual effect is neglectable.
Wilfried

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Ed Whitney
sage

Reged: 07/08/10

Loc: Palm Coast, Florida
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5415402 - 09/11/12 02:28 PM

I concur with Alexander.

I split 23 Aql first with the C8-EdgeHD to "see" the secondary. Primary is golden color, sec is very pale blue. I also split it with the SW102AR at 200x with a 5mm TMB Planetary II ep. Then, I used an 80mm mask (made of birch plywood) and clearly saw the split with dark sky between. The skies here were Mag ~5.0 with slight haze, but generally a very clear night.

At first I tried using the SW102 to make the split, but think my eyes were still dark adapting, so got out the C8. I was amazed at how dim the secondary was and knew this was the problem with not seeing the split with the 4in. I then went back to the SW102 and saw the secondary, but not easily. I then got daring and again saw the split with the 80mm mask in place. Without the mask, it was 50x per inch of aperture, with mask 63.5x per inch.

Thing is, I probably never would have seen the secondary if I didn't see it first with the C8, which showed me exactly what to look for.

It was a fun night!

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: Ed Whitney]
#5466330 - 10/12/12 04:22 AM

Next Delta Cyg (2.7" STF2579 +2.9/6.3mag) with delta-m of 3.4 giving 116/2.7*3.4 =146mm for reflector and 146*2/3 = 97mm for refractor.
Starting with 140mm I could easily split Delta Cyg with a magnification of x140 and a bit better with x208.
I reduced then my aperture using my new 145 to 8mm iris until I could no longer resolve the secondary - this happened a little bit below 100mm but with 97mm I could still call it a split.
Looks quite good for the rule of thumb.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5469432 - 10/14/12 09:08 AM

With so far only 3 samples the RoT 116/sep*delta-m (with delta-m set to 1 of less than 1) for reflectors and 2/3 of this value for refractors can not be considered as confirmed but until now it can at least not be considered as falsified. So a lot more samples are required.
Interesting point: Paul Rodman will have this rule implemented in the next release of his AustroPlanner program as criteria for selecting doubles for observation sessions.

From a personal point of view I think this rule is quite useful and easy to apply but needs an enhancement concerning the brightness of the components of the double star, especially of the companion. While I can put a stop at the minimum brightness of the sedondary when selecting doubles (considering light pollution I usually set this parameter to +10.5mag near my resolution limit) this is not flexible enough because this way
- I miss doubles with a slightly fainter secondary but still splittable due to a larger separation which allows me to see companions at the limit of my scope
- I get doubles I cannot split because faint companions with small separations are beyond the resolution power of my scope depending on values I can now only assume.

So the next step in testing the RoT will be a set of doubles with given separation and delta-m with incereasing magnitudes to find a hopefully simple relation between magnitude (of the secondary?) and the required aperture for example like magnitude of the secondary divided by 6 (base value for the Dawes limit) as multiplying factor.
But I fear it will not be such simple. To be investigated further.
Wilfried

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drollere
Pooh-Bah

Reged: 02/02/10

Loc: sebastopol, california
Re: Putting the "Rule of Thumb" to test [Re: Ed Whitney]
#5469997 - 10/14/12 03:19 PM

Quote:

Thing is, I probably never would have seen the secondary if I didn't see it first with the C8, which showed me exactly what to look for.

i'll reiterate that ed points to a significant issue. unless you start with a very small stop aperture and work to larger apertures, you will underestimate the necessary separation required.

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: drollere]
#5470155 - 10/14/12 04:53 PM

Bruce, thank you for the reminder - I think you are completely right. But I am looking for border values representing a small challenge even under favorable conditions and therefore I do not follow the procedure you propose because my observing skills are certainly limited and the conditions of my location are certainly not very favorable. So with going down in aperture I simulate better conditions and skills.
Wilfried

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fred1871
scholastic sledgehammer

Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5470625 - 10/14/12 09:49 PM

I can only agree with you Wilfried, that we need more data points - though I came to my version of the rule of thumb based on quite a lot of data points, using mostly refractors and SCTs and an occasional Newtonian, some years ago.

Sissy Haas's project is an attempt to devise something more rigorous (if pragmatic rather than based on optical theory) of the same kind.

I'm pleased to see that the AstroPLanner program will use our current rule of thumb - it still seems to me useful in practice, though needing qualification - I don't think it will apply to very big telescopes, and it might be surpassed by small ones. Obviously, too, observer experience/skills make a difference.

When I get time I'm going to dig out, from my long-term observing notes, all of the unequal pairs that can be used for evaluating the RoT from observations I've already done with particular telescopes. Then a follow-up on pairs that fit for my current equipment.

And there's an obvious further limit in terms of sky brightness where one observes - light pollution, sometimes moonlight as well. A delta-m of 4.0 might be possible with stars of mag 6 and 10 at a particular separation, but not at mags 8 and 12 at the same separation. What's the sky limit tonight with telescope X? - and it'll be less good if the star is close to a brighter one.

I haven't begun stopping down my refractor yet to see at what point secondary stars become invisible; but I do know it's easier as Bruce said earlier to detect an object "when you already know its location" - however, like Wilfried, I think I'll mostly stop down, rather than start with less aperture. It does introduce a modest degree of bias, but I tend to be pessimistic about what I think I've seen (was it a seeing artefact? versus an "it should be visible so that possible speck with averted vision should be it"?).

Working at the threshhold is always a bit uncertain. And air steadiness makes such a difference, night by night - I have notes on pairs re-observed, with the same telescope, only days or weeks apart - a secondary star invisible one night was easy on another. The difference is astonishing.

This explains Chris Lord's attempt to factor in 'seeing' in his algorithm; though I don't personally find 'seeing' easily quantifiable, even using the Pickering scale or similar.

I'm currently inclined to think the RoT is close to being as good as we'll get, and useful if applied for typical mid-size amateur telescopes, for experienced observers, and on nights of steady air (I don't find one can always "punch through" the seeing with very high magnification, as Bruce suggests - sometimes yes, sometimes no).

More observing to do.
I had a clear sky last night, so the go-to system went into a sulk, preventing a productive night. Tonight (if fine) I'll be back observing.

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: Putting the "Rule of Thumb" to test [Re: drollere]
#5470725 - 10/14/12 10:55 PM

Quote:

point of experimental procedure, wilfried ... start with the smallest aperture and work up. detecting an object when you already know its location is a different task from detecting an object when you don't know where to look.

Nice call Bruce. Wilfreid I liek your work here.

Pete

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5470975 - 10/15/12 03:42 AM

Quote:

... And there's an obvious further limit in terms of sky brightness where one observes - light pollution, sometimes moonlight as well ...

I am doing most of my observing from a light polluted location and I have the impression that while I "loose" about 2 magnitudes from my telescope limit this does not have serious impacts for splitting doubles up to this reduced limit - may be for very faint and very close companions. In my observations concerning the RoT I do not consider light pollution as serious influence - as stated elsewhere I even have the experience that the seeing her is most of the times better than in darker places with a stronger drop in temperature in the evening.

Quote:

... A delta-m of 4.0 might be possible with stars of mag 6 and 10 at a particular separation, but not at mags 8 and 12 at the same separation ...

I am working now on a list of doubles with same separation and delta-m with increasing magnitudes to check the influence of different magnitudes to the RoT.
Wilfried

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drollere
Pooh-Bah

Reged: 02/02/10

Loc: sebastopol, california
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5472685 - 10/16/12 02:33 AM

wilfried, maybe you mentioned this already, but how are you choosing your magnification? you mention 140x frequently and 208x once.

one concern is the use of magnification to get the optimal contrast or glare suppression for faint close companions. it's typical to try different magnifications on a tough split.

i agree that light pollution isn't disqualifying. a good RoT would take sky brightness into account in terms of the contrast it produces with the fainter companion. it will raise the "floor" on pairs you can resolve. but i think it is probably ok to omit it. i think there is going to be so much uncertainty and inaccuracy in any RoT that making it complex is not productive. simpler the better.

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: drollere]
#5472700 - 10/16/12 03:24 AM

Quote:

... how are you choosing your magnification? you mention 140x frequently and 208x once ...

Bruce, I navigate the old fashioned way with star maps (I have DSC and Sky Commander available but use it only occasionally for specific targets). After locating the target with a 55mm eyepiece (FoV about 3°) I go down my preferred eyepieces with 24/13/7/3.5mm until I split the double and sometimes I use in between eyepieces with 10mm and 4.7mm if I think this may give a better view.
7mm gives with my 980mm focal length scope x140 and 4.7mm gives about x208.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5476901 - 10/18/12 12:46 PM

As substitute for new sessions I looked for splits at the limit of my scope and found for example 1.6" +9.1/10mag STF2488: RoT gives 48.3mm refractor for this and I needed 140mm. This is a factor of 2,90.
Next I found 1.6" +9/10.2mag STF2482: RoT gives here 58mm. This is a factor of 2.41. Must think about this.
Wilfried

Edited by WRAK (10/18/12 12:59 PM)

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fred1871
scholastic sledgehammer

Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5477687 - 10/18/12 08:33 PM

One of the limitations of the RoT is that it needs a different version when applied to the fainter pairs. This is why I think the Sissy Haas project is not going to come up with a simple rule that applies universally.

Thomas Lewis of Greenwich Observatory made an attempt on this issue in a publication back in 1914 - and while his numbers are not regarded as definitive, there was a clear difference between fairly bright and rather dim pairs in resolvability, in relation to telescope aperture.

Lewis looked at the most difficult pairs observed by quite a few double star astronomers with a variety of telescopes. And based his conclusions on his analysis of their published measures.

The limit of resolution for a telescope was less good for faint pairs than for relatively bright ones. You couldn't expect to reach the Dawes Limit on dim pairs; also the uneven dim pairs required larger telescopes than fairly bright uneven pairs of the same delta-m and separation.

How much different? Lewis's numbers are reasonably easy to surpass on the dim pairs, even or uneven, with moderate size telescopes. And his numbers for brighter uneven pairs can be surpassed as well - again, I'm referring to moderate size telescopes - roughly, in the 13-25cm range. Not unlike the telescopes used by Dawes in his study of equal 6th magnitude stars.

Small telescopes (6-10cm) seem to do better than expected at times; the bigger mid-sized, say from 30cm upwards, are less able to push the boundaries because of atmospheric turbulence. Even so, the big-un's will beat the mid-size as a general rule - just by not as much as the size increase suggests. Personally, I'd be happy with an 18-inch (46cm) refractor in a dome in my yard, so I could tackle a lot of the closer and fainter pairs. But I know, from years of using (a borrowed) C14, so I can compare with my current C9.25 and past C8, that the improvement while large isn't as big as one would hope. All three telescopes were optically good for their type; the best was a hand-picked C8, and that had the benefit of less effect from atmospheric seeing. Even so, the C14 surpassed it easily on difficult pairs. So if the next lottery ticket comes good I'll have a C14 again
And it'd fit in my small observatory, unlike an 18-inch refractor. The 140mm refractor will stay, regardless - the images are so neat. And it's also a portable scope.

To return to the main point. Yes - I agree, Wilfried - dim pairs don't behave like bright ones. And if you try your 140mm refractor, stopped down to the small apertures you've calculated from the RoT, you'll not be likely to see the doubles as double. In a very dark sky, away from artificial light and without moonlight, you'd do better - what needs 140mm in a poor sky might be possible with 100mm in very good conditions. I've had that experience, both for double stars and other DSOs. So I think that, given your heavy light pollution, you'll have more difficulty establishing an RoT for dim pairs than people who can observe in a darker sky. But you should be less affected with brighter pairs.

Edited by fred1871 (10/19/12 07:29 AM)

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fred1871
scholastic sledgehammer

Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5477711 - 10/18/12 08:46 PM

For those who want to look at Lewis's original paper, it's in a journal called The Observatory - Lewis is in volume 37, p372 onwards. It's online through the ADSABS database of old journals.

His conclusions, often reprinted, where 'a' is the telescope aperture in inches:

Equal bright pairs 4.8/a , mean mags 5.7 and 6.4

Equal faint pairs 8.5/a , mean mags 8.5 and 9.1

Unequal 16.5/a , mean mags 6.2 and 9.5

Very unequal 36.0/a , mean mags 4.7 and 10.4

He doesn't give a figure for unequal and faint - such as 8.5 and 11.5. I suspect that that one would vary with telescope size, although thinking about Paul Couteau's remark in his book, that 10th magnitude is a sort of limit for visual sharpness of star images even with big telescopes, it might prove not usefully quantifiable regardless of aperture.

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5478235 - 10/19/12 04:25 AM

A lot of useful information, thanks Fred. The Haas list does not include a serie of increasing mags for given sep and delta-m as far as I remember so this project will probably not consider this aspect.
I still think that it should be possible to find a factor to adapt the RoT for fainter doubles. But the concept of considering difficult pairs for a given scope is probably misleading as the limit is a bit unprecise - so I made the error of including STF2488 beside STF2482 as the latter is certainly more difficult. So I will return to my concept of reducing the aperture with masks to be on the safe side considering limits. I am working now on my list of doubles with similar sep and delta-m but changing mag. And I do not look for perfection here but only for an useful approach for selecting doubles for observation sessions.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5482086 - 10/21/12 03:00 PM

Found a glitch in adapting the RoT formula 116/sep*delta-m (delta-m set to 1 if smaller) for refractors by reducing the required aperture by one third. This results for doubles with delta-m smaller than 1.5 in suggested apertures smaller than the Dawes-Limit requires. First idea would be to set the suggested aperture in this case to the Dawes-Limit. I am not sure if this makes sense because this means ident suggested aperture for refractors and reflectors for doubles with delta-m below 1.5.
Wilfried

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fred1871
scholastic sledgehammer

Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5482942 - 10/22/12 12:27 AM

I was expecting others to notice this glitch. In another thread - somewhere - I'd noted a problem with the RoT when Delta-m is small, particularly when it's less than 2 magnitudes. I've been thinking that there needs to be an adjustment for pairs where Delta-m is around 1.5 to 2.0, and likely a slightly different version again with pairs ~1-1.5 delta-m. For pairs with delta-m below ~1 mag, Dawes or Rayleigh will do, though with a large CO (as in SCTs) a delta-m near 1 is becoming noticeable as making a pair harder than the same delta-m with a refractor. There might be less of this effect with fainter pairs, because the diffraction rings are less bright and don't interfere as much. Hmmm. More things to check.

I'm still fiddling with the numbers at the moment, so I can't immediately offer a series of adjusted RoTs.

Separately, I've been looking through my files of notes and looking at pairs, bright and faint, and of various delta-m levels, to see which pairs I could use based on my own observing to refine the RoT further. That's a work in progress - I'll report later.

Edited by fred1871 (10/23/12 09:08 PM)

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5491881 - 10/27/12 04:07 PM

It seems then probably better to develop a RoT formula for refractors and calculate the required aperture for reflectors by using the percentage of obstruction on top.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5509360 - 11/08/12 03:14 AM

After weeks of clouds and fog finally no fog and clear sky patches between fast moving clouds with some additional veil clouds above - you have to take what you get. Moon still under horizon, naked eye magnitude limit bit less than +3mag.
Having prepared a small double star session in Peg I had first to wait for a cloud to clear, meanwhile I tried Delta Cyg again - with x140 a fuzzy blob instead of the usual needle point with only a fuzzy hint for the secondary. Reducing the aperture in steps down from 140mm to 65mm I got suddenly a much better image with a crisp star disk and I could convince myself to seeing still a hint of the companion.
Then to Peg and to 3.9" STF2958 +6.6/9.1mag - with 140mm and x70 hint of companion in the right position, with x140 clear split, but the companion seems fainter than +9.1mag. RoT (116/sep*delta-m) would give this one about 75mm for reflector and 2/3=50mm for refractor. I reduced the aperture down in steps down to 70mm with still faint glimpses of the companion, maybe a bit optimistic for these conditions.
I have now come to the conclusion that with all due respect to Bruce and Fred the discussed RoT is too simple to work.
Especially the calculation of difference of brightness as delta-m=m2-m1 does not make much sense as the magnitudes are on a logarithmic scale with the base 2.512 which means the difference in brightness is 2.512^m2-2.512^m1.
As I have with an iris diaphragm now a fine tool for finding limit apertures for doubles within the reach of my scope I will use each observation session to fill up a small database with aperture limits for all observed doubles and then doing some number crunching with the principle of least squares error sum. Meanwhile I can study the many valuable approaches of this topic from professional and amateur astronomers (Lord, Peterson, Haas, Arguelles, Funakoshi ...) to get some ideas for a senseful formula.
Wilfried

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fred1871
scholastic sledgehammer

Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5510650 - 11/08/12 09:56 PM

Wilfried, your sky sounds like mine - "weeks of clouds"...
What you're finding with the diaphragm on your refractor is interesting, though I'm not sure it tells us as much as might appear. I think it's become clear that small apertures do better, comparatively, than medium apertures, and medium apertures do better, comparatively, than large apertures. A great deal of this effect is due to atmospheric ("seeing") factors.

A smaller factor, though it could have a slight but noticeable effect, is the longer f-ratio you get when stopping down your refractor, because it improves eyepiece performance with many eyepiece designs. The spot diagrams in Rutten and van Venrooij's book demonstrate this. I get a similar small improvement with my Petzval f/5.7 refractor by using a 2.5x Televue Powermate, which gives an effective ~f/14 for the eyepiece. Star images are neater with this than the same magnification achieved by eyepiece only. And, no, I'm not using Huyghenian eyepieces. A mix of orthoscopics, Naglers, Pentax XW, etc.

STF 2958 in Pegasus is a double I'm familiar with, and I have notes on it from several occasions in the last few years. With my 140mm refractor it's an easy one - clearly double at 62x, though I like it better at 114x. I don't have the impression that the secondary star is fainter than m9.1, at least not by a significant amount. So that impression might be an effect of your local light pollution levels. My local naked-eye limit is, on the better moonless nights, around mag 5, though dust or water vapour can reduce this sometimes (4-4.5).

Where did you get your iris diaphragm? I haven't noticed these being listed commercially.

Your list of people to read is a mixed collection. Peterson won't tell you much about telescope limits. He used one small telescope at quite low power (45x) and his diagram tells us more about the limits of vision with such an arrangement.

Sissy Haas's table in her book is based on a study of stars reported separated (in some sense) in the long list of observing notes in the Revue des Constellations. You'll need to look at the telescope sizes used to see how useful that is.

Chris Lord is a different matter. His is a detailed and comprehensive study, and he takes into account past work (Lewis, Treanor) as well as his own observing with a number of telescopes from 3-inch (76mm) to 10-inch (254mm). It's very useful.

Arguelles - well, I have difficulty with the "difficulty index", not least because it crams into a tiny part of the index anything that's difficult. My feeling is that Arguelles needs to re-analyse his data into a different form in order to be useful. Funakoshi I've looked at but haven't analysed yet.

I think a detailed study of Lewis's table, cherry-picking certain observers who habitually pushed the limits, is more useful than his aceraged results. The averages tend to be too easy to establish limits, unsurprising given the observing program choices of some of those listed, and the putting together of large with medium with fairly small telescopes.

Large telescopes do noticeably less well than moderate to small ones. Louis Bell, in The Telescope (1922), commented on this in regard to the results Lewis had tabulated for SW Burnham, in regard to the Dawes Limit - we're not even looking at uneven pairs here. Bell noted that Burnham did better than the Dawes Limit with 6-inch aperture, and 9.4-inch - "with none of the others did he reach it and in fact fell short of it by 15 to 60%" - that's with 12, 18.5, and 36-inch telescopes. "All observations being by the same notably skilled observer and representing discoveries of doubles, so that no aid could have been gained by familiarity...."

Treanor (1946) in addressing the issue of resolution, particularly of unequal pairs, ends up with a distinction between larger and smaller telescopes, and in graphing results has a split between under 15-inches and over 15-inches, using Lewis's data.

Treanor attempts to determine a "modified Rayleigh Limit", based essentially on diffraction theory, as per Rayleigh. He looks at the relative brightness level of the diffraction rings, translated to magnitudes, and requires a star to fall on an interspace in the rings based on its brightness relative to the rings, which become increasingly dim as we move outwards from the diffraction disk.

If we list his figures, in terms of the Dawes Limit (treated as a practical criterion), we get the following:
delta-m 1mag 1.2DL as a limit
2m 1.5DL
3m 1.8DL
4.4m 2.3DL
5.9m 3.24DL
Some of these figures are approximate, based on measuring Treanor's graph.

Treanor remarks that "this curve [the modified Rayleigh Limit curve] appears to form a tolerable limit to the observations, though as a criterion of resolution under astronomical observing conditions, it appears rather optimistic".

The RoT shows clearly the effect that various of us have noted - it needs modification at small delta-m levels.

So, to list - if we take the RoT in its refractor version, as 2/3Dm as a multiplier for DL, we get:
Dm 1 RoT 0.67 DL - clearly not valid
Dm 2 RoT 1.33 DL - close to Treanor's 1.5DL
Dm 3 RoT 2.0 DL - close to Treanor's 1.8DL
Dm 4.4 RoT 2.9DL - Treanor 2.3DL
Dm 5.9 RoT 4.0 DL - Treanor 3.24 DL

Treanor is more optimistic than RoT as the Dm increases - observing experience suggests that the Treanor levels with large Dm factors are very hard to achieve, fitting Treanor's own comments.

Treanor also mentions the work of Danjon and Couder in the 1930s (in Lunettes et Telescopes) regarding the "correction to be applied to obtain the effective from the theoretical resolving power for given apertures and states of atmospheric turbulence. Their tables show the increased importance of turbulence with large apertures, even in rather good observing conditions". Chris Lord has also tried to factor this in.

A further useful point - "Moreover, these authors point out that slight imperfections of spherical aberration, even within the lambda/4 tolerance limit, will greatly increase sensitivity to turbulence". I'd add that central obstructions have a similar effect in increasing sensitivity to turbulence, as well as moving more energy into the diffraction rings.

Much of the above is based on studies I did back in 1996-98and wrote up at the time, in looking at resolution limits for unequal doubles. Since then I've increasingly realised the complexity of the issues, but I still think Treanor's work very valuable in working toward better predictions of what's possible.

So - a few more things to think about. I'll stop there, for now, before I turn this into a monster length note.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5511029 - 11/09/12 04:26 AM

Quote:

... Where did you get your iris diaphragm? I haven't noticed these being listed commercially...

Fred, thanks for your comprehensive answer, I will certainly have a look at the work of Lewis and Treanor.
Regarding the iris diaphragm: I know one commercial version from Baader (http://www.baader-planetarium.de/solarspectrum/an_iris_gross.gif) but this is sold only together with the expensive H-alpha sun filter.
So I just searched for "Iris Blenden" in the internet and found the offer from SAHM of interest (http://www.irisblenden.net/iris_sprengN.html). I handicrafted a kind of cap over the sliding baffle with the iris diapraghm (outer diameter 198mm and max. inner diameter 145mm) on top of a 10mm foam strip fitting the diameter of the baffle. Weight is about the same as of a heavy eyepiece and is easily balanced by retracting the baffle. Nice tool to convert with reasonable effort any double star observation into a limit observation.
There are even larger iris diaphragms available from Edmund optics (http://www.edmundoptics.com/mechanics/apertures/iris-diaphragms/standard-series-iris-diaphragms/1461?showall#products) usable for larger refractors.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5533333 - 11/22/12 03:16 AM

Persistent fog prohibits observation sessions so my list of limit aperture observations is growing rather slow - 20 objects so far. But this gives me time to check the details of other Rules of Thumb for further investigation.
The most prominent is certainly Lords RoT and while the mathematical content of his paper (http://www.brayebrookobservatory.org/BrayObsWebSite/BOOKS/TELESCOPIC%20RESOLUTION.pdf) is a bit intimidating the performance of his algorithm is less impressive. Compared with the so far discussed too simple approach of "Requ.App=Dawes/Sep*Delta-M" Lord's formula "S = 1.033 * 10 ^ [ 1/n * ( Abs(delta mag) - 0.1 ) ] * rho" is certainly far more advanced as it includes a 10^Delta-M component and therefore takes account of the nonlinear character of increasing Delta-M. But it disregards the increasing difficulty of splitting doubles of given separation but decreasing brightness - so you get for a 2" +4/7mag and for a 2" +7/10mag double the same result and this is certainly wrong. Lord gives a correllation coefficient of 0,9998 which is quite high but does not provide an indication of the average error of his formula. Applied to my small data set (performance factor n choosen as unrealistic 10 to get the smallest possible error of the formula with my data) I get in terms of required aperture for a given separation an average error of 40mm - and this seems quite huge with lagest deviations -97 resp. +37mm which means a bias towards requirement of too small apertures for fainter doubles as is to expect from the mentioned weakness of this formula. Quintessence: A reasonable good RoT will have to allow not only for Delta-M but also for increasing faintness of the double.
To be continued.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5534493 - 11/22/12 09:28 PM

Wilfried, I can only agree that Chris Lord's mathematical content is a bit intimidating. For that reason I use his nomogram as an easy way to read off resolution levels. My experience is that some of the time the result is backed up by doubles I've observed with various telescopes, but not always. Fainter pairs certainly don't follow the rule of brighter ones, especially when they're uneven as well.

I think Lewis was on the right track with his work, but his numbers don't always match up to observing experience because he didn't distinguish, as I remarked before, obervers pushing the limits versus those not doing so - and didn't separate out categories of telescope size, small, medium, large. They all went into the same categories of doubles.

I'm currently compiling lists of the more difficult pairs I've observed in the various categories, and with the telescopes with which I've done the greatest numbers of pairs - 20cm and 35cm SCTs, and 14cm, 15cm and 18cm refractors. I have less material on pairs I've seen with Newtonians (15cm and 25cm).

Many of the doubles I have notes on are not on the Haas list for the current project on unequal pairs. Some of them are, and I'll send my notes on those to Haas.

Meanwhile - I think anyone compiling observations will find their limits on fainter pairs are not as good as on brighter ones, which shows up in Lewis's data lists as well. With the 18cm refractor I had access to some years ago, close pairs around magnitude 8.0 to 8.5 were not much harder than those around magnitude 6, but those around magnitude 9.0 to 9.5 were noticeably harder. That was with a suburban sky with a naked-eye limit about 4.5 on moonless nights.

And in the case of doubles near the limit of visibility the observer's eyesight becomes a significant factor as well. We're not all equal either in sharpness of vision nor in ability to see faint stars. That remains true even if we only compare experienced observers, who have the practise (experience) to make the most of their eyesight.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5534840 - 11/23/12 03:54 AM

Quote:

... I'm currently compiling lists of the more difficult pairs I've observed ...

Fred, the approach of setting "difficult pairs" equal to "limit observations" is as I see it the problem of most studies done so far in this area. I am quite often surprised how much room is still for decreasing the aperture for "difficult pairs".
One exception is Peterson - he included also non splits in his analysis and could this way better define the "frontiere" between splits and non splits. He had also a different approach concerning the relevant factor with the magnitude of the secondary. Next I will check his formula with my so far small data base.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5534864 - 11/23/12 04:30 AM

I have a list of "failed to see" objects as well. But often enough when I go back to these, same telescope on a better night, I can see them. Not always, of course. Some stay permanently beyond reach for a given telescope with my eyes and even the best sky conditions.

Peterson is of minor relevance in these matters. His study was ultimately a work on what he could and could not see with a low magnification that did not allow his telescope to reach its limits either for separation or faintness. It does demonstrate that as stars get fainter, eventually they need to be further away from the primary to be seen. But I think we knew that. Perhaps the significant point of his plot is that the separation limit is steady until a certain level of faintness is reached, and after that pairs need to be wider.

However, because of the low magnification, even for a 3-inch telescope, this is less informative than it might have been.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5535588 - 11/23/12 02:04 PM

I have checked Petersons algorithm (min.sep = (10^(5/8(m2-TML+2.4)))*Seeingfactor with TLM=9.1+(5*LOG10(D_inches)) and Seeingfactor is the greater of 1) Dawes limit or 2) the size of the seeing disk)) which is therefore based on the difference between the magnitude of the companion and the telescopes magnitude limit - the closer the harder to resolve, not much of a surprise.
Applying to real data results in a mixed bag with a lot of heavy deviations from observations and a far worse average error than Lords approach.
Never the less I think that the magnitude of the companion is a relevant factor for a satisfying RoT formula.
Your mentioned go/no go cases seem perfect limit observations and I would be grateful if you could share some of these observations with me - if possible with an (estimated) naked eye magnitude limit (seems also be a factor of great influence) and focal length (who knows?).
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5536071 - 11/23/12 06:55 PM

If Peterson had observed with a higher magnification his limit of resolution would have been much closer than 3 arcseconds. Even a 3-inch refractor can easily beat that - so the "wall" effect in his diagram represents the limit of his visual acuity with that telescope - an apparent separation of ~125" (45x at 3" separation).

In the distant past I had a 3-inch refractor and could separate pairs below 2", and see "figure-8" shapes on even pairs around 1.5", roughly the Dawes Limit. And I used higher magnifications to do that. Likewise, higher power showed fainter stars than magnitude 11, even from a suburban site with a mag 4-4.5 limit.

Looking at Peterson's diagram again, one interesting feature is the lack of information on the magnitude of primary stars - we have only secondaries' magnitudes. This will make a difference with the closer pairs, and with fainter secondary stars. If Peterson can see some mag 8.7-8.8 stars at 3.0"-3.5" from the primary, were the primary stars magnitude 5 or 6 or 7 or 8? So that when he sees companions around magnitude 9 at 10" or 20" separation, is this because the primary stars are much brighter with those examples? - one might expect this to be the case.

James Mullaney in his book on Double and Multiple Stars recommends that "observers desiring to create a Peterson diagram for their telescope use higher powers than that employed in the original study" because the "resolving magnification" is "at least 25x per inch of aperture". That would be a minimum of 75x for a 3-inch telescope. When I had a 3-inch, I commonly used 133x (9mm Ortho, 1200mm focal length) for the closer doubles, and 200x (6mm Ortho) for the most difficult. That's 45x per inch and 67x per inch respectively. If I were to do a repeat of Peterson's work with a 3-inch, I'd probably use 133x as my standard eyepiece - allows the Dawes Limit pairs to be detected, and goes nearly as faint as the aperture makes possible. I'd also keep a record of the primary stars magnitudes. And, yes, it would become much less simple than Peterson's work suggested.

The above comments are not meant as an entire dismissal of Peterson's work. It has its usefulness - though not much in the direction it was often interpreted, because it's too much a study of what Peterson could see (the limit of Peterson's eye under a badly chosen magnification limit) rather than what he could have seen by pushing the scope to the limits of what it could show him. The latter is what Dawes and Lewis and Treanor and Lord and Arguelles etc - and ourselves - have been investigating. There will always remain the variable which is the observer - even under near-perfect seeing and with near-perfect telescopes. Factoring that in to the equation - the capable and experienced but not exceptional observer - will be a bit fuzzy.

Edited by fred1871 (11/23/12 07:54 PM)

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5536426 - 11/23/12 11:05 PM

A few thoughts on limiting observations. With regard to pairs that are pretty equal in brightness, I can report that a binary such as Gamma Centaurus, that has currently closed beyond reach (~0.15"), was a fairly easy pair in the late 1990s at 1.1", but by 2009 at 0.4" was beyond my 140mm refractor. The same telescope has succeeded in elongating several pairs in the 0.50"-0.55" range. That appears to be its limit for showing definite elongation. Splitting requires more separation - Dawes and Rayleigh fit well.

On unequal pairs, 10 Arietis, mentioned in the thread on 72 Pegasi, did show as a pair with the 140mm - mags 5.82 and 7.87, a delta-m of 2.05m, at 1.3" - on a night of "good+" seeing it was split at 230x. That's one of the tighter uneven pairs I've separated. But I haven't tried it with an aperture mask to see where the "not visible" point occurs.

Likewise, Theta Gruis, which is on the Haas list of test pairs, I saw as a neat split some years ago at 180x with an 18cm refractor; last month with the 140mm refractor I could see it as a lesser star adjoining the primary at 250x, and a neat split at 400x - it was not far from overhead that night, and seeing was very good. Magnitudes are 4.45 and 6.80, delta-m 2.35, at 1.5". Again, I've not attempted it with less than 140mm.

Also in Grus, RST 5560 (part of DUN 248) was split with the 18cm refractor at 330x - mags for the close Rossiter pair are 6.15 and 8.93, so delta-m ~2.8, at a separation of 1.3". This one I'll try again with my 140mm refractor, when I get a sufficiently steady night. Same separation as 10 Ari, but larger delta-m. It might prove too much for the 140mm. The RoT for refractors suggests it'd need to be a little wider - 1.55" - to see as a double.

However I definitely did better than the refractor RoT some years back with the 18cm - Upsilon Gruis, mags 5.70 and 8.24 - delta-m 2.54 - separation only 0.9" - at 330x the companion could just be made out as a brightening near the first diffraction ring. This was on a clear moonless night of above average seeing.

The 18cm telescope was an f/9 apo from AP (Roland Christen), focal length 1600mm, normally used at f/9; I had access, not ownership; regrettably beyond my budget. The 140mm is a lowly Petzval achromat from Vixen, that I commonly use with a 2.5x Powermate (f/14) on the tougher pairs. Not sure how I'd rate the focal length of that arrangement. With the Powermate it's effectively 2000mm, instead of basic 800mm.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5536618 - 11/24/12 03:26 AM

Quote:

... I commonly use with a 2.5x Powermate (f/14) on the tougher pairs. Not sure how I'd rate the focal length of that arrangement. With the Powermate it's effectively 2000mm, instead of basic 800mm.

Fred thats interesting - higher focal ratio is assumed to be combined with larger depth of focus and I always wondered if this effect is also to get with a Barlow/Powermate. Will have to try this whenever I have the next opportunity.
Focal ratio could very well play also a role for splitting thight unequal pairs - but I have not considered yet the complexity of a then required recursive function, seems better to make this not too complicated.
A RoT with reasonable small error range could go as follows: Dawes as base + Lord for delta-m + Peterson for m2 (idea, not algorithm) + function for m1 + function for NEML.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5536759 - 11/24/12 08:05 AM

Footnote to my previous note - I've now found another observation of RST 5560, again with the 18cm scope, this time just split at 180x - seeing was better on this night. So I'm now more optimistic that the 140mm might show it split as well (at higher power).

I don't think the Powermate increases the depth of focus - focus is quite critical, and I'd say similarly critical, at similar powers, whether with eyepiece only or using the Powermate with a longer focal length eyepiece.

Interesting suggestion on a more complex RoT. I'll have a look at it.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5538304 - 11/25/12 05:50 AM

Fred, regarding 10 Ari and Theta Gru - could you please estimate your naked eye magnitude limit at these observations?
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5539717 - 11/26/12 01:25 AM

Wilfried, I doubt the naked eye limit was a factor in those observations, given the fairly bright stars. I don't have exact numbers for each observing night, usually only a note on moonlight if there, and haze or cloud if present.

These were clear sky observations without moonlight, so the naked eye limit was likely 4.0-4.5 for the location of the 18cm refractor, and ~4.5-5.0 for the 140mm.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5545486 - 11/29/12 12:51 PM

Check of the concept of Funakoshi did not bring new insights. 2002 he suggested an algorithm based on a multitude of "delta-m^n" components leading to unreasonable differences to real values. 2009 he suggested an improvement in form of an additional component based on a modification of the Dawes limit "(1-k)*116" with k as "threshold of Airy disk's light intensity (0<=k<=1)" but also this new approach produces unreasonable differences to real values.
Similar components in the algorithm as in Lord's (means Dawes and delta-m factors) but even worse results.
Back to the start.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5546013 - 11/29/12 06:53 PM

Wilfried, I agree with you about Funakoshi. He re-runs some material from previous work on uneven pairs, but I didn't find anything new that was also likely to be useful. His algorithms, as you say, appear to give rather erratic results.

Not entirely back to the start.

I think Treanor with his work based on diffraction theory is useful, in terms of best possibilities (very good seeing, very good optics, very good eyesight being assumed).

Also the RoT seems to be fairly accurate within certain limits of telescope and delta-m. It also fits quite well with some of the observations that appear close to the limit, from my own observing, and from looking through the best results (most difficult pairs seen) in a selection of the data Lewis compiled, and with telescopes in the 6-12-inch range (15-30cm).

As I've said earlier, I think small scopes (6-10cm) do better for their size, and big ones (40cm+ and especially 50cm+) do less well for their size, due to atmospheric seeing effects.

But I do agree, there's no easy answer in sight, and a fair way to go on looking for a general purpose algorithm, rather than a within-bounds-RoT.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5549082 - 12/01/12 04:53 PM

For lack of own observations due to ongoing cloudy and foggy nights I thought it clever to add some of the obervations Lord lists in his paper (http://www.brayebrookobservatory.org/BrayObsWebSite/BOOKS/TELESCOPIC%20RESOLUTION.pdf) to my data and selected those closest to Dawes to ensure as good as possible "limit" observations.
Then came the moment of doing some calculations with the different RoT approaches - no one delivered any good results for the added pairs, not even Lord's own algorithm.
I then applied Lord's algorithm to all of his for 3" and 6" refractors listed observations only to find that the average error in required aperture is 39mm - and for example "to split this double with 66% probability you need an aperture between 81 and 159mm" is certainly not a useful result.
So I returned to Lord's paper to check the details and found some sobering facts:
- I found at least one bogus observation (J781 - if observed with 3" as listed then it should have been evident, that this double is about 2mag fainter as advertised - WDS is meanwhile corrected)
- I found some observations clearly to be not on the limit as there were for same scopes other doubles with same separation but with higher delta-m listed
- There are no observations below 75mm (3") - but many unequal doubles have their limit in this range
- There are no observations between 75 and 150mm (6") - but most of the for an amateur interesting unequal doubles have their limits in this range
- All observations are with given apertures, so any listed "limit" observation has a random character and an error range covering the gap to the next smaller resp. larger scope.
So in total the used data shows statistically serious flaws in my opinion especially in the range of small telescopes.
Then Lord grouped the observations, calculated average observation ratios based on Dawes limit and developed his algorithm on base of these averages - this procedure does not seem statistically correct to me.
Especially the nonexistence of observations in the range of 60-140mm (with the exception of 3") makes the approach of Lord completely dubious at least if applied for this range and most of us do exactly this.
There is no Chris Lord bashing intended here but this is quite disappointing – but maybe I made wrong conclusions, so any corrections would be welcome.
Wilfried
PS to Fred: Thanks for the hint with Treanor, will have a look at his work

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5550658 - 12/02/12 04:48 PM

After a first reading of the Trenaor article on this topic (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1946Obs....66..255T&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES) I find his approach based on the theory of the diffraction pattern and based on Rayleighs criterium certainly of interest - this need a follow through.
The data base for his final conclusions is identical to Lord's (Lewis) and lacks therefore valid observations in the small telescope range of 60 to 150mm (with exception of 75mm) so these have to considered with care.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5551225 - 12/02/12 10:58 PM

Wilfried, your analysis of Lord's work is very interesting. And the point that various examples of stars split are not near the limit of the telescope used does indicate a problem with setting boundary conditions for resolution. This I suspect will be a problem for the Haas Project as well (one of several).

What is not surprising is that Lord's resulting algorithm has difficulties when used for small telescopes. These appear at times to re-write the rules for splitting doubles, and a good example, apart from some observations mentioned in this forum in the past, is Jerry Spevak's work as written up in Bob Argyle's book on "Observing and Measuring Visual Double Stars".

Spevak, with a 70mm refractor, detected doubles ("elongated")down to around 0.7"-0.8" - the Dawes limit for that aperture is 1.65". Curiously, he reported pairs near the Dawes limit not as "touching", which one might expect, but "notched" - the one example of "touching" is at 1.9", near the Rayleigh limit.

But there are so many reports from experienced observers with good telescopes, detecting duplicity in pairs that might be thought beyond the aperture, that there's a need to take notice - clearly, small telescopes can perform better for their size than larger ones. Quantifying that will be an interesting job.

With regard to Treanor: I don't think he has ultimate answers, but by using Lewis's large database and analysing it in a different way, a way that I think is far more productive of reasonable results and numbers that come closer to the reality of what's possible, he provides what I see as some "limiting conditions" for medium and large telescopes. That's in terms of the Rayleigh approach to doubles via diffraction theory. If it turns out that some doubles can be detected without being a close fit to the simle version of diffraction theory - so that a secondary star might be seen as an dimmer extension to the primary, without falling neatly into the dark interspace between the diffraction disc and the first bright ring - then that would be an advance on our knowledge, and indicate observing possibilities beyond what we'd expected.

And perhaps this condition might be more readily met with small telescopes where seeing is less problematic, and the amount of light gathered is less.

That's obviously a preliminary thought on my part - to be followed up, like so much else.

Meanwhile, I'd suggest continuing with Treanor - he has some useful ideas in that study. And you might get some new insights that could extend his study.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5551600 - 12/03/12 07:29 AM

If I understand Treanor right then he assumes that unequal pairs can be split at the minimums of the diffraction pattern with the lowest possible brightness of the companion equal to the brightness of the next maximum.
This would mean:
- pairs with a delta-m up to 2.86 can be split at Rayleighs limit (=radius of the airy disk)
- pairs with 2.86 < delta-m > 3.88 can be split at the second minimum
- pairs with 3.88 < delta-m > 4.56 can be split at the third minimum
- pairs with 4.56 < delta-m > 5 can be split at the fourth minimum.
The minimum aperture for these splits would be the scopes with the required size of the diffraction pattern - assuming that average wave length can be used for all pairs would make this a feasible approach for a RoT.
One curious side effect of this concept would be that with a larger aperture than required as mentioned above you will not be able to resolve a binary as the secondary will then sit in the next maximum an can therefore not be seen as long as the aperture is not big enough that the secondary is again outside of this maximum. This has certainly to be checked - but this would also be an explanation, why there are so many 60mm observations of doubles which seem to be difficult to split with somewhat larger apertures.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5552970 - 12/03/12 10:13 PM

Treanor does not seem to accept that pairs with delta-m up to 2.86 can be split at Rayleigh limit, and his graph indicates that - even though one might read his discussion as allowing such a high delta-m at Rayleigh.

The nearest we get is the graphed result of Howe's bright double stars, where a delta-m of 2.4 is almost at the Rayleigh limit. However the graph suggests that at 2.86 magnitudes the limit is about 1.5 x Rayleigh.

Remember also that all of Lewis's data points are from refractor observations, so the brightness of diffraction rings will be less than with obstructed telescopes.

Looking at Howe's original publication of doubles measures, with the Cincinnati 11-inch refractor, I'm left wondering if Lewis kept Howe's original magnitude estimates which were rough and in 0.5 mag steps, or whether he sought improved photometry for the study. A change in delta-m figures would move Howe's data point - likely to be lower, and therefore not as remarkable. As it is, that's the standout data point on the graph, so it needs investigation. Accepting Howe's measures, if we get modern photometry for the Howe pairs that fit the close and bright criteria, do we end up with the same data point?

Your thought on why smaller telescopes might do better is interesting.

It is the case that sometimes using a different aperture telescope can move a companion star from an interspace to a bright ring, hence making it less visible. Whether that's the whole story I doubt - seeing definitely impacts less on small telescopes, especially refractors.

Your telescope diaphragm could be used to study some pairs where the dimmer secondary star might be on the first diffraction ring at one aperture but not at another. The first ring, being much brighter than the 2nd, would be the more interesting to experiment with.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5553935 - 12/04/12 12:55 PM

A first very quick tests with the delta-m parameters as discussed above resulted in a similar to slightly better average error than with Lord. This seems encouraging - with a bit of tuning this could may be much better. What is missing and has to be added is the consideration of magnitudes of the primary fainter than +6mag.
If weather gets better I will certainly study the maximum faintness I can see within the first diffraction ring.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5555148 - 12/05/12 05:52 AM

Quote Treanor "As the result... it appears that... resolution occurs if the faint companion falls on a minimum of the brighter star, such that the adjacent maxima are not brighter than the faint star itself."
Some observations like for example Delta Cyg do not confirm this - with a delta-m of 3.4 resolution should occur at the second minimim with an aperture of about 97mm but there are reports of much smaller apertures down to 60mm which means a companion fainter than the first diffraction ring can be seen at or within it even if this sounds not very plausible.
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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5556558 - 12/05/12 10:21 PM

Wilfried, I haven't run the numbers to see what magnitude the first ring is equivalent to, but your noting that 97mm aperture puts the companion of Delta Cygni into the second minimum does suggest that calculating the aperture for putting it into the first interspace might be informative. I'll try it and see what the numbers look like.

Meanwhile, a star less bright than the first ring could presumably be seen if its magnitude allows it to form a noticeable brightening at one point on the ring; there should be an additive effect of light despite the interference effect from the star image being on the diffraction ring of the primary. Obviously some stars are too dim to be noticeable when they coincide with the diffraction ring. In the case of Delta Cyg the secondary star is bright so it could be seen with some small telescopes as a ring spot brightening.

The whole subject of uneven pairs with small telescopes has been very little looked at, presumably because, even in the 1800s, double star astronomers typically used medium or fairly large telescopes for serious observing. That meant most of the time from about 5-6-inch (13-15cm) aperture as a "small" telescope. 7-inch to 15-inch was more usual. Remember the point from my brief write-up on Robert Jonckheere - in the early 1900s his father provided him with an 8.7-inch (22cm) refractor which he decided was too small (!!) for his double star ambitions. Hence the 14-inch (~35cm) refractor he set up near Lille.

So I suspect there's a fairly unexplored area relating to small telescopes and double stars. I no longer have a small long-focus (traditional) refractor to experiment with this - my f/16 75mm telescope was sold long ago, and I'm not convinced that my 80mm f/5 is up to the job of assessing small scope performance.

But I do know that the old 75mm was surprisingly good on doubles, and gave very neat images with little scatter despite being an achromat. At that small aperture, chromatic aberration is not much of an issue at f/16.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5556876 - 12/06/12 04:21 AM

The first minimum would be ident with Rayleigh means 138/2.6 giving 53mm - may be a 50mm bino could do this job, but I doubt it. This would mean a 3.4 delta-m could be resolved at Rayleigh.
But I agree that a companion fainter as the first ring could be seen as a brighter spot on the ring.
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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5557854 - 12/06/12 04:46 PM

Fred, the following is kind of mysterious for me: Treanor states "The intensity of the third maximum is to that of the Airy disk as 415:100,000. The magnitude difference is thus 2.5log10 I1/I2 = 5.95 approximately." but this value would according to my information be valid for the sixth maximum and in the third maximum we have 1.5% of the total energy of the Airy disk and therefore the magnitude difference is 4.56. Maybe a little error of Treanor with whatever impact on his results or do I miss something here?
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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5558309 - 12/06/12 09:22 PM

Wilfried, I think part of the difficulty with brightness levels is that there is a difference between the total amount of light in a diffraction ring, and the maximum brightness of the ring, because the rings have a gradation of brightness across their width in the same way that the disc has a gradation of brightness across it.

So the total energy of the first ring, for example, is 7% of the total image light of a star, with 84% in the disc. That might suggest a ratio of 12:1 between disc and ring, but it's not that simple.

Although the disc has a gradation of brightness from centre to edge, the light is more concentrated in the disc, where the ring, being much larger, has its light spread out more.

Lewis (on page 374 of his article in "The Observatory") gives a table of illumination levels at a series of distances from the centre of the disc. The maximum illumination of the first bright ring is given as .017 (relative to 1.000 for the disc centre). That gives a ratio just short of 60:1, or near enough, 4 magnitudes instead of ~2.6 (12:1).

So in the case of Delta Cygni, where the secondary star is mag 6.3, it will be noticeably brighter than the brightest part of the first ring, which is equivalent to about mag 6.9. As well, the separation (2.6 arcseconds) will put the secondary's star image not on the brightest part of the bright ring, but towards the inner edge of that bright ring, where illumination is much less.

Rayleigh for 60mm is 2.3", and the brightest part of the first ring is around 3.0-3.1" from the disc centre. Where the secondary star is located, at 2.6", the illumination of the bright ring is about half the maximum, so closer to mag 7.6. Yes, I'm ignoring illumination fall-off in the secondary star disc, which makes the apparent size of the disc smaller, because that's a factor to be looked at later - though I suspect it makes not much difference overall, at least to the visibility of the star, placed where it is in diffraction terms.

The above may go some way towards explaining why a double such as Delta Cygni can be seen as a double with a 60mm refractor, when the telescope has good optics and seeing is very good, so it ceases to be a factor.

I'd expect that a similar delta-m and separation would be less readily observed with stars that are less bright. The light gathering capacity of 60mm has no difficulty with 3rd and 6th magnitude stars. At magnitudes of say 6.3 and 9.7 we'd be facing lack of light as a problem with a fairly close pair. In between magnitudes? - perhaps someone with a 60mm or similar scope might like to create a list of pairs around 2.5" separation, with delta-m of 3 to 3.5, but with the primary star at mags 4, 5 or 6, and see what's possible. Is Delta Cygni near a "sweet spot" for small telescopes? And are there some other bright pairs that show this pattern?

Hmmm... suspect I need some more thinking time on this... meanwhile, I'll hope the above ideas about brightness levels in the diffraction image might be in the right direction as part of explaining the sometimes surprising performance of small telescopes.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5559189 - 12/07/12 12:10 PM

Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5559592 - 12/07/12 04:42 PM

Quote:

...Lewis (on page 374 of his article in "The Observatory") gives a table of illumination levels at a series of distances from the centre of the disc. The maximum illumination of the first bright ring is given as .017 (relative to 1.000 for the disc centre). That gives a ratio just short of 60:1, or near enough, 4 magnitudes instead of ~2.6 (12:1)...

Fred, applied this to my small data set - does not help much as it increases the average error about 25% compared with my conservative approach concerning the delta-m between diffraction rings.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5559830 - 12/07/12 07:04 PM

Wilfried, the Lewis article is in The Observatory, for 1914, vol 37, pp372-379. The mention of it in Argyle (Observing and Measuring Visual Double Stars has the wrong volume number - in both 1st and 2nd editions).

I'm not suggesting my attempted analysis will be immediately applicable to an algorithm with predictive capacity. Rather, I was trying to explain why I thought a "special case" could occur. Generally, I'd expect placement neatly between the diffraction rings to be the best model; edging away from that gets into low probabilities of visibility. Delta Cygni seems to me a pair that
"sometimes" is visible with 60mm - that telescope, that observer, that night.

No algorithm is going to be completely accurate because of variable factors - observer eyesight, observer experience, interaction of telescope and seeing, are a few. I was reminded of this two nights ago when observing some difficult uneven pairs - even changing the eyepiece had an effect on the visibility of dim close companions, and the most difficult flickered in and out of visibility.

So, I was dealing with a matter - small telescopes, not medium or large - that did not fit the type of model I'd proposed for medium telescopes. And my feeling is that there are windows where the small telescope does better, comparatively, than medium telescopes. That would require a different algorithm, or predictive equation, and one with boundaries placed on it to allow for the modest light-gathering of small scopes.

I thought that my closer analysis of the diffraction pattern might be informative in the issue of Delta Cygni. I haven't yet got as far as applying it to medium-size scopes or other examples of doubles. But I have had the experience, not often, of having a "small scope" experience with my 140mm refractor, where I could definitely separate a double I'd expect to be somewhat beyond that aperture based on the RoT. I've not had that experience with somewhat larger telescopes such as my 235mm SCT, or a C14 (35cm) that I had access to in the past. With them, the ragged edge of visibility was pretty much where it was expected on the best nights. So I'm inclined to think something similar to the RoT has good predictive capacity within certain limitations. I agree it needs refining. And I'm beginning to see why Lewis didn't attempt an overall model, but gave a series of patterns (wry comment).

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5560421 - 12/08/12 05:37 AM

Fred, this is going in small steps to a common ground I think:
- splitting doubles with small scopes is a separate game with own rules (I feel even no longer sure if Dawes is valid for small scopes as also his numbers are probably derived from observations with larger scopes)
- there is no one singular RoT but a set of rules like for example:
--- m1 < 6 and delta-m < 1 then Dawes
--- m1 < 6 and delta-m < 2.5 then Rayleigh
--- delta-m > 10 then TLM including NELM
--- inbetween maybe a rule derived from crude number crunching
- any serious RoT should not only provide one number for required separation or aperture but also the average error range
- this error range should allow deriving probabilities for splitting with a given aperture and the same time cover the vast number of side effects not taken into calculation

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5565412 - 12/11/12 05:16 AM

Applied part of this step by step approach to Lord's data set for 3" and 6" refractor, but it did not bring much improvement - and once again I got the impression that this data set is not consistent on the "limit".
If for example 3" STF51 +6/12mag is a limit observation for a 150mm refractor how can then said the same of 3" A2225 +7.5/12mag and therefore 25% less delta-m?
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5566446 - 12/11/12 06:59 PM

Wilfried, I think it's clear that Chris Lord's observations set does not have enough examples that are at or near the limits of the telescopes. If all his data is used, the range (from not difficult to very difficult) means there's no clear pattern. I think only his most difficult with each particular telescope examples are useful for establishing limits.

I've had a similar problem in going through my observing notes. I have observing records for thousands of double stars, hundreds of them difficult with the telescope I used in each case. The problem is determining which examples are the borderline cases, those where I was working near the limit of the telescope. All this would be much simpler if I'd had a diaphragm on the scopes I used, so I could stop down the aperture on the difficult pairs on the best nights, to see how much aperture reduction was possible without losing sight of the secondary star.

Even so, I'm gradually getting a list of pairs that do look close to the limit of the scope used. When that's finished, I'll see what pattern I can find from my own observing. Because I've been using mid-size amateur telescopes - 14cm to 35cm aperture - it fits Treanor's 15-inches or less, while avoiding the "small scope syndrome", most obvious around 60-80-100mm aperture refractors.

I'm also starting to go through the observations of others, similar to Lewis's data collection, but including some observers he didn't look at, notably some in the southern hemisphere, and some post-1914 northern observers (as his study was published in 1914).

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5567468 - 12/12/12 12:21 PM

Applied the step by step approach now to my own data set (including 2 of your observations and some of the closest to limit from Lewis for 3" and 6" scopes) and feel stuck now - the best I could do so far is an average error in aperture of 20mm and this seems not this good as this the same value I got with more or less crude number crunching with a program for statistical analysis with hypothetical functions without much regard of optical theories.
I think I will take a recreational break with some reading on this topic and wait for opportunities for observation sessions to get some more data on limit observations in the range of 50-140mm aperture. Maybe some enlightment will come with time.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5568074 - 12/12/12 06:42 PM

Wilfried, I'm inclined to think that +/- 20mm isn't too bad related to a 140mm aperture - though I'd like to see it closer. Down at the 50mm aperture level that variation tells us nothing useful. It's proportional, as I'm sure you know.

I've had the experience of observing a double star that another experienced observer could not see, same time, same telescope, same eyepiece. The two of us looking alternately. To me the companion was fairly obvious; to him it was invisible, then after "look in this position" it was "maybe I can see it". So we have the observer factor as well. Some observers will need a bigger telescope, or higher power, or more practice on doubles.

I haven't mentioned another published paper on resolving doubles that I think you (and others) would find of interest. It was published in the (free, online) JDSO (Journal of Double Star Observations) - the particular item was in volume 4 no 4, Fall 2008 - by Tim Napier-Munn, "A mathematical model to predict the resolution of double stars by amateurs and their telescopes" .

It details a study based on observations by quite a few observers with telescopes from 80mm to 508mm on a variety of doubles to see what the limits were. And it deals with probability factors for predicting "splittability".

One thing I'd mention here is a graph that plots resolution against delta-m by aperture - for 80mm, 203mm, 356mm. There were 4x80mm, 1x203mm, 1x356mm scopes. The 80mm scopes did less well than I'd expect; the 203mm also less well; but the 356mm about what I'd expect from the RoT.

The paper discusses background - diffraction, Rayleigh, Peterson, etc etc - but the useful thing is the study based on new observations by 15 observers with 25 different telescopes. "315 valid observations were made". That's a reasonably significant total, despite the aperture spread being very large. There's no full data list, and the author does say that he rejected some observations for a variety of reasons, just as the USNO orbit catalog plots show some observations are well out of line with the pattern. Haas will have a similar experience - my impression is that one particular observer is already offering false positives on some doubles.

Last night I finally got a clear and dark and STEADY sky - able to take 400x with clear discs and neat diffraction rings - so I was able to try some difficult pairs again, and succeeded with some of them. Notes to follow after I've checked current WDS data etc.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5569469 - 12/13/12 03:31 PM

Quote:

... +/- 20mm isn't too bad related to a 140mm aperture - though I'd like to see it closer. Down at the 50mm aperture level that variation tells us nothing useful. It's proportional, as I'm sure you know...

Thank you for pointing out the obvious, I already got some blind spots here. The average error relative to aperture at this data status is 23% and this is certainly too much - but there is a focal point on fixed aperture observations (including the infamous 60mm observation of Delta Cyg) and these are almost always to some degree dubious.
I found the mentionded Napier-Munn article on the web and will study it with interest.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5574313 - 12/16/12 03:09 PM

I found the article of Napier-Munn "Model to Predict the Resolution of Double Stars" very interesting and I like the approach of statistical analysis of single observations. I modified the described algorithm of Napier-Munn giving the probability of splitting a specific double with a given aperture to providing the required aperture for reaching a 50% splitting probability for easier comparison with my other calculations - this did not give convincing results with my small data set (average error too huge to be mentioned here) and the behavior of the algorithm ist not gracious as for some parameter values it provides no solution for a 50% probability.
But the approach of statistical analysis of individual more or less "limit" observations encouraged me to resume my own efforts in this direction - I meanwhile got down to an average error in required aperture of 13mm (partly by eliminating 3 Lewis observations with statistically obvious deviation) and I am optimistic to get eventually to a single digit average error. My main problem remains the tiny data set available to me but I hope to solve this issue during the next year with a lot of limit observations with my iris diaphragm.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5575531 - 12/17/12 11:12 AM

Nae buttin' in like; but here's an 'infamous' quote fae Michael E. Bakich,(second in command at 'Astronomy' magazine.

"The Dawes limit is certainly only a guideline...Using this formula, my 4-inch f/15 Unitron should, at best, split a double star with a separation of 1.14 arcseconds. In May of 2,000, on a night where the seeing could only be described as "legendary," I was able to obtain a clean separation between a pair of double stars only 0.9 arcseconds apart. This observation was from my backyard in El Paso with six other people, three of whom were seasoned observers."

Source: The Cambridge Encylopedia of Amateur Astronomy, 2003. CUP, pp240.

Stick that in yer pipe and smoke it.

Eye.

Edited by astroneil (12/17/12 11:13 AM)

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5575792 - 12/17/12 02:17 PM

Quote:

...Stick that in yer pipe and smoke it...

Thanks for your input - there are always amazing observation reports.
Some remarks:
1. "The Dawes limit is certainly only a guideline" ... this is certainly correct as the Dawes limit is an empirical value to be considered as 50% probability for a split in the form of an 8. The only fault here is the missing indication of a standard deviation range in the sense of a Gauss distribution
2. To obtain a clear split of a 0.9" double with a 4 inch refractor is according to the confirmed theory of diffraction pattern rather impossible as the spurious disks should overlap - may be it would be wise to recheck the advertised data on this double
3. I am disappointed that this observation was not done with a 60mm/f15 refractor
4. The above mentioned meaning of the Dawes limit as 50% chance for a split is valid for all so called limits for resolution - so a limit is no limit but a value with a 50% probability for a split according to the defined properties (for example a clean separation for Rayleigh) and can be taken seriously only with a given average error or standard deviation.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5576437 - 12/17/12 09:17 PM

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered.

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy .....

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5576785 - 12/18/12 03:32 AM

Quote:

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered.

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy .....

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.

"And you shall not bear false witness against your neighbour." Exodus 20:16

Take the matter up with him and not me. He's got a physics background so I'm sure his reply will be interesting.

Merry Christmas to you and yours.
Nelly

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5577445 - 12/18/12 02:53 PM

"If yer quote another one you have taken own responsibility" WRAK 18:12
Best wishes
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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5578204 - 12/19/12 12:13 AM

Here's a little something to spice up the conversation -- using stars that are closely matched in magnitude:

Using a 3.8" Dolland refractor, which by the good Reverend's own forumula results in a Dawes limit of 1.20", that same Reverend Dawes measured the separation of Xi Librae(magnitudes are 5.2 and 4.9)in 1831 at 1.15" at a magnification of 295x.

He included this comment: "Occasionally divided. Fine night. Measures very good."

He measured it again in 1834 at 1.17".

For comparision, the senior Struve came up with these figures:

1825: 1.15"
1832: 1.22"

Using the same refractor to measure Zeta Cancri (magnitudes of 5.3 and 6.3), Dawes recorded a separation in 1831 of 1.09" at a magnification of 226x and included this comment: "Discs just separated when steady. Decidedly elongated with 140."

Again, for comparison, the elder Struve measured the separation at 1.05", also in 1831.

Data for Dawe's measurements comes from pages 82 (Zeta Cancri)and 87 (Xi Librae) of "Micrometrical Measurements of the Positions and Distances of 121 Double Stars, taken at Ormskirk, during the years 1830, 1831, 1832, and 1833", which was published in Volume 8 of the Royal Astronomical Society's journal, Philosophical Transactions, which can be found HERE, starting on page 61.

So it would appear that the good Reverend Dawes beat his own limit at least a couple of times.

Cheers,

John

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Re: Putting the "Rule of Thumb" to test [Re: 7331Peg]
#5578338 - 12/19/12 03:13 AM

John, thanks for the comments and especially for the link - very interesting.
"So it would appear that the good Reverend Dawes beat his own limit at least a couple of times" - this has to be necessarily so because his "limit" is calculated as average value derived from many observations so about 50% of his own observations have to be below his "limit". To know the average error would be of high interest - this way we could calculate the probability of a resolution of for example 10% below Dawes limit.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5579077 - 12/19/12 02:47 PM

At this late date, I'm afraid it would be a bit difficult to determine the average error -- but I certainly understand your point. That was part of the reason I included Struve's measurements -- they at least provide a reference point as well as a basis for comparison.

John

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Re: Putting the "Rule of Thumb" to test [Re: 7331Peg]
#5580139 - 12/20/12 06:51 AM

John,

In an age where men are sending space probes to Mars and uncovering the deepest secrets of the Universe, amateur astronomers on the cutting edge of double star research are looking to Dawes for answers.

Isn't it ironic that it's not the Apo or Newtonian, Maksutov or SCT that is setting the standards, but a humble, early 19th century spy glass, built with a token nod to optical theory.

Regards,

Neil.

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5581191 - 12/20/12 05:59 PM

I don't think anybody is looking for answers from Dawes - diffraction theory is the base of the discussion here and the Dawes limit is a potential starting point for any usable Rule of Thumb for splitting of double stars with unequal brightness and doubles with a primary fainter as +6mag.
Some errors are certainly not avoidable here as the Dawes limit is derived from observations with fixed aperture size and with advertised data for doubles less then perfectly exact corresponding to the available methods then - both factors together let expect an error range of 10% or more but even this is good enough for a starting point.
I think I am now at an interesting point of investigation with a multi step approach giving an average error of less than 10mm in required aperture but my data set is still far too small to take this seriously. Most interestingly statistical analysis of limit observations does not suggest any exponential effect of magnitude differences (especially not 2.512 as base as one would expect) but the effect of decreasing separation is exponential as one would expect.
I asked Napier-Munn for use of his raw data to counter check these results but so far without positive response.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5581725 - 12/21/12 12:06 AM

My reply is much the same as Wilfried's, first off - Dawes is a starting point but not a final answer. Dawes already had Airy's work on diffraction available by the time he came up with what we call the Dawes Limit, long after his early observations that John mentioned above. And I find it interesting Dawes does better than predicted using a smallish telescope - later he used larger scopes more typically around 6- to 8-inch aperture. And didn't do quite as well per aperture?

Wilfried, is the mentioned 10mm average error in aperture consistent over a range of apertures, or does it apply at some particular point? 10mm on 60mm is much bigger than 10mm on 150mm. Sorry to keep harping on this...

Re the data used by Tim Napier-Munn - no doubt some of the results in the raw data will be of use, but I find most interesting his graph for the 356mm aperture, which fits fairly well with my old suggestion of the RoT for significantly obstructed reflectors. The graph for 80mm and 203mm indicate under-performance for their sizes compared to the RoT and compared to my own experience.

That the magnitude differences don't follow a log scale (as per magnitude 2.512) is perhaps surprising but I'd come to a similar conclusion. Separation, however, I'd agree does appear to follow a model that's beyond linear - I'm wondering how much effect here is increased difficulty from seeing, as well as light spread, diffraction ring interference, and approaching the (diffraction) limits of the particular aperture.

Seeing in particular can make a huge difference. There are pairs I can't see one night in apparently steady conditions, and another night, looking similar on seeing, the pair is obvious. SW Burnham commented on the same experience. It does make finding the limits more difficult, because seeing appears to affect uneven pairs much more than even ones.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5581861 - 12/21/12 04:25 AM

Fred, the average error in relation to the calculated required aperture is 10,85%. You are right, seeing is all important but how you handle this depends on the intended use of the RoT model - I see it as tool for selecting doubles for sessions and then you have given the advertised data for the doubles, your scope and light pollution on your site. Seeing and possible other factors should therefore covered by the indicated average error.
The proposed model for small telescopes means refractors from 60mm to 150mm (work clearly still in progress) works as follows: Required aperture rA for a split is
1. If sep larger 10" then rA = derived from TLM modified by light pollution (this part is not yet implemented)
2. Else base is Dawes limit (116/sep) - this covers the beaten path of equal bright pairs up to +6mag
3. If delta-m >1 or m1 > 6 then rA = Dawes + f(delta-m) = 7.82302995069649*(m2-m1)/sep^0.814655479470003 else zero - this covers delta-m
4. If m1 > 6 then rA = Dawes + f(delta-m) + f(m1) = 8.28247140956849E-02*(m1+31.0737334876114)/sep^-0.999405092970208 else zero - this covers faintness of primary above +6mag
5. If m2 > 9 then rA = Dawes + f(delta-m) + f(m1) + f(m2) = 19.7728649102522*(m2-8.84688581507273) else zero - this covers increasing faintness of the secondary
6. If NELM < 6.5 then rA = Dawes + f(delta-m) +f(m1) + f(m2) + f(NELM) = 2.33967425240235*(6,5-NELM)^2/6,5 else zero - this covers light pollution.
The resulting rA is to be interpreted as 67% chance to split a spedific double within a 11% range of this value.
The unwieldy numbers are the result of a statistical analysis - different runs produce slightly different values with similar final result so there is no theoretical optical background for this numbers.

Some examples for NELM of 3 means rather heavy light pollution:
23 Aql 3,2" +5,3/8,3mag -> 68mm with error compared to obervation of 2mm
STT216 2,2" +7,38/10,28mag -> 133mm with error 13mm
STF2482 1,6" +9/10,2mag -> 123mm with error 17mm

Some examples for NELM of 6 means no light pollution (advertised data from Lord's paper mentioned earlier):
STT279 2,2" +7/9mag -> 77mm with error 2mm
STT140 2,8" +7/9,5mag -> 87mm with error 12mm
HO161 2,9" +7/11mag -> 155mm with error 5mm.

These examples were selected by chance and 4 of 6 values are within the expected range and therefore within the expected probability range.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5582855 - 12/21/12 05:13 PM

Quote:

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

That's tosh as well.
There's a whole bunch of reasons why this project is downright silly. But here's one specific objection for ya.
Angular resolution (in radians) is approximated by Lamda/D. For the Dawes limit Lamda is set at 562nm. But an average human eye can detect radiations as low as 390nm. Doing the math (which I'll leave for you to do) shows that you can resolve stars down to a smidgen lower than 0.8".
Sticking a blue or violet filter on an eyepiece would easily allow a 0.9" split in a 4-incher and compounded still more if the stars are already bluish.

I believe Mike Bakich; it was something about the way he said it, unambiguously and plainly. And with several witnesses.

Far too suspicious you lot.

Edited by astroneil (12/21/12 05:33 PM)

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5583156 - 12/21/12 08:20 PM

Okay, Neil, so the Michael Bakich quote had to do with observing through a blue filter (say, 430nm), so that the Rayleigh Criterion becomes 0.9", as per the description. The context of the claim wasn't given, if that's the basis for it.

Likewise, we could observe through a red filter, and the resolution becomes a lot worse than Rayleigh or Dawes.

The discussion we've been having is posited on an agreed wavelength point, roughly where the human eye is most sensitive in photopic mode. Sensitivity is much lower at blue wavelengths, and at red, hence the convention.

So, yes, if I use my 140-mm refractor with a narrowband blue filter, as per Bakich's 4-inch Unitron, I can increase its resolution compared to non-filtered use. So I might expect to see elongation on a 0.4" double (even components) instead of my current unfiltered limit of ~0.5" for elongation? If it's a bright double the light loss won't be a killer.

Suspicious? - I'd say properly sceptical. Such as when one observer claims to split a pair with 120mm that wasn't split by experienced observers under very good seeing with bigger, including much bigger - 400mm and 600mm - scopes. We're inclined to doubt in such a case. And when someone appears to say that diffraction theory isn't accurate - because they've shifted the goal posts, something we discover later - we unsurprisingly question the claim until it becomes clear what its real status is.

There is, incidentally, a nice illustration of resolution by wavelength in a series of images by Damian Peach, reproduced in Bob Argyle's Observing and Measuring Double Stars 2nd edition - Gamma Virginis in May 2005, imaged with a C9.25 at three wavelengths - Red, Green and Blue. Red is an oval smudge, green an elongated image (Sparrow Limit?), and blue a neat close resolution. The pics are accessible on the internet as well.

However, it doesn't change the basic story. It's a difference that works better with imaging rather than visual observing, because cameras can do things eyes can't in terms of relative sensitivity. And it's not going to help much for the visual observer with very uneven pairs where the secondary star is pretty dim.

A side point re cameras - Rainer Anton, in writing about "lucky imaging", suggests using red filters to reduce atmospheric seeing effects. This implies that resolution limits are more adversely affected by seeing at short wavelengths than there are gains via higher resolution at the shorter wavelengths. Which fits with adaptive optics on huge telescopes being used at Red/near-IR wavelengths for that reason. And, yes, there's a whole collection of issues to discuss there.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5583162 - 12/21/12 08:27 PM

Eye

http://www.telescope-optics.net/eye_spectral_response.htm

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5583326 - 12/21/12 10:44 PM

If adding color filters did anything to apparently increase angular resolution levels perceived, it was more than likely the dimming of the spurious disk to the point only its brighter centers showed and hence appeared smaller. Using a violet or blue violet filter on many a star would dim it substantially but the diffraction pattern never changes size.

Pete

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Re: Putting the "Rule of Thumb" to test [Re: astroneil]
#5583620 - 12/22/12 06:14 AM

Hi Neil

I somewhat disagree with you here. The sensitivity of the eye in the blue end of the spectrum is extremely low. It drops to below 10% already at 470 nm when photopic vision is used, which is what we want to use when looking at doubles, and is near zero at 400nm. It is thus not impossible to drastically improve resolution with a deep blue or violet filter, but the number of equal doubles bright enough to benefit from said filtration is very small. It must also be remembered that as our eyes age, they get increasingly yellow and opaque to blue light. This is why older observers tend to see less false color in achromats.

In theory, it's an interesting technique, but in practice, it has many limitations and is thus hardly useful.

Clear skies!
Thomas, Denmark

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Re: Putting the "Rule of Thumb" to test [Re: azure1961p]
#5583623 - 12/22/12 06:20 AM

Quote:

Using a violet or blue violet filter on many a star would dim it substantially but the diffraction pattern never changes size.

That is actually wrong. They DO change size with wavelength. The spurious disk ALSO change size with changing brightness.

Clear skies!
Thomas, Denmark

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Re: Putting the "Rule of Thumb" to test [Re: Astrojensen]
#5583679 - 12/22/12 08:11 AM

Quote:

Quote:

Using a violet or blue violet filter on many a star would dim it substantially but the diffraction pattern never changes size.

That is actually wrong. They DO change size with wavelength. The spurious disk ALSO change size with changing brightness.

Clear skies!
Thomas, Denmark

Aperture and spectrum together with brightness of a light source give a specific diffraction pattern - looking at this given diffraction pattern with a filter does not change the diffraction pattern itself but influences only what you see of it.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5583680 - 12/22/12 08:13 AM

Some extra spices in this discussion are always appreciated - but related to the topic of this thread ("RoT for required aperture for splitting unequal bright or fainter than +6mag double stars") this idea of using tainted filters to "improve" the diffraction pattern is of minor relevance. Even if it works it would only mean a small shift at the base of a RoT now suggested as Dawes limit - but this would anyway be covered by the unavoidable statistical error as such an approach can not be part of a standard setup.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5584421 - 12/22/12 05:45 PM

Agreed, that using filters for changing resolution levels is a side issue - standardising the wavelength where the eye is most sensitive eliminates a variable, that can be re-introduced if one wishes, as a factor modifying the numbers.

Where I'll support Thomas is in his (briefly) pointing out there are two matters regarding how we see a diffraction pattern - first, the size does change with wavelength - see the standard equation which includes lambda (wavelength) in determining the angle subtended by the image.

The other factor is perception - a fainter image will have an apparently smaller spot size (Airy disc) than a brighter star, because the eye sees less of the full diameter of the disc. Here, of course, the spacing of the rings is unchanged, though they become dimmer too.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5585110 - 12/23/12 05:12 AM

Quote:

...Where I'll support Thomas is in his (briefly) pointing out there are two matters regarding how we see a diffraction pattern - first, the size does change with wavelength - see the standard equation which includes lambda (wavelength) in determining the angle subtended by the image.

The other factor is perception - a fainter image will have an apparently smaller spot size (Airy disc) than a brighter star, because the eye sees less of the full diameter of the disc. Here, of course, the spacing of the rings is unchanged, though they become dimmer too.

Fully agree. Wavelength is a mixed bag given by the spectrum of a star, so what we see is a multitude of wavelenghts and for simplicity we calculate with an average value for yellow light. This assumed the diffraction pattern is a given as mentioned. If you look at this diffraction pattern through a filter you dim out some wavelenghts which gives only a relative enhancement of others, so this does not change the diffraction pattern but only your perception of it - if this is of any benefit is another question.
Same goes for the size of the spurious disk - fainter stars have smaller spurious disks. If you dim your image with a filter the spurious disk will get seemingly smaller - if this would be of any benefit for splitting doubles then it would be easier to split fainter doubles with same separation than brighter doubles. And this is certainly not the case as we all know the contrary.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5585160 - 12/23/12 07:21 AM

To spell it out a little more - I had in mind using a relatively narrowband cutoff filter, so that light outside a certain wavelength range was largely eliminated. Even with a passband of around 100nm, the effect shows nicely in the Damian Peach images I mentioned. The blue image (350-450nm) shows separate star discs; the green image (450-550nm) shows an elongated single image. Same object, same telescope, etc.

Regarding fainter pairs - an issue here is the human eye losing resolution as light levels drop. Which is a major factor in why fainter pairs can't be resolved as well as brighter ones. However, I've noticed that the loss of resolution comes in at a fainter level than I'd expected based on Lewis - and some of the observers he used had the same experience. SW Burnham (again) did very well with dimmer close fairly even pairs using the smaller telescopes he observed with. NOt as exceptionally well with the larger ones.

Which might lead us back to the mag 10 limit, suggested by Couteau, that was discussed a little while ago. Modest apertures don't run into the Couteau barrier as readily because of their lesser light gathering.

Much more to discuss but I'll have to go quiet for a few days given the arrival of Christmas.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5585735 - 12/23/12 02:40 PM

Have finally come to a usable formula for doubles with separations larger than 10" - required aperture should be depend only on the magnitude limit of the scope reduced by light pollution (are there today locations for amateurs without any?).
There is a lot of rather complicated calculations for TLMs (considering even the color of the eyes of your grandpa) on the market but a rather simple of general use goes TLM = 2,7+5*LOG10(D_mm). Remains the topic light pollution expressed in terms of naked eye limit magnitude NELM down to values below +3mag for locations in large cities. With the help of some limit observations I found with statistical analysis the rather unwieldy relation TLM(NELM) = 3.2*LOG10(D_mm)+6.7392231622074*(NELM/6.5)^0.533365942734249. This gives for doubles with sep>10 a required aperture = 10^((M2-6.7392231622074*(NELM/6.5)^0.533365942734249)/3.2) - for example 110mm for POU3851 14.2" +9.5/10.5mag.
This was the last item on my list for a RoT proposal based on my quite small data set on limit observations. Between the holidays I will make an Excel spreadsheet with this RoT proposal with a link for downloading it if anybody is interested in testing it.
Next step is certainly enlarging the data set of limit observations for further enhancement and higher statistical reliability.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5603144 - 01/03/13 02:39 PM

Quote:

This was a bit premature - when checking the current model with a test data set covering all relevant data points for separation, delta-m, m1, m2 and light pollution for graceful behavior I found several glitches. These are partly due to the too small data base of real limit observations and partly due to not so clever assumptions concerning the model functions. One example is the relation of increasing m1 (increasing faintness) and required aperture depending on separation - it seems that after a steep increase counteracting the fast decline in required aperture by increasing separation there comes a plateau of indifference. First tries so solve this with logarithmic or trigonometric functions did not work out so I thin I will have to work out just another if-then condition.
So there will be a delay for posting a spreadsheet with a proposed model for testing.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5608610 - 01/06/13 03:06 PM

I am still not satisfied with the interacting of the different components of my RoT model but I managed some improvements and eliminated the component for doubles with separation > 10 arcsec and the component for faint companions on the border of telescope magnitude limit for now.

Here the promised link for downloading the spreadsheet with the present state of the RoT model for small refractors: "http://www.sterngucker.eu/XLS/WRAKs RoT.xlsx" as a starter filled with doubles from Taurus sorted by required aperture.
You can use the spreadsheet by simply enter the data of doubles manually but it is certainly better to get a list of all double stars in your required field of view (for example with the help of a tool like AstroPlanner) and insert it with copy and paste. You can then sort the list by required aperture and select the part of interest to you for your observation planning.

Any comments on obvious or not so obvious errors or suggested improvements are welcome.

Besides trying to improve the quality of the structure of the model the main future step will certainly be the enlargment of the existing data set of limit observations to get a better statistical relevance for the parameter values of the model. Another vital point of interest would be to add a component regarding the CO for reflectors.
Clear skies for you and me.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5609959 - 01/07/13 11:03 AM

Wilfred, sorry for coming in late. I have not read the other post where the RoT was suggested, but what is the rational for the division of sep by delta-m? Most math is derived from logic, but I am not familiar with how that came about. It is intuitive, however.

S = 116/D. Multiplying by D and dividing by S yields D = 116/S. Sure, resolution is determined by both separation and brightness between the two stars. The primary offers the bright diffraction background and the companion must be bright enough to show through. So, dividing S by delta M provides a way to scale D, when delta M is large S/delta M is small. This in turn increases D. Makes sense, intuitively.

But is the variable sep/delta M valid? I guess that's what you want to know. I guess it would help to understand the logic of why delta M was introduced in such a way. It is important variable, though, just asking why it was applied there.

One thing I suspect is missing is accounting for the bright diffraction field surrounding a star. That is a variable, too. As we have been discussing, a perfect unobstructed aperture puts 16% of the light into that small bright diffraction radius. It's possible a 9th magnitude star could be detected much closer to the primary.

However, an obstruction of .3D puts 32% of the star's light into the diffracted field, and it draws down the peak intensity of both the primary and the companion. In this instance, a brighter diffracted pattern and the companions lower peak intensity push that detection radius out much further. Or requires a lower delta M at a given radius.

It seems possible to calculate a RoT for one type of scope that would not apply to another. So, if there were a variable introduced to account for the bright diffraction field delta M has to contend with, then an appropriate aperture would be estimated. Of course, since a refractor is unobstructed, this variable would fall to zero and we'd be back to D = [116/(S/delta M) * 0.]

Actually, I am thinking that variable might actually be a constant of some value dependent on the relative diameter of the obstruction. It would simply scale aperture upward proportional to CO. Again, if unobstructed, it would have a value of zero.

Edit: I see where the value 2/3rd is applied for unobstructed scopes. Sounds reasonable.

So, lets say aperture is known because I have one scope, and I want to know the possible separations for observing doubles. I would rewrite the equation to S * delta M = 116/D, then divide by delta M to get S = 116/D * 1/delta M. But problems arise with delta M in the denominator, when it is zero for example. And S decreases with larger delta M, it's not the behavior I am looking for. Something in the logic (or the my math) does not appear to work: the left side does not always equal the right side, I think. The equality does not hold.

Anyway, just getting caught up and went off on a tangent. Still reading.

Edited by Asbytec (01/07/13 11:44 AM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5610067 - 01/07/13 11:58 AM

Quote:

I do not consider light pollution as serious influence - as stated elsewhere I even have the experience that the seeing her is most of the times better than in darker places with a stronger drop in temperature in the evening.

I would agree, when doing a rule of thumb simple is best. There are just too many variables, such as seeing, collimation, focus, cooling, light pollution, observer experience, etc. Those should be assumed either perfect, negligible, or constant. The variables that matter are separation, diffraction brightness, and companion magnitude (the latter two are factors of delta M.) If the the resolution RoT fails in light polluted skies, resolution should occur under dark skies being limited only by the laws of diffraction (governing ring intensity of the primary and peak PSF of the companion.) If seeing is bad, the RoT will fail, too. It does not mean it's not a valid RoT, it just needs appropriate conditions to work. That's why it's a RoT and not a precise mathematical equation.

Someone should say, a 10" SCT can split this pair. And indeed it can. However, like everything else, if conditions do not permit...then they do not permit. Wait for a better night for success that is STILL possible IAW the basic and simple RoT. Allow the observer to decide if a 9th mag pair is appropriate for his local conditions. Maybe, or maybe not. But the split IS doable - the important consideration - for someone else under better conditions.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5610167 - 01/07/13 12:44 PM

Norme, there have been so many intermediate steps in this process that I have to some degree lost the overview - but I cannot remember a suggestion for division of sep by delta-m. If you mean the very first step in our discussion D=116/(sep/delta-m) you should read this as D=116*delta-m/sep - sorry for the confusing notation.
In case you have not yet downloaded the spreadsheet with the current suggested RoT version (based on statistical analysis of a small data set of observations with a refractor with an iris diaphragm to be able to reduce the aperture to the limit of splitting) and therefore not read the introduction I repeat here shortly:
Rule of Thumb Model for estimating the required aperture for splitting unequal and faint doubles for small 1-6" refractors per 2013-01-05:
rA = required Aperture in mm = rA1+rA2+rA3+rA4+rA5 with a split probability of 50% and an average error of 10%
rA1 = Dawes limit = 116/sep with sep = separation in arcseconds
rA2 = f(dM) = function of delta magnitudes = dm'*7,6220905762799*(m2-m1)/sep^0,713969668906051 with dm' = switch for delta-m < 1, m1 = magnitude primary and m2 = magnitude secondary
rA3 = f(m1) = function of m1 = m1'*1,83163170523935*(m1-3,02833460276676)/(m1''*sep^-0,415228540946423+(1-m1'')*(14-m1)^-0,415228540946423) with m1' = switch for m1 <= 6 and m1'' = switch for sep <= 14-m1
rA4 = f(m2) = function of m2 = m2'*19,6060894270314*(m2-9,18074376678362) with m2' = switch for m2 <= 9
rA5 = f(NELM) = function of NELM = 1,81466984138841*(6,5-NELM)^0,901484005717405/6,5 with NELM = average naked eye magnitude limit for a given location.
The structure of the model was gained in a multitude of steps with some theoretical reasoning, formulating accordingly functions and running statistical analysis. After eliminating all approaches with bad results in terms of correlation and average error this is what remained, but there is still a lot of work to do and some parts of the model seem a bit counter intuitive and not according to any optical theory.
But we are looking here for a Rule of Thumb usable for selecting doubles for session planning and not a new optical theory.

One of the next steps could be an extension for reflectors with CO. My current basic idea for this is
- modifying the Dawes limit for reflectors regarding the somewhat smaller Airy disk depending on the CO size - means a little smaller than for refractor
- applying CO to the other components rA2-rA5 with a factor in relation to the CO percentage - means somewhat larger than for refractor
giving in total a small advantage for the reflector for close and equal bright doubles and an increasing advantage for refractor for doubles with increasing unequal brightness.

The problem in verifying this approach is the lack of limit observations with reflectors as the use of aperture masks is somewhat questionable (the percentage of CO would increase unreasonable) and all observations with fixed apertures are at "limit" only by chance - only doubles with a mixed bag of positive and negative results under similar conditions could be considered as "limit" for a given aperture/CO combination.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5610203 - 01/07/13 01:02 PM

Thanks, Wilfred, I know some very good minds are working on it. I am simply struggling to keep up.

Okay, I see much more went into the equation, and thank you for the correction.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5617561 - 01/11/13 04:30 PM

The evidence that Rayleigh and Dawes criterions have to be adapted for a smaller Airy disk radius for scopes with CO is growing even when empirical evidence is still a bit shaky. But also the in the mentioned paper of Lord published single observations show for a 150mm MAK significantly better performance near the Dawes limit than with a 6" refractor This means that for a potential CO component for the RoT Model two steps are necessary:
- Modify the Dawes limit base 116/sep accordingly to the smaller Airy disk radius due to CO (I have meanwhile found a numerical function for calculating this radius from the CO value)
- Apply a CO dependent factor on the other components regarding delta-m, m1>6 and so on. First shot would be an exponential function like multiplying these components with 1+CO^2 but with missing empirical data this is so far more a shot from the hip than an educated guess.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5618801 - 01/12/13 10:57 AM

The observation reports of Fred concerning BU 1040 and BU 91 made me aware of a serious flaw in my current RoT model regarding the influence of light pollution - it is simply far to simple to add a few mm in required aperture for a bad light pollution because this is certainly an exponential component with decreasing faintness especially of the secondary. This is curious insofar as I have already made a concept for a component for very faint companions based on a TML function including NEML. The formula for the req. aperture for resolution of a star with magnitude m is 10^((m+LN((6.5/neml)^2.512)-2.7)/5) giving for example 138mm for +13,4mag and perfect NEML of +6.5mag as good approximation of the theoretical TML of a 140mm scope and approximately the same required aperture for +11.4mag with a rather bad NEML of +2.9mag. Even if these formula might be a bit too optimistic for the TML with bad light pollution it can be used to calculate the required extra aperture for light pollution giving for example an add on of 30mm from 54mm to 84mm for a +11.4mag star with a NEML of +4.5mag. So for faint companions it seems to make sense to first calculate the NEML dependent TML required aperture and add then the additional factors for delta-m, m1>6 etc.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5618883 - 01/12/13 11:37 AM

Wilfred, I am becoming aware of the complexity of developing a rule of thumb. I applaud your efforts and wish you success.

The complexity and difficulty seems to come from not only the large number of variables, from NELM to observer experience to seeing, but also the vast range of those variables, from 6/10 to 9/10 seeing to the entire Bortle scale. Accounting for all of these seems to turn a rule of thumb into a sophisticated calculation.

I would think most observers have a feel for their NELM and seeing conditions, and maybe about any other condition that affects them. So, I would think a RoT might be just that, under reasonable conditions one might expect to split this star limited only by diffraction. If the companion is a 13th magnitude star in 7/10 seeing, the observer can estimate his own chances of splitting a double (that can be split) with his aperture under his conditions.

It may be possible to refine a RoT with each successive layer of complexity, but maybe it would be best to have one that is "diffraction lmited" (if you don't already), then scale and test each layer of complexity (NELM and seeing, etc.) individually.

Each time a variable is added to your RoT, the level of complexity rises. Maybe exponentially. I would think it's best to use the KISS rule for a rule of thumb. Then, once established, add a layer of complexity. Working a puzzle with fewer pieces is easier.

Just some thoughts, Wilfried, in support of your project. Not a complaint against it. I offer them for you to (re)consider (I am sure you have) because I want you to succeed.

Edited by Asbytec (01/12/13 11:41 AM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5619485 - 01/12/13 05:24 PM

Norme, thanks. I understand your reasoning for keeping it simple and in the beginning of this task I started with quite a simple approach. But meanwhile I found that it is not this feasable to add components step by step as they are interacting. Main problem seems to me is not the resulting complexity but the much too small data set so I am happy for each observation report on doubles of interest giving me an opportunity to eliminate errors in my current approach.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]

Wilfried, I suspected there might be some interaction that required simultaneous solving. I applaud your work.

One thing that keeps bugging me is phase interference. I can't help but wonder if there is not another level of complexity where out of phase waves from the primary interfere with the companion at some angular distances.

"Since, according to Van Cittert-Zernike Theorem, light arriving from stars is coherent in amateur-size telescopes, as long as it is near monochromatic, it is an interesting question how much this coherence factor, combined with the coherence-lowering polychromatic spectrum and OPD differential between two close stars influences their actual resolution limit in the field."

http://www.telescope-optics.net/telescope_resolution.htm

I would think, a very simple rule of thumb might just say a companion must be both above the visible threshold (aperture limiting mag and NELM) and at least 5% brighter than the surrounding ring structure.

Something like below where the red are the PSF of the companion at varying magnitudes and separation, the yellow line is either a linear approximation or a curve defining the diffraction intensity, and the green line would be the RoT at varying NELM (white dashed lines.) But, alas, it's not that simple, eh?

Edited by Asbytec (01/13/13 04:01 AM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5622244 - 01/14/13 08:25 AM

Norme, this approach reminds me somewhat on the concept of Treanor that a faint companion can be seen at the minimum next to the diffration ring of the same brightness. Basically this concept would be of high interest because it would be fully based on optical theory but it has some difficulties. I tried some weeks ago to translate this concept into numbers but found it difficult to calculate magnitudes for diffraction rings from the energy distribution in the diffraction pattern - how do you compare the light energy in a ring to the light energy in a spurious disk? Calculating with the percentage numbers I came up for refractors with a delta-m of 2.86 for the first, 3.88 for the second and 4,56 for the third ring but when I translated this numbers into required apertures for given doubles the results were not convincing. On the other side Lord comes up in his already often mentioned paper with a delta-m of 4.39 for the first ring - and here things get a bit out of hand: While it may be reasonable to see a 2.86mag fainter companion at the Rayleigh criterion this seems a bit unreasonable for a delta-m of 4.39mag.
May be you can find a good source for magnitude values of diffractions rings comparable to magnitudes of spurious disks then we could consider this concept once more as potential base for a RoT.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5622538 - 01/14/13 11:51 AM

Yes, I was struck by Treanor's work and a little proud to have the same line of reasoning. I would yield to you on how to calculate the ring brightness in terms of delta magnitude. It might involve flux and an area terms, and that might be a bit hard to do for a range of magnitudes and scopes. So, again, I would yield to you or simply use Lord's figures.

Even then, it still might not work because I suspect there is more than brightness happening in the rings. There is also constructive and destructive interference at varying optical path differences. I just do not have a good feel accounting for these phase differences, nor know whether or not they are significant enough to matter.

I have been eager to observe some of the remaining Tau list and begin some of the Orion list, but the weather is just not clearing as expected. And my time is short, in two weeks I begin traveling through June of this year. Our observing season is over by then.

Anyway, I am only interested in the subject, pondering it, and discussing concepts. I am not trying to make life hard for you. Thinking about the RoT and observing a few stars, I do realize how daunting the task is. Never the less, it's a fascinating area of discovery.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5629482 - 01/18/13 08:40 AM

The need for more limit observations in my data set is great, not only for my own but also from other observers to cover different observing situations.
In the first moment it seems easy to go through existing literature and pick out observations but in detail it gets difficult because when should an observation considered to be at least near the limit (as observations with fixed apertures are "exactly at" the limit only by chance):
- the easy ones have to be eliminated or else the statitical analysis will show a bias towards easy splits. Existing criterions or RoTs are of some help here
- the overperforming ones have to be considered with care and existing criterions or RoTs are not always helpful here. And in this cases we have always the individual interpretation what is a successful resolution and what not - is an occasional flicker enough for the identification of a faint companion or is an elongation without a clear indication of the position of the secondary a positive result? Absurdly overperforming observations have even when doubtless "being true" certainly to be eliminated to avoid a statistical bias towards the overly difficult challenges
- the reported advertised data of pairs is especially for historic observations in many cases obsolete. The magnitudes are relativly easy to correct because they should have been the same 50 or more years ago. Separations are another thing because meanwhile these may be different now depending on orbits, so you have to take what has been reported then
- ...
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5629595 - 01/18/13 10:05 AM

Wilfred, I completely understand the need to eliminate bias. The subject interests me on many levels. First, it's new aspect I am not familiar with and challenging. Second, it's just a fascinating look into optics and observation.

I'd love to offer some better defined splits, unfortunately I have had few clear nights and none recently. Now with the moon rising into the sky, it appears there will be few dark nights remaining before I travel to the US.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5629748 - 01/18/13 11:23 AM

I have meanwhile developped a formula for modifying the Dawes criterion for scopes with central obstruction as follows:
Dawes (CO) = 116/1,2213*(0,0950502775050452+(1,12627632206642)/((1+(A2/0,302756091410027)^2,26536793426585)^0,152776210790626)).
Results are as follows:
CO Dawes_mm(CO)
0 -> 116
0.1 -> 115
0.2 -> 111
0.28 -> 107
0.3 -> 105
0.33 -> 104
0.35 -> 103
0.4 -> 100
0.5 -> 95

So the Dawes criterion for a 150mm scope with 0.28 CO would be 107/150 = 0.71" instead of usually 116/150 = 0.77" and for a C925 with 0.35 CO 103/235 = 0.44" instead of 116/235 = 0.49".
I own a C925 but do not like it for double star observing but occasionally I could try to check this even if verifying such a small difference might get a bit difficult. But I have one very good reason to trust in this calculation: The observations for equal binaries listet from Lord in his paper on "Resolving unequal binaries ..." for scopes with CO are in their relation to the Dawes criterion significantly better than the scopes without CO.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5629837 - 01/18/13 12:08 PM

Wilfried, sure, your calculation for the 150 28% CO is the same as mine derived from:

http://www.telescope-optics.net/obstruction.htm

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5631311 - 01/19/13 10:49 AM

Revisit of HO 20 in 9/10 seeing and mag 4.5 skies resulted in a good split. The faint companion was held steady for seconds at a time at 163x (18mm UP HD ORtho 1.6x Celestron Shorty.)

HEI 670 was a failed split. No indication of the companion. It appeared to be much like C Ori, but the latter did offer some clue to the companion's position. HEI 670 did not.

BU894 and STT133 also failed to get a good clean split. However, with some significant effort, I did manage a few possible glimpses of the companion. But, not enough to be a good, legitimate split and certainly very difficult and time consuming observation.

Wilfried, I am beginning to notice a bit of a trend on the few doubles I have attempted. It does seem somewhere around required aperture 144 or less, I can achieve a good legitimate split and hold the companion's disc steady for a period of time. Around 147 or so they become very difficult resulting in those brief, fleeting, and merely possible glimpses.

I wanted to attempt STT 517, but I lost the sky to high overcast. As a close double very near the 0.71" arc Dawes limit, I think it would have been a good test.

I also revisited BU 1040, but failed to split it, again.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5635440 - 01/21/13 05:48 PM

Norme, thanks for putting time into checking doubles from the Ori list. Your troubles with BU894 and STT133 probably give a hint that there may be a current ROT model problem with companions fainter than +11mag. You could countercheck this suspicion with BU13 and STF849, both are in the ~150mm req. apterture range with companions brighter than +10mag and should be no problem for you.
The topic of companions coming near the TML of the scope will be the next extension of the current RoT model after including the factor CO with reasonable results.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5635457 - 01/21/13 06:00 PM

For me with 11 and 12 magnitude doubles in pairs under 2" the vague graininess becomes apparent as the eye seems straddled between photopic and skotopic vision. The way the stars would morph into seperate bodies than rejoin in poor seeing was even spooky. Compelling and beautiful but a little eerie to . Doubles are usually such bright cheery things.

When time permits I'd like to weigh in on some of the RoT objects . Weather has been so lousy and when it was good I either had the flu or I was eorking or like last nite it was gusting to 25 knots.

This has been a progressively interesting pursuit you guys have taken on. Perhaps I can add something at some point.

Cheers,

Pete

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5635556 - 01/21/13 07:11 PM

First, some doubles observed - with a fair bit of moonlight, my most recent nights were given to doubles where the companion is not at the fainter levels of magnitude. I figure that with Orion around for a while, I can pursue those after the next Full Moon has departed a while.

Norme didn't get a split on HEI 670 - I was luckier. The 140mm refractor, and at 285x I got glimpses of a small companion; 400x confirmed it, the companion clear in the steadiest moments. Air steadiness good, with very good moments; 8 day moon. This was the night before last.

STT 133 was easier than I expected - moonless night, earlier this month, seeing becoming good by the time I got to STT 133. Moonless night, good dark sky, so the 11.2 mag companion I didn't expect to be a problem. And it wasn't. I found STT 133 with my 80x eyepiece, a Pentax 10mm XW, which gives a field of ~50' or so - first surprise was seeing a hint of the companion at 80x. So instead of going to 160x, I put in the 7mm XW (114x), and that was enough - the companion was a tiny speck close to the primary, roughly NNE. Much easier than expected. Air steadiness must have been better than I thought! The data list gives mags 7.3 and 11.2 at only 3.3" for STT 133 - hence my surprise. I expected it to need higher magnification if it showed.

STT 517 - Norme has reported further on this one in another thread. I have notes on it from this time last year - I've not got back to it again - yet. This one is a long-period binary, orbit currently listed at 530 years but only grade 4, so it'll be refined over time. The pair is slooowly widening these days, but should be near enough 0.7" as per the 2010 measure. The night I observed it was not great for steadiness - only fair-plus, with fuzz and flicker. 140mm refractor, best I could do was an elongated image in a fuzzy surround at 400x. I'll try it again on a steadier night.

Another pair on Wilfried's list is HO 22 - mags 8.5 and 8.6 at 1.0". Being less bright makes such pairs tougher with moderate apertures. I've seen pairs at 0.5" at mag 8.5 with a C14, but a C14 has 2 magnitudes gain over my 140mm refractor. HO 22 - 140mm refractor, visible split (two star points separated) at 285x, using the 7mm XW with 2.5x Powermate. Easier than I expected; seeing good/good-plus.

I'll have a few more to add when I get time to go through my notes.

One thing I'm noticing is a similar effect to that shown in the Petersen diagram - where Harold P found no change in resolution until he got closer to the magnitude limit of his telescope/magnification combination. Then things changed noticeably.

To be expected, I'd think - it's the "fainter doubles" effect, where the interaction of eyesight limits comes more into play as the stars get dimmer. And that becomes evident somewhere around the Couteau Limit of 10th magnitude - maybe around 10.5 or so - for reasons separate from mere dimness as Couteau remarks with regard to bigger (big) telescopes. Magnification goes only so far. Eventually there are trade-off factors between the eye's ability, the atmospheric seeing, and what the telescope is doing.

There's been some good discussion of that in a thread on the effect of CO versus other factors in the Cats forum recently, and elsdewhere - with comments on bringing the eye (and its MTF?) into conjunction with the telescope's abilities/limitations. Rather like the photographic discussions of what you get in an image after considering what the lens can do PLUS what the film or sensor can do - final results depend on both.

Edited by fred1871 (01/23/13 02:26 AM)

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5635853 - 01/21/13 10:29 PM

Wilfried, I'd be happy to observe BU13 and STF849, maybe tonight. I was curious about the seeming disparity between RoT and actual aperture. I have not read Fred's comment, yet, but does the RoT use the clear aperture rule? It seems, if close unequal pairs act like planetary contrast (same scale, same problems with diffraction), then those two rated above (D - co) would be difficult. In my case, that would be 150 - 41 = 109mm, same as a refractor according to MTF approximation.

Still, I am getting the feeling something is working in the RoT. There seems to be a cutt off point for my own aperture/CO ration between 144mm and 150mm. They do progress from confirmed, distinct Airy disc for the companion to being extremely difficult or impossible within that range. So, it seems the scaling is working, but maybe the scale might shift entirely up or down to fit. But, again, my own sample size is small to say. It's just an impression that seems to hold over the samples tested.

Pete raises an interesting point on scotopic and mesopic vision. One of the reasons I did not go after some dimmer samples is the increasing use of averted vision needed to observe them. Using rod based vision does seem to reduce visual acuity, but offers increased sensitivity. Not sure which is most important when observing point sources.

Fred, yes, HEI 670 has a sep very near the bright first ring. It really makes some sense it is very difficult in an obstructed aperture. I found it impossible, more difficult than c Ori.

Likewise, STT133 sits on the fourth ring, which is not really bright but more broad (as seen on the brightest stars.) The second and third rings are bright with a 28% CO, but very thin in comparison. So, it's curious, even though the fourth ring is well below the visible threshold, it seems to have some effect on resolution.

I cannot 'explain' why BU 894 companion was not seen at over 5" arc sep. That was one that seemed to be easy, but it was not. Maybe the Couteau effect has something to do with it, both ST133 and BU 894 have companions below 11th magnitude.

Revisiting HO 20, I got a clean, steady split, too.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5636204 - 01/22/13 04:01 AM

Pete, would be great if you could join in with some hints and observations.
Fred, great to get some more observations for my data set.
Norme, depending on the degree of light pollution we get with secondaries fainter than 11mag already rather close to the 150mm telescope magnitude limit of ~13.6 (for NEML of 4.5 I calculate currently TML ~12.6) and then it seems to get really hard even with not this small separations. I have still not figured out what separation is then necessary to be able to see a companion effectively at the scopes magnitude limit - it seems to require at least a two digit number.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5637956 - 01/22/13 11:01 PM

I've never ever tried for 11v at any appreciable separation under 10". Pairs of that magnitude but neverv, say, mag 11 at 2" from mag 6. I think my cut off for whatever reason was 9.5v. I think I was so put off with that difficulty I backed off a bit. I want to contribute when the weather obliges.

Pete

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Re: Putting the "Rule of Thumb" to test [Re: azure1961p]
#5638207 - 01/23/13 03:03 AM

I've now found I can see fainter stars than I'd thought likely when there's moonlight. No, maybe not around full moon, but a few nights ago, with an 8 day moon in the sky, I had a look at HJ 697 in Orion (0521.5, -0025). The two wide companions had "old" magnitudes on my observing list, 10th and 11th mag.

I found both stars were fainter than I expected, even allowing for moonlight - the brighter companion was clear enough at 160x (glimpsed with less) and the fainter was averted vision only; both were easier at 230x, though the fainter remained near the limit of visibility.

Later I looked up the data in the Washington Catalog, and found modern photometry for both (double-digit) - the easier companion was mag 11.9 (not 10.6) and the fainter one was 13.05 (!! - I had 11+ listed). So, 13.05 in fairly bright moonlight - with 140mm aperture.

Because both are very wide of the magnitude 5.7 primary there's no significant effect from it - the brighter companion is at 42", the fainter at 33".

So I'll now be willing to try for fainter companions in moonlight.

Obviously, for the tight pairs, unlike this one, bright moonlight will remain a problem for faint companions, adding to the primary star's effect. But I now think it's less destructive than I'd expected (except maybe for a few days around Full Moon).

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5638223 - 01/23/13 04:04 AM

Fred, interesting report - this would mean that at least for a separation above 30" there is no longer a resolution effect on the companion. I assume this could be valid down to about half of this separation.
Anyway it is quite a feat to resolve a +13.05mag star with a 140mm refractor in "fairly bright moonlight" - this is already very near the advertised telescope magnitude limit of 13,4 for 140mm and to reach such numbers requires already perfect seeing near zenith and exzellent skills on the side of the observer. This would also support the claim in the article "Some notes on Visual Urban Astronomy" from Tom Bryant that you can resolve stars up to the TML even under severe light pollution. From my own experience I do not buy this - my 140mm TML with average NEML 3 is so far about +11.5mag but I have to admit that I never pushed this topic very much.
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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5638243 - 01/23/13 04:59 AM

Quote:

I assume this could be valid down to about half of this separation.

Anyway it is quite a feat to resolve a +13.05mag star with a 140mm refractor in "fairly bright moonlight"...This would also support the claim in the article "Some notes on Visual Urban Astronomy" from Tom Bryant that you can resolve stars up to the TML even under severe light pollution.

I would assume the same, Wilfried. Of course diffraction is infinite, but at some angular distance it becomes meaningless.

On TLM, I have to say on some nights (near the crab nebula) I picked up stars about 14th magnitude, but other nights failed to see stars down around 12th in weak sky glow to the north (Iota Cass, for example.) On BU 1040, I spotted some field stars other than the two nearby bright ones. I cannot find magnitudes on them, but if the dimmer "bright" one was 13th mag, the fainter field stars had to be pushing 14th mag (at around 250 to 300x.) And I saw them both on dark nights and with a crescent moon in the sky. NELM was 4.5 and 4, respectively.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5638551 - 01/23/13 10:04 AM

Concerning the validity of "modern photometry double-digit" magnitudes in the WDS catalogue I tend to "believe" them but not without some reservation. One example for "being not so sure" is STF450 in the Pleiades (one of the stars in Ally's braid) with advertised data 6.2" +7.29/9.10mag suggesting an easy resolution with a small scope down to 50mm aperture. But I failed several times with an 120mm refractor despite two fainter than +10mag stars were easyly seen in the same field of view. I have no explanation for this besides assuming a clearly wrong magnitude in the WDS catalogue as I would estimate the STF450 companion around 11mag.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5638582 - 01/23/13 10:18 AM

I am very new to double star observing, but even I am getting the feeling there is just so little data on doubles. Few reports, discrepancy in reporting, and maybe few are recent. There must be errors in the catalogs.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5639387 - 01/23/13 06:31 PM

Wilfried, I'm a little puzzled about STF 450 in the Pleiades - I'll have to re-observe it with my 140mm refractor. My only notes on it, from 4 years ago, were with my C9.25, and I described it as "an elegant, uneven moderately close pair" with 98x (24mm Panoptic eyepiece). In other words, it looked easy at that power and I didn't think at the time the listed magnitudes were wrong - that's something I do make a note of when I have that impression - as happens with, for example, some of the Jonckheere pairs.

Errors in photometry? - of course, and you picked up an example with a J pair, when the AAVSO photometry survey appeared to give more accurate magnitudes than those in the WDS. The WDS typically uses Tycho for its modern magnitudes. Generally, these are of good accuracy. Obviously there are other sources as well, as we've both noticed with some of the IR magnitudes for some doubles. The WDS collects data from many sources.

Norme, it's not generally true that "there is just so little data on doubles". For some, yes; for others, a great deal of data, and the typical double has quite a lot. The WDS gives summary lines on each pair. There's a lot more known for most of them, and a data request for a double of special interest will show that. Of course, requesting floods of data files won't be appreciated by the good folk who are responsible for the WDS; but I like others do put in occasional data requests, when there's good reason for it, and usually there's a lot of data that comes back.

Errors in the catalogs? Of course. But many doubles have multiple examples of photometry, many measures over the years, and sometimes detailed studies or calculated orbits. The quality of the material varies, that's to be expected. But getting all the data together can often give patterns, or allow analysis that gives more accurate information than the summary line might suggest.

One recent example of this - I requested data on a double where the earliest and most recent measures suggested the separation had been 1.5" in the 1870s, and 2.3" now - the full data suggested the first measure was in error, and 2.0" was the likely correct figure. So the pair has changed much more slowly than the summary line suggested.

Another - first and last measures suggest no change in separation - getting intermediate era measures shows a changing binary that has closed, then widened again. This kind of thing might be picked up from getting data listed in Sky Catalog 2000, or other readily available sources, so as to have measures from an "in-between" time. Two data points can be not enough to have an accurate picture.

Agreed - sometimes there's not enough data. The recent experience with Gamma Equulei, discussed here in some detail, tells us this - we need a new measure to see what's happening there, as it appears likely the pair has been closing quickly in recent years, perhaps with a significant change of angle as well. We won't know until someone with a large telescope re-measures it, probably using adaptive optics (as with the most recent measure) because the large delta-m makes it a problem for speckle interferometry. Then we'll have a better picture of the orbital change. And further measures, in years to come, should eventually allow an orbit calculation. For now, we're guessing about the orbital period and shape. One of many like this.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5639584 - 01/23/13 09:26 PM

Fred, okay, thanks for the enlightenment.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5640091 - 01/24/13 06:58 AM

Quote:

Wilfried, I'm a little puzzled about STF 450 in the Pleiades - I'll have to re-observe it with my 140mm refractor...

Fred - it is a curious positive side effect of light pollution and smaller apertures that you can see resp. not see stars at the fringe of a rather low level of TML. This way you can detect questionable data on magnitudes you will not notice with greater apertures and excellent seeing. With 140mm and NEML > 4 you will most probably resolve the STF450 companion without trouble and therefore not bother to compare its brightness with advertised fainter but visually brighter stars in the same field of view - but as you have now a hint you will may be also find that there is something wrong here.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5640301 - 01/24/13 09:58 AM

Wilfred,

I was able to split both BU13 and STF849. They are what I would consider easy splits with both primary and companion resolved into distinct discs. BU 13 companion appeared to rest just inside the first ring, while STF849 appeared more like other very tight, nearly equal magnitude doubles. At 320x, I could tell STF849 companion (preceding the primary) was a tad dimmer. BU 13 companion was held steady at moments, but drifted in and out. Still, it was distinctly residing at PA 140, and at 263x it was split while 320x was easier.

Now, the exciting thing is, this is with a gibbous moon about 4 degrees away. In fact, the FOV was so bright I could see floaters. (LOL) Star hopping to STF849 was pretty difficult, it took several tries to nail it's tiny speck and position from 69 Ori (using HIP 28978 and 29001 as pointer stars) against a well lit finder background. It was just faintly visible only during moments in the finder. But, I managed to find it with perseverance.

NELM was about 3.5 in the vicinity of Meissa and seeing averaged 7/10 or better.

I have about a week of observing time, if there are others you are curious about, please post. Weather permitting, I will observe them. The moon will be moving away from Orion in the coming nights, so star hopping should get easier.

Anyway, I am going to post this as a separate observation, too.

Thanks, Norme

Edited by Asbytec (01/24/13 02:36 PM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5641909 - 01/25/13 03:32 AM

Norme, thanks - glad to hear that there exists such a thing like a clear sky. So BU13 and STF849 behaved like expected. Next step could be to go to a bit fainter companions like A320 1.1" +10/10.5mag (may be a bogus double as it was observed last time 1963) or A2804 1.1" +9.79/10.46mag.
Then very interesting could be BU1190 1.4" +6.95/9.81mag with a req. ap of 156mm - this one could be already a bit difficult despite a companion brighter than +10mag.
Then with A2634 1.6" +8.7/11.34 you could try another double with a companion fainter than +11mag - this one should be already very difficult - no split would be of no surprise.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5641916 - 01/25/13 03:54 AM

Wilfried, will observe those and some Fred mentioned in my other thread. Will report back when I get a chance to observe them. Weather looks to hold tonight, fortunately. Wish I had some spare good weather to share with you, but it's been in short supply here, too.

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5642126 - 01/25/13 08:51 AM

Wilfried, some thoughts.

First, regarding some of the suggested pairs - A 320, A 2804 - I'm inclined to think they're becoming as much a test of the observer's eyesight as of what the telescope can do, if we're talking about 150mm telescopes. These pairs seem to be a test of Lewis's "faint pairs" visibility. I observed some pairs like this in the 1990s with a 7-inch (18cm) refractor, and thought such doubles were as much a test of sky brightness and observer vision, along with air steadiness, as a test of what the telescope could do.

They're of interest of course, but I suspect results will prove even more varied than with less faint pairs, making an RoT for such pairs uncertain, and if factored in perhaps reducing the accuracy of an RoT for less faint pairs as seen with modest telescopes. I'm thinking aloud here, not attempting anything definitive.

BU 1190 is a different category - obviously difficult, but depending more on nearly 3 mags delta-m at quite close separation (1.6") - because the secondary star is mag 9.8 this is less of a test of eyesight.

I'd be surprised if A 320 is a "bogus double" - as 7 measures are listed in the WDS. Of course, if the detailed list tells us that most of these were attempts without success it could be "bogus", but that seems an unlikely scenario. More likely is that it's a neglected double because it had not changed very much between 1902 and 1963.

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5642220 - 01/25/13 09:48 AM

Wilfried, I have A320, A2804, BU1190, and A2634 on my short list. Weather was clear tonight with a nearly full moon. A quick observation of Psi 2 Ori, a nice, clean split, however showed seeing was going to be a problem.

So, working up the list in order of Ra, I struggled with A2705, an equal magnitude, close pair. It should have been pretty easy, but truth is I could only get a hint of it's companion. And it was not easy, not at all. So, I tried STF 849 again with the same result. I just could not get a good split in those conditions.

Seeing is weird here, I could hold the Airy discs pretty steady for periods of time, but the star images were jumping around quite a lot. I suspect some larger scale seeing issues. And, the moon was not far removed from last night, yet there was no improvement in NELM (still about 3.5.) The sky was still fairly well lit, about the same or worse. Visually, I just could not make out stars near 11th magnitude.

I am sure I can get a better split on A2705, but it will have to wait for steadier seeing. I did not pursue any others, observing Jupiter and the moon just showed me how futile it would be to attempt some difficult observations.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5642987 - 01/25/13 05:06 PM

Norme, sorry to hear that conditions were not good enough to give this a serious try.
Fred, concerning A320 and A2804 you are probyably right - this is why I have a +9mag switch in my model for the influence of the magnitude of the secondary for the required aperture. Even the statistical analysis tends in the same direction as as the least square method for the parameter pr2 in pr1*(m2-pr2) results in a value near 9.
Now I am considering a further component for the influence of m2 fainter +11mag as there seems to begin another level of difficulty here.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5645673 - 01/27/13 09:31 AM

Wilfried,

I was able to observe A2705 and confirmed a clean split at 263x and 320x: a tiny disc and a faint speck of a companion at PA ~250. I could hold the faint companion steady for brief periods. In fact, it looks pretty close to any limit with NELM 3.5 to 4 in good seeing on this night. Since I had trouble with STF 489 on the previous night in rough seeing, I reconfirmed the split made a few nights earlier. STF 489 was indeed split.

I attempted A2804, but failed to split it. The primary was bright enough, barely, but I did not see the companion. On this pair, I found myself using more averted vision. I had some difficulty finding it, it did not show in my finder, but nearby HIP 25066 was, so I hopped over HIP 24997 to get on A 2804. I am sure I was on the right star. Want to try again later this week when the moon moves away.

I could not find BU1190 at the stated coordinates. It is near 59 Ori. I got clouded out and was unable to try A320.

Anyway, seeing was pretty good at 8 or 9/10 and 3.5 < NELM < 4.0. The moon is one day past full, I believe.

Edited by Asbytec (01/28/13 11:34 PM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5646448 - 01/27/13 05:00 PM

Norme, thanks - I have added ADS2705/AG72 to my data set, will have to think about this because the current RoT model shows a req. ap below 100mm but this seems a bit low.
Wilfried
PS: BU1190 is HIP 28187 and should be therefore not so difficult to locate

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5646920 - 01/27/13 08:52 PM

A comment on fainter pairs. I've found that below mag 9.0 the difficulty of seeing pairs increases significantly. So Norme's current failure with A 2804 is not a surprise, especially with so much moonlight added. This is a pair of mags 9.8 and 10.5 (rounded), at 1.1". We're hitting the 10th mag wall here as well as the stars being a challenge to the eye, which has less resolution as things get dimmer. Averted vision will show fainter, but is less good for detail. A 2804 is listed for 161mm. Much the same I'd expect to apply to A 320 (listed 160mm)- same separation (1.1"), slightly dimmer primary (10.0).

My past experience with a 7-inch refractor would suggest these pairs, faint and very close, would be a good challenge for that - a bit larger than Norme's 15cm, and with no CO and higher transmission otherwise, a further small bonus in light grasp. And for dim pairs, avoiding averted vision with its reduced resolution matters for close pairs; wider ones allow a.v. to give benefits.

More thoughts - historical examples - in the next note.

Edited by fred1871 (01/28/13 06:36 AM)

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5647086 - 01/27/13 10:29 PM

Fred, thank you. Double stars can be challenging, and a successful split is rewarding. I want to split them all.

Wilfried, since BU1190 is HIP 28187, maybe I can find it. Thanks.

I agree, something weird seems to be happening around mag 10, companions are getting fainter and we tend to use more averted vision with less resolution, maybe.

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5647109 - 01/27/13 10:41 PM

The large number of rather faint pairs in Wilfried's list for Orion got me wondering what had been possible for some of the 19th century observers, using moderate sizes of telescope similar to many of us currently. So I went back to Lewis's lists from his 1914 paper and, ignoring the overall averages which I think are generally unhelpful, looked instead at averages for individual observers with specific telescopes.

One who struck me as of particular interest was Ercole Dembowski (1812-1881), where Lewis gives averages for Dembowski's use of his 7.4-inch (~19 cm) Merz refractor. Dembowski had a particular interest in a revision of Struve's Dorpat Catalogue, and was regarded in his time as an exceptional observer for accuracy. After his death his observations, from various sources, were collected and published, the editing being done by Otto Struve and GV Schiaparelli.

To the point - the average for nearly equal faint pairs of Dembowski, 7.4-inch scope, was mags 9.3 and 9.5 at 0.7". Remarkable with a Dawes' Limit of 0.62". This is a stand-out result when compared to the other observers Lewis lists with telescopes under 25cm. SW Burnham with his 6-inch has 0.9" for mag averages of 8.6 and 9.8 (though somewhat less equal pairs, increasing the difficulty). Burnham with 9.4-inches (~24cm) has 0.6" at mags 8.3 and 8.8 averages. W Struve and Secchi, similar apertures (9.6-inch), manage 0.5" with stars 8.4 and 8.7 (Struve) and 8.4 and 8.9 (Secchi).

For 9th magnitude pairs (average 9.6 and 10.0) at 0.9" we have to go to Hough with the Chicago 18.5-inch (47cm) Clark refractor. Yes, it might be under-achievement with that size of telescope - because Schiaparelli with 19.2-inches (48.8cm) manages 0.4" at mags 9.2 and 9.5. The Dawes Limit for 19.2-inches is 0.23".

For now, not much point looking at what various observers did with 28-inch and 36-inch telescopes. Scary close with faint stuff.

One could of course scale these results for different apertures to get a rough idea of what might be possible - or follow Treanor's example, graph the results - but this time for faint pairs, instead of unequal pairs. Both approaches could be informative.

Potential problems? most likely the photometry of the pairs. To eliminate that would require re-doing Lewis - find the original publications, identify the closest faint pairs, then get modern photometry (Tycho, etc) for these. In the case of doubles that appear not to have changed much, or binaries with high-graded orbits, identification would provide a check on separation measures as well.

The above is a "thinking aloud" exercise. I feel the old observations (yes, all done with refractors) might throw some more light on the faint pairs issue after further analysis. So the above notes are offered for others to also consider in relation to the (multiple) vexed issues of the limits of resolving doubles of various types.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5647372 - 01/28/13 03:00 AM

Quote:

Norme, very well done in splitting ADS 2705 - at only 1.0" and listed magnitudes 9.24 and 9.95 this is a tribute to your eyesight and observing skills...

Ups - what are we talking about? May be we should indicate the WDS# for clarification: For ADS 2705 I found WDS03428+3016 AG72,ADS2705 6.4" +10.52/10.78mag.
Obviously you and Norme mean A2705 with WDS05307+1154 and for this one I get with CO 0,28 a req. ap of 153mm.
Fred thanks for the necessary hints to make this evident.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5647444 - 01/28/13 06:06 AM

Yes, an easy mistake (and careless on my part too) - confusing A (Aitken's own discoveries) with ADS (his obsolete general catalog of doubles, with discoveries by all and sundry). Different numbering. The 'A' doubles are still listed in WDS. ADS numbers need a translation. It's almost like John Herschel's GC of deep sky objects (nearly all discovered by John and William Herschel) being confused with Dreyer's NGC. The earlier numbering is no longer used, that avoids confusion.

So I'd agree, we should do best to use WDS designations - my long-time preference anyway - that gives us the RA and Dec and the Discoverer designation - the standard way of referring to doubles. And it should avoid confusions.

I'll now look at the lists again and see if I need to revise any comments. I've been trying to stay with "A" not "ADS" designations.

Added comment - I've now revised my previous post to delete discussion of a pair I mis-identified.

Suggestions I made there, regarding scaling of telescopes relative to each other with different sizes, I'll repeat at another time when I've worked through some new examples.

Edited by fred1871 (01/28/13 06:40 AM)

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5647503 - 01/28/13 07:27 AM

My apologies, yes, A2705. Careless on my part and corrected, as well.

Fred, I am curious why I was able to get down to a 9.9 mag companion (a distinct tiny speck fluctuating in and out, but not difficult) where some of the great observers topped out at lesser magnitudes at similar separations. I did have exceptional seeing and some moon light.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5647579 - 01/28/13 08:31 AM

Quote:

... curious why I was able to get down to a 9.9 mag companion ...

Norme - this does not seem so difficult. My own so far best result in this area was J781 in Cyg. Jonckheere advertised this double with 3" +9.4/9.4mag but the latest WDS entry is 3" +11.4/11.5mag. While I do not fully buy the WDS data (nearby +10.81mag TYC2669-00673-1 seemed a bit brighter than J781) this was a positive resolution with a 140mm refractor even if already with averted vision.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5649004 - 01/28/13 07:14 PM

Quote: some of the great observers topped out at lesser magnitudes at similar separations

I think the data used by Lewis , which gives averages for the individual observers, is biased by selection. First, it deals with pre-1914 work. So later observers, like Jonckheere, who increasingly worked on finding faint doubles, as the brighter ones were largely discovered already (so they thought), are not included.

In the earlier era there was far more interest in the bright to middling pairs. These appeared to provide plenty of examples, were more accessible to moderate telescopes, and easier to measure than faint pairs. Also, if you assumed that on average faint means further away, then fainter pairs (on average) were less likely to show orbital motion. So were less interesting.

Some early observers did list a lot of dimmer fairly wide pairs, John Herschel in particular. But the Struves, Burnham etc were plenty busy enough without checking through 10th magnitude and fainter stars for new pairs. Aitken did add a lot of fainter pairs, especially when he took to using Lick Observatory's 36-inch refractor, rather than the 12-inch he'd used for some surveys.

The Southern Hemisphere observers added a lot of fainter pairs after the large refractors (26-28-inch) became available in South Africa. But that was in the later 1920s, continuing into the 1950s. Earlier work in the south had been mostly with more modest equipment - Russell's Sydney Observatory group (11.4 and 7.25-inch refractors) 1870s-90s, Innes (mostly a 9-inch refractor) early 20th century. There was a brief period when TJJ See took the Lowell 24-inch refractor to Mexico, which resulted in some more southern discoveries, but See didn't spend long enough in Mexico to add huge numbers of new pairs. Many of his southern doubles are faint companions to fairly bright stars (from Lewis - m8.0 and 11.5 at 0.9"; mag 7.4 and 12.6 at 1.4", as averages).

The emphasis on (dim) red dwarf binaries is post-Lewis, likewise most of the work of Jonckheere, plus the Nice (France) surveys by Couteau et al which found bright new pairs as well as a lot of faint ones, especially with the 30-inch refractor.

But if you look at Lewis's averages for observers with the Lick 36-inch you'll find dim stars; and that's true to some extent with the 18-inch and larger scopes as well. One example - Hough with the Chicago 18.5-inch is listed for uneven pairs (averages), mags 7.1 and 11.5 at 1.1", and for the very unequal, 6.6 and 12.2 at 1.9".

Typically, even with the biggest telescopes, there was simply less interest in finding faint companions to faint primaries. Lewis (28-inch), Burnham and Aitken (36-inch), do have dim very close pairs to their credit. These are around mag 9.0 to 9.5, at 0.2"-0.25". Hough with the 18.5-inch did average mags 9.6 and 10.0 at 0.9", but that's still within the magnitude 10 limit and it's about as faint as anyone went in that period with less aperture than Lewis on the Greenwich 28-inch. "Close" rather than "how faint" was the watchword for the bigger scopes; with allowance for dim companions to brighter stars - Aitken is listed, for very uneven pairs, 36-inch again, as mags 7.5 and 13.7 (!!) at 2.5"; Burnham, same scope, 5.7 and 12.3 at 0.9" (!!!). Don't try this at home.

Edited by fred1871 (01/29/13 04:35 AM)

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5649687 - 01/29/13 04:12 AM

Fred, you impress me with your insightful in-depth knowledge of double stars and their history.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5649786 - 01/29/13 07:20 AM

Thanks, Norme. Twenty years ago I started taking a more serious interest in doubles, so I've had a good amount of time to learn what I can from the experts, and to do a lot of practical observing. Because I have some background in history studies that was a natural extension.

It's good that we have forums like this to discuss astro matters. It allows a range of people with different areas of knowledge to contribute. Each of us can bring something useful to the group discussions, and we all benefit. I offer what I can.

Having said that, I'll say I'm finding the RoT issue more complex than I'd previously thought, and I didn't expect it to be simple.

I'll now have to get my SCT sorted out so I can do some experimenting with CO effects again. And, unlike much of my past SCT observing, push the limits. Except for faint pairs the C9.25 (235mm) didn't really do better than the 140mm refractor. Wilfried has likewise commented he prefers, for doubles, his 140mm refractor to his C9.25. So the next step is trying tougher doubles to see what the particular limits are for the SCT.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]

Going forward step by step I have some days ago included the effect of CO in my current RoT model using the observations published in the mentioned paper of Lord with 6" and 10" reflector. While I think the CO implementation is quite OK (modifying Dawes criterion as base and including CO in the delta-m component) there are other issues open, especially influence of light pollution (NEML component works linear over all aperture sizes and this is certainly wrong) and influence of secondary magnitude fainter +11 is not very well handled. And I am also not sure how to handle the not this good quality of the advertised data of the included observations mentioned above. I will adapt the magnitudes to the current WDS data and let the separations as they are but would be happy to have better data available. Some observations have to be excluded as they are appearently wrong in all aspects. And I am not sure how to handle the heavily overperforming observations. The model states the modified Dawes criterion as lower limit as I do not see any sense in a RoT requiring less aperture than Dawes - should be enough for a 50% chance. But if I include observations with effective aperture below Dawes then I get a bias in the results of the statistical analysis or at least a significant higher average error.
Since it will take some time to get a handle on all these questions I upload the current state of the ROT model (filled with Orion doubles as a starter for CO 0.28 and NEML of 4.5) to give the opportunity to check the CO-implementation against own observations.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5649833 - 01/29/13 08:18 AM

Yea, when you start getting down to a modified Dawes, you really need a "perfect" aperture. Those do not exist. I think a reasonably good Strehl can get close, though, when induced aberrations are controlled.

For example, modified Dawes in my scope is right at 0.71" arc. Best I have done so far is 0.74" arc (as reported), right in the middle of theoretical and modified Dawes. STT 517 was too tight at 0.67" arc (but I will look again tonight.)

But, for an inherently aberrant aperture (Strehl of 0.94) to match or even exceed calculated Dawes means it's important. Most scopes (including SCTs, and especially refractors) seem to be optically this good or better these days. Well, IMO...

As for overachieving, I hate to fail. I will observe something until I am reasonably sure I saw it, even if that takes a hour. But, I've toned it back for the sake of getting a confirmed and readily visible disc. For example, even though I know where 42 Ori companion is, it was not easy nor clean. Success, maybe, but probably not good useful data. And, yes, you simply must screen the outlying observations, the most errant data points. That's smart data collection.

Edited by Asbytec (01/29/13 08:30 AM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]

It cleared late tonight, so I revisited BU1190. I gotta say this was not a clean and distinct split allowing the companion to be readily seen. So, no, it was a fail. However, on a personal note, I did manage the companion enough times to pick it out at PA 330. But, that took a long hard observation. So, while it was an enjoyable challenge, it was not one that shows a clear disc often enough to call it a good split.

I also revisited STT 517 AB in what I hoped was good seeing. It was not, about 6/10. So nothing new to report there: elongation with a pinch. But, I do have to ask a question. Even though this one is very tight, why is it I very occasionally get a hint of dark space? I would not call it a split based on the elongated and pinched appearance predominating, however there are those curious times when it does look separated. Can moderate seeing cause this effect?

I did try BU1048, but failed to split it even in over performing mode. BU1048 is one of those doubles seemingly easy enough with 2" sec sep, but I could not split it. The rolling first ring gave tantalizing hints that attracted my attention, but no faint speck ever materialized.

I did not attempt many of the much fainter doubles on the Orion list. With the weather, seeing, and a few other reasons, I went with some of the brighter 8th and 9th mag pairs. The ones I thought might have the best chance of success.

Seeing was 6/10 as Orion hoovered over a nearby apartment complex. BU 1190 was higher in the sky and seeing was a little better at around 7/10 with a brief period of very calm skies after a patch of cloudiness passed. NELM was right at 4, maybe slightly better.

Wilfried, I have one more night before I put my scope in storage for my vacation to the US. If you have a couple of doubles near the zenith, maybe in Gemini, you'd like some reports on, please post them. I will try to get them for you.

Attached is my Orion list. Green highlight means a distinct companion was readily seen or a dark space separated the pair. Red means I failed to achieve a clean, distinct split. The blue ones were on my "to do" list.

At a glance, what I thought was interesting was I managed a couple tight ones above the 150 Ra limit, but failed a couple of wider pairs at or just below that limit. It's a small sample, for sure, but interesting none the less.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]

Norme, thanks for your support. I am grateful for your additions to my data set of limit observations.
I have uploaded a list of doubles in Gemini of interest for any double star observer with a small telescope based on an intermediate state of my current RoT model for CO = 0.28 and NEML = 4.5 sorted by required aperture for a 50% split probability. I have marked the for you probably most interesting range from 140-160mm required aperture in yellow. Any observation report out of these range would be of interest to me.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5651351 - 01/29/13 11:12 PM

I will try some of them tonight and report back, Wilfried. I am happy to have gotten involved with your fascinating project. Thank you for both the personal learning experience and the opportunity to participate. If I had the time, I would spend the rest of our observing season working on it.

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5651684 - 01/30/13 06:59 AM

6/10 seeing Norme? Why you just had good seeing for Connectivut in winter!

Pete

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Re: Putting the "Rule of Thumb" to test [Re: azure1961p]
#5651690 - 01/30/13 07:02 AM

Yea, Pete, it's not been stellar like the past tropical dry seasons and earlier this season. Something screwy with the weather, well last month or so since Christmas.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5651696 - 01/30/13 07:10 AM

Quote:

... BU 1190 was higher in the sky and seeing was a little better at around 7/10 with a brief period of very calm skies after a patch of cloudiness passed. NELM was right at 4, maybe slightly better...

Norme, I think we may consider BU1190 and STT517 as positive limit observations. Congratulation on STT517 - even the modified Dawes limit for your scope would require 159mm aperture.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5652007 - 01/30/13 10:40 AM

Wilfried, sure, that sounds correct. One observation I mentioned above really seemed like a limit. STT 517 was very, very tight. Touching, elongated, and slightly notched and certainly not enough dark space to call it comfortably split.

Okay, got a few tonight in Gemini. I began sampling ADS2525 and HEI 121. Both are dim stars in a sparse star field, star hopping took a lot of time. My neighbor's security lighting was reaping havoc with my view through the finder and my dark adaption (worse than the moon earlier this week...LOL.) I spent a good amount of time trying to find them, but was just not able.

BU 100: Try as I might, I failed to split this double. I even cheated and looked up the Rho and Theta for the companion and still failed. I could, however, see a dim star about 6" arc south of BU 100. I have not looked up that star's magnitude just yet, but I am curious about it. I did spend a lot of time with this first double of the evening, because at mag 11 I really needed to be fully dark adapted to have a chance. Still, no success. At 3.2" sep, it sits very near my 4th diffraction ring (~3.6" arc.)

STT 145: Split. Companion easily seen near PA 340 just outside the first ring at 263x (UO 12mm HD Ortho, 1.6x Barlow.)

A2450: Split. Faint companion easily seen at ~3" arc sep near PA 120 to 130 (south east, anyway.) However, it's PA is listed at 053. I suspect this is incorrect, but I just don't know. If it's correct, then I failed to split it and simply observed another star near PA 130. But, my gut tells me the listing is incorrect. That pair just looked and felt like a double. Stellarium, ironically, shows the companion more south of PA 90, too.

STT 171. Split - maybe. Okay, now we're getting into easier splits with Ra near 140, right? Wrong. This was a very difficult split. In fact, I had to cheat - look up the PA to find it. Afterward, however, I was able to observe the companion. But, it was not easy, not obvious, nor clearly a double star, it was truly difficult just to see the faint companion even fleetingly. So, I guess, NOT SPLIT. (LOL) Wow...very difficult.

Tonight, seeing varied from 6 to 7/10 with NELM of 4.4.

Wilfried, I wish I had gotten more. I just spent too much time early in the evening trying to find the dimmer stars and ran out of time later in the night.

I hope to keep tabs on your progress while I am traveling and wish you the best of luck.

EDIT: Wilfried, just ran across this. Sounds interesting.

http://fisherka.csolutionshosting.net/astronote/astromath/ueb/Unequalbinaries...

Edited by Asbytec (01/30/13 10:46 AM)

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5652879 - 01/30/13 05:57 PM

Norme, thanks for your reports, quite interesting. Thanks also for the link - thats a very interesting website for double star aficionados I knew already. It gave me a lot of ideas for the RoT quest. The tables are a bit hard to read, but the formulas and algorithms are excellent.
Wilfried
PS: Have a nice trip

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State of the affairs [Re: WRAK]

Heading for a short vacation (out from the winter into the spring) it is may be a good time to try an evaluation of the current quality of the RoT model even if certain weaknesses are already known and the existing data set of about 100 observations is far too small (I think I need at least more than 300 observations). I decided to compare it with the best of the other RoT models I know so far - and I think this is Lord's approach. Due to my respect for Lord's work I gave his algorithm the benefit of minimizing errors by choosing the best possible value of the parameter n with value 4-12 depending on aperture class, obstruction size and seeing quality regardless of the actual data. As you can see in the chart Lord's algorithm works extremely well with a broad range of observations but freaks out rather extreme with others - especially with close but faint doubles.
My current RoT model gives slightly larger errors in a broad range but does not freak out - certainly because it works with it's own data set and this is kind of compensation. The weakness of the RoT model is certainly the range with very faint secondaries. There is also some bias to recognise concerning the used data of the Lewis collection - Lord's alorithm does rather well with these observations and my RoT model rather not this good although I have adjusted the advertised magnitudes to the current state of knowledge.

Statistical evaluation: Standard deviation for Lord's algorithm is 25.4mm (error in relation to the used aperture) and correlation between actual aperture and predicted aperture is 0.947. Standard deviation for the current RoT model is 14.7mm and correlation is 0.963 - means in total slightly better values for the current RoT model.
After a creative break I will continue and attack the faint secondaries.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5657536 - 02/02/13 02:59 AM

Wilfried - what software are you using to generate the observing lists by constellation?

The various software packages I have do not always include standard (WDS) identifiers for doubles, even when they claim to, but give me single identifiers for SAO, or WDS, or HD, or just about anything. I don't want to waste time going through multiple identifying catalogs to get to the WDS standard designations (which means accepted discoverer, as well as position). I want a program that can give me the standard designation for each double, even if like your lists I get multiple extra identifiers as well - that's not a problem, and might at times help.

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Re: State of the affairs [Re: fred1871]
#5657567 - 02/02/13 03:55 AM

Fred, I use AstroPlanner. It allows you to directly select doubles with selected properties from the WDS catalogue or else if you have any identifier for a double you can lookup synonyms and select the appropriate WDS designation for it.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5657595 - 02/02/13 05:29 AM

Second thoughts regarding the error chart shown above: The RoT model shows a tendency to request slightly smaller apertures than used for the observations - as most of the observations are done with fixed apertures it seems reasonable that the same observations could have been done also with a slightly smaller aperture. So these "errors" do not seem this bad.
Concerning the cases with required apertures greater than used for the actual observation - these are quite often observations with apertures quite below the Dawes criterion and I do not allow the model to go below the (for reflectors modified) Dawes criterion. So this is a must have deviation and is not to be sonsidered as "error".
Wilfried

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Re: State of the affairs [Re: WRAK]
#5659166 - 02/03/13 12:04 AM

Wilfried, thanks for the information about AstroPlanner. The trial version is so limited, now I've looked at it, that I didn't get a sense of how much it could do.

Some observations. You mentioned STF 450 in Taurus being more difficult than you'd expected. I had a look at it a couple of nights ago and found it very easy. Despite modest altitude(~26 degrees) and seeing not great in that direction, I could see the companion at 80x, and it was obvious at 114x (140mm refractor).

I've been working through more Orion doubles and some of these won't be "at the limit" examples. But two I've looked at in recent nights don't appear to be on your Orion list - or I've overlooked them there.

One is BU 15 (0547.8, -0218), mags 7.4 and 11.6 at 2.0". The separation appears to be the same in 1987 (last measure) as it was when Burnham discovered it in 1872 with 6-inch refractor. This one took a bit of magnifying to see the companion, but 285x showed the lesser star as a tiny speck separated but close to the primary. Seeing was very good at that time.

The other one I didn't find on your list was STT 119 in Orion. Again, it's a pair which seems to be at the same separation recently (2009) as it was when discovered (1843). Magnitudes in WDS are 8.08 and 8.93 - separation only 0.6"! 140mm refractor again, this one took a lot of magnifying, being "not single" at 285x, and at 400x a definite pair, a bit uneven, notched but not resolved into separate points. Seeing very good - I looked at this one straight after BU 15. Very pleasing result given the stars' modest magnitudes; and NELM was at least 5.5.

I'll add some more observations as I work through the details of them and cross-match my observing list with your Orion list. My main problem at the moment is late sunsets plus daylight saving (Summer), so it doesn't get properly dark until 9:30pm, and I sometimes get clouds rolling in well before midnight. The weather pattern this Summer has been very unusual and not great for astronomy.

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Re: State of the affairs [Re: fred1871]
#5659293 - 02/03/13 02:12 AM

Fred, yes - STF450 should be easy in a 140mm refractor. But I had somehow the impression that the companion is fainter than advertised compared with +10mag stars in the same field of view.
Congratulation to BU15 and STT119 - both doubles seem to be very limit observations with a 140mm refractor. Both are not on my list for reasons I don't know - maybe the selection feature of AstroPlanner is not this perfect.
No experience with the trial version - you need access to the full database of catalogues including WDS, so the trial version does not show full performance concerning double stars.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5661202 - 02/04/13 06:57 AM

A couple more observations. Norme managed a "sort of" split with BU 1190 in Orion (0557.4, +0002)- I've now had a look at it in fairly good conditions, and the close companion was visible at 285x and 333x (7mm and 6mm orthoscopics with 2.5x Powermate). Like Norme, I found it not a clean easy split, but it was a definite one with my 140mm refractor. [mags 6.95, 9.8 at 1.4"]. With averted vision I caught glimpses of the mag 12.1 companion at 6.7" (same magnifications). No moon at the time. A tough combination for 140-150mm.

BU 13 (0534.5, -0429) I also caught up with - mags 7.2 and 9.2 at 1.0", so I thought it'd be not too tough - it was harder than I expected, and took 400x (140mm refractor) to give a clear separation in the steadiest moments. That appeared to be a seeing effect, and my impression was that less power would show it in steadier conditions.

The continuing issue with this project of observing marginal pairs for the telescopes used, is getting "good enough" atmospheric conditions to make it possible. As so often remarked, a pair that's invisible as such one night is clear and obvious on another - SW Burnham went further, and remarked on the difference occuring even with nights that appeared to be equally good. Hence, I suppose, Wilfried, your "50% probability" model.

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Re: State of the affairs [Re: fred1871]
#5661868 - 02/04/13 02:09 PM

Fred, it seems that you have excellent conditions now.
With the STT119 observation you have reached a sensational 0.73 Dawes ratio if the advertised data is correct. Regrettable STT119 is a bit too faint to try to measure the separation with a self made interferometer consisting of several simple aperture masks with two 10mm holes in different distances (minimum contrast of the interference lines at 95mm distance would mean 0.60" separation and a minimum at 85mm distance between the holes would give 0.67" separation with an average error of only 0.05" - but due to the small holes it works only with equal doubles brighter +6mag). I have to admit that I never tried such measures myself but it sounds this interesting that I will do this cerainly on occasion.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5662819 - 02/05/13 01:28 AM

Wilfried, some nights I have (nearly) excellent conditions for part of the night and in some parts of the sky. STT 119 is not unique among close pairs I've seen as double, whether split (separated) or elongated. A few brighter ones have been even closer - in the 0.5"-0.55" range - only elongated of course.

At 0.5", I'd be getting near-enough to 0.5 of the Rayleigh Criterion. And that would fit with what Couteau gives as the limit for detecting elongation with the Nice 20-inch (50cm) refractor. As 14cm will be less atmosphere-limited than 50cm, I think that's a reasonable target to aim for, under the best conditions.

Taylor (in the Argyle book) detects elongation down to around 0.5 of Dawes, 0.4 of Rayleigh. That's remarkable, but a few other observers are on record for similar feats - the oft-mentioned SW Burnham for one. I think I'm doing quite well as an observer but I've definitely not reached those remarkable levels of discerning close pairs.

One example among the closer pairs I've seen - Zeta Bootis, a binary at present getting closer year by year. I observed it in May 2009 and May 2010 with the 140mm refractor - both times with 400x. In 2009 it was elongated with a hint of notching. In 2010 it was a "rod" without a hint of a notch. I plan to get back to it this year to see if I can get any suggestion of elongation. Separations, based on the grade 2 orbit (~124 years) are just under 0.6" in 2009, 0.55" in 2010, and will be 0.47" by May this year. So, this year if I detect anything "out of round" I'll set a new personal record. Delta-m for Zeta Boo is only 0.1 magnitude.

The interferometer idea sounds interesting, but as you say the stars need to be pretty similar in brightness, and with only 140mm I'd think STT 119 a bit faint, well below mag 6. For measuring, especially for close pairs, I'd think the CCD technique described by Rainer Anton in the 2nd edition of the Argyle book might be more useful.

Edited by fred1871 (02/07/13 05:28 PM)

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Re: State of the affairs [Re: fred1871]
#5667148 - 02/07/13 01:59 PM

I think I found a solution for my dilemma regarding Dawes criterion and overperforming observations - currently I do not allow the RoT model to result in values below Dawes because I think this is hard enough for a 50% split chance. On the other hand I need at least some overperforming observations as counterbalance to the certainly existing underperforming observations in my data set - but this results in some bias as the statistical analysis has to struggle to minimize errors it cannot avoid.
So I think I will allow the RoT model to result in values below Dawes but in an additional cut off step I will set all sub Dawes values to Dawes criterion (modified for CO if necessary). This will may be result in a greater standard deviation but the quality of the model should be improved this way.
And I will apply a similar approach to the other end of the observations with very faint magnitudes of the secondary - here I will first made a more or less "educated" guess for an additional component of the model but also make a cut off for all results above the required aperture according to the TML (corrected by NEML) required by the magnitude of the secondary.
Wilfried
PS: The CCD would make it necessary to split the double I think. Curiously this is not necessary for the interferometer at all

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Re: State of the affairs [Re: WRAK]
#5667599 - 02/07/13 06:14 PM

Wilfried, I think allowing for "overperforming" (detecting doubles closer than Dawes) is necessary to allow for - these are mostly fairly bright pairs where a split is not possible, but a notched or elongated - rod or olive - image is visible.

That's different from what is seen with significantly uneven pairs. Pairs with moderate delta-m can show, be detected, as elongated in some cases. But those with a larger delta-m are more difficult to see in this form; usually the primary so overwhelms the dim companion that it's not detectable, unless separated, rather than overlapping or an extension of the primary.

That's part of what makes an RoT hard to establish. There's a gradual change in what can be seen. If delta-m is large, we depend on the fainter star being in a diffraction gap; if it sits on a diffraction ring it immediately becomes much more difficult, how much more depends on the ring brightness and the star brightness.

And it gets messy. A CO changes the relative brightness of rings according to the CO size (% of diameter of main optics). Looking at some of Suiter's illustrations, I notice on p.165 (2nd edition of Star Testing) a set of pictures showing "in-focus diffraction patterns resulting from central obstruction".

Unobstructed, first ring moderately bright, 2nd ring less, 3rd ring less than second.
25% CO - first ring bright, 2nd ring very faint, 3rd ring middling bright.
50% CO - first ring very bright, 2nd ring bright, 3rd ring faded to near invisible, 4th ring increased though very faint.

A very interesting pattern of change, according to CO obstruction ratio!

Low-order spherical aberration is often treated as having much the same effect as CO. However the pictures on p.191, showing the effect on the diffraction pattern of various levels of SA, with obstructed and unobstructed apertures, is different from the pure CO effect.

With an unobstructed aperture, increasing SA firstly reinforces the brightness of the first ring, then the second as well. With an obstructed aperture (33%), the first ring gets brighter, but already with no SA there is some reinforcement of the 3rd ring, visible at 1/8 wave SA as well. By 1/4-wave SA the 2nd ring is broader and somewhat brighter than the third (itself reinforced), and with even more SA the pattern of brightness, 1st brightest, 2nd is 2nd brightest, 3rd is 3rd brightest shows.

What I find interesting here - first, with no CO the diffraction ring brightness pattern of increasing SA is different from adding CO without SA.

Second, 33% CO, as with 25% CO, reinforces the third ring brightness rather than the second, with little or no SA; but with increased SA, the pattern is similar to, though worse than, the unobstructed pattern for increasing SA.

A lot of SCT and Mak-Cass scopes have CO in the 25-35% range. Those that have very little low-order SA may show this effect of faded second diffraction ring and reinforced third diffraction ring. Of course, atmosphere makes such a difference that in the real world this effect is likely lost as a visible effect, merely becoming one of multiple factors mixed together to determine what one sees.

My conclusion is the obvious one - the less SA the better, and smaller CO ratios are better than large ones. Nothing new there.

How much effect there is on uneven doubles observed in Mak-Casses, where low-order and high-order SA need to be balanced, but some aberration remains, I don't know.

Very faint pairs? - I'm increasingly feeling these are an eyesight test to a much greater degree than uneven pairs of middling brightness. I've got my C9.25 going again and the extra light (a whole magnitude!) over the 14cm refractor is very nice, despite less perfect optics and more sensitivity to atmospheric wobbles. Perhaps I'll try some of your faint Gemini pairs with that. They're certainly beyond my eyes with 140mm - super-vision people like SJ O'Meara might manage them.

Regarding CCD imaging - yes, some kind of split is necessary for measuring. Agreed, an interferometer works differently. You've reminded me to look up information on Finsen's eyepiece interferometer, which allowed him to measure pairs too close for normal micrometers, down to around 0.1" or better with the Innes 26.5-inch (67cm) refractor in South Africa (1940s-1950s). I'll find the reference and give it in this thread - I'm fairly sure it's in one of the journals online through ADSABS.

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Re: State of the affairs [Re: fred1871]
#5668175 - 02/08/13 12:20 AM

I've now found the reference for WS Finsen's own article about his eyepiece interferometer.
Monthly Notices of the Royal Astronomical Society, 1951, v 111, p 387 ff.

Bob Argyle, in the 2nd edition of his Double Star book for the Webb Society (1986), remarks :
"with this instrument more than 13,000 examinations of 8,117 stars ...were made. As a result 73 new pairs were found, 11 of which have periods ranging from 21 years down to 2.65 years. In addition, 6,000 measures of pairs too close for the [filar] micrometer were made".
These results appeared in various papers over time.

The interesting thing is the micrometer itself. Whether something similar could be made for amateur use on mid-size scopes? I'll leave that for the instrument designers and engineers to work out.

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Re: State of the affairs [Re: fred1871]
#5668910 - 02/08/13 12:28 PM

Quote:

...The interesting thing is the micrometer itself. Whether something similar could be made for amateur use on mid-size scopes? I'll leave that for the instrument designers and engineers to work out.

Look at this: http://www.observatory.org/bfm.htm - may be a bit expensive but seems of high quality.
Concerning eyepiece interferometer: Do you know any commercial products?
Wilfried

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Re: State of the affairs [Re: WRAK]
#5669681 - 02/08/13 07:57 PM

Interesting filar micrometer, sounds good, price is up where I'd expect as a minimum if it's well made. Should be suitable for long focal length instruments. A 25mm eyepiece suggests very long focal length systems to get decent magnification; I'd hope the thing would still work with shorter eyepieces, or only wide pairs would be measurable (at 4m fl the magnification is only 160x). Personally, I'm more tempted by CCD imaging, maybe with a video style camera for "lucky imaging" in the same way the planetary imagers do it.

Finsen's eyepiece interferometer? - there are photos of the device with the article. Likely made as a 'one-off' by the instrument shop at the observatory. I've never seen an advertisement for this kind of micrometer. Several other types, yes, in the past, but not this type.

An alternative for very close pairs, not too uneven, is speckle interferometry - and the article in Argyle's current book suggests ways for the amateur observer to do it. The potential accuracy is very good. However people like myself, who like simpler techniques, will probably follow Rainer Anton et al into "lucky imaging". That could be next year's project - this year I'm staying visual.

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Re: State of the affairs [Re: WRAK]
#5669916 - 02/08/13 10:42 PM

Wilfried, I'm still wondering about some doubles that you didn't get on your list with AstroPlanner when you used it to filter the WDS for a list. Have you been able to find why those pairs (I think around 2-3 February the comments on these) did not show on your list?

My reason for asking is that I'm looking for software that can produce lists, by constellation, with data from the WDS - and all the software packages I've tried so far have either edited out too many doubles - perhaps they use default criteria that are wrong - or want to give me lists with unhelpful names for stars (HD, SAO, HIP, etc) instead of staying with the WDS names, which refer to discoverers.

AstroPlanner looked likely to be what I was seeking, until I found it had left out doubles that should have been on your list. So I'm now wondering if there are limitations to it that mean it won't give me what I want - the ability to filter by magnitude, NOT separation, and use the WDS, and have selection by constellation.

Your lists show it can do what I'm looking for EXCEPT that some doubles were somehow missed, when they should have been listed.

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Re: State of the affairs [Re: fred1871]
#5670127 - 02/09/13 04:13 AM

Fred, I found these "missing" doubles via AstroPlanner without problems with a new search with the accordingly parameters. I do not remember how I exactly did this search for the Orion list so may be it was my combination of parameters leading to this result but I have no real explanation - but I think AstroPlanner is an excellent tool for double star session planning.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5671205 - 02/09/13 06:51 PM

Thanks, Wilfried - sounds as if AstroPlanner will match up with what I'm looking for. There's a lot of useful software around, but the problem is finding the examples that do what the individual observer wants.

I'll have some more observing data soon. I'm analysing some recent, and some not so recent, observations, including some with the 9.25" SCT - a good'un for testing CO effects (~36% by diameter!) and for fainter but not very uneven pairs - it makes the faint ones much easier to see merely through extra light, before any other factors are considered.

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Re: State of the affairs [Re: fred1871]
#5671253 - 02/09/13 07:20 PM

Hello guys, interesting conversation. I especially appreciate Fred's input on SA and CO. The complexity of which speaks to the difficulty and seems to be a necessary aspect of such a project.

I was really enjoying observing stars associated with this project while testing both my own limits and those of my scope.

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Re: State of the affairs [Re: Asbytec]
#5672635 - 02/10/13 04:21 PM

The effects of spherical aberration for double star resolution seems to me to be a complex topic - anyway as most observers will not know any specific SA value for their scope it cannot be used in a RoT model with benefit, so I tend to see SA as random factor in this regard.
Other factors with some relevance could be the existence of spiders producing spikes at least for brighter primaries and therefore changing the diffraction pattern and also the focal ratio especially of Newtons as "fast" reflectors seem to be of no good use for double star resolution due to coma. But for now I tend to shelve such considerations for possible future extension as I am struggling to come to a decent enough RoT model with the factors in evaluation so far.

Fred - looking forward to your C925 observation reports with great interest.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5672935 - 02/10/13 07:40 PM

Wilfried, yes, using SA explicitly would seem too complex and unhelpful. I found assuming Strehl to be interesting for calculations involving MTF. With Strehl, peak intensity is either explicit for unobstructed apertures or implicit for obstructed samples. Strehl and obstruction both determine light distribution, of course. Light distribution seems to be part of the problem. So, while specific measures of SA are both difficult to know and use, assuming a Strehl might offer some utility.

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Re: State of the affairs [Re: Asbytec]
#5674305 - 02/11/13 03:59 PM

Norme, I fear Strehl is in the same leage with SA - an amateur observer knows rarely the Stehl value of his scope I think and it is usually certainly not part of an observation report at least as far as I know. My data set of limit observations would shrink to zero if I would require Strehl as known factor including most of my own observations - I know the Strehl value of two of my scopes but not of my preferred 140mm refractor used with the iris diaphragm.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5675159 - 02/12/13 01:49 AM

Wilfried, I can only agree that the short Newtonian is generally found to be problematic for doubles - there is the occasional one of exemplary optical quality and with a Paracorr and thermally stable and with a (relatively) small CO, plus very accurate collimation, that might well be good for double stars. But I suspect that it's a minority of short Newtonians that fit the whole description. Pete's experience in going from a 10-inch f/5 to an 8-inch f/9, and the big improvement for doubles, is a useful cautionary tale.

Spherical aberration is a common issue with all kinds of telescopes. In small amounts it need not be a big problem. Indeed, WR Dawes in 1867, in the introduction to his doubles catalog where he also announced what is now known as the Dawes Limit, remarked on SA in some detail: in particular, that a larger refractor with obvious SA outperformed a smaller one without noticeable SA - but the effect of SA was to produce a large amount of "false and scattered light" around brighter stars. Nevertheless, this affected "how a telescope shows a difficult object, than whether it can show it at all" [obviously for double stars, not detail on Jupiter]. His conclusion, that test objects are of "comparatively small importance in the trial of a telescope" because "so much must depend on the eye and habit of the observer, and the circumstances under which the scrutiny is performed", sounds curiously modern.
But it does suggest that for high contrast objects (doubles) SA is less of a problem than for low contrast objects. Dawes is more optimistic than I am about scattered light and its effect on faint companions.

More thoughts on SA, including its interaction with CO etc shortly. Meanwhile, thanks Wilfried for the AstroPlanner recommendation. I find it does quite well what I'm looking for, and without needing to do acrobatics to get standard double star designations, such as chasing through multiple tables of equivalence, or manually re-labeling most things, or trying to re-program a program when it doesn't do what it says it does. Some software writers don't appear to know enough about astronomy. And their "preferences" (if one can call it that) then get used by lots of other folk, leading to further confusions and extra work and identification muddles. The Haas project struck this, with a need to translate the original lists into equivalences for some observers for non-standard (in doubles terms) designations such as SAO, a catalog that's effectively obsolete, needed due to the software packages they had and the limitations of those. Yes, some software makes me grumpy.

Strehl? - MTF? - EER?. Comments to come on all that.

Edited by fred1871 (02/12/13 01:51 AM)

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Re: State of the affairs [Re: WRAK]
#5677221 - 02/13/13 08:47 AM

Quote:

...
So I think I will allow the RoT model to result in values below Dawes but in an additional cut off step I will set all sub Dawes values to Dawes criterion (modified for CO if necessary)...

This was not such a good idea - the statistical analysis resulted in a parameter value of very near 1 and did not bring any reasonable advantage in terms of standard deviation and correlation.
I think I will simply dump the obvious over- and underperforming observations to get clear of the huge errors they produce.
Wilfried

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Re: State of the affairs [Re: WRAK]
#5677818 - 02/13/13 02:53 PM

If your using actual observations with real world Strehl and SA, then tweaking the model to those observations would seem to account for them on average and implicitly.

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Re: State of the affairs [Re: Asbytec]
#5679164 - 02/14/13 10:55 AM

Norme, you may probably be right about Strehl and SA, but I don't have any observations reports including these values - but what I will do is at least eliminating the obvious underperforming observations resulting from using fixed apertures and lack of better competing observations, because these are certainly "wrong". This will give then more room for real limit observations including the overperforming ones.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]

Quote:

The large number of rather faint pairs in Wilfried's list for Orion got me wondering ...

... me too with the rather moderate proposed apertures for splitting these - as already mentioned there exists certainly a weakness in the current model regarding secondaries fainter than +11mag. As we come here close to the telescope magnitude limit at least for smaller scopes in combination with light pollution we need here an additional component working with the difference between the magnitude of the secondary M2 and the with NEML adapted TML similar to Peterson's approach.
A possible procedure could be to run the current model and then calculate the NEML adapted TML for the proposed aperture and compare this value with M2. If the TML is clearly above M2 then no further action is needed but if it is rather equal or even below then the proposed aperture is to be increased accordingly - what this means exactly is meanwhile not very clear, I will have to work this out.
First step is certainly to have a clear model how NEML works on TML. My first idea was that for a scope it certainly does not mean a full magnitude loss according to NEML, rather may be half of it. But this did not correspond very well to the existing observation data set suggesting a dependance on aperture in terms of less aperture means less magnitude loss.
On next possibility I will make a set of observations for the influence of NEML on TML with different apertures for a better data base for this purpose. Meanwhile I will work with a first approach for delta_TML = LN((6.5/NEML)^2.512)*(TML/13.43)^2.512 with TML = 2.7+5*LOG10(D_mm) and 13.43 as the assumed turning point from which the magnitude loss increases above the assumed half magnitude loss indicated by NEML. The image shows the effects of this algorithm for a NEML of 3.5.
Wilfried

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Final steps [Re: WRAK]
#5684994 - 02/17/13 11:21 AM

I hoped to be able to derive from the formula above the for the compensation of NEML required TML value but failed miserably - may be due to my cold induced loss of clear thinking. Peterson's approach works surprisingly good with M2 fainter +11mag - but not this good for brighter companions and did not provide any help for considering light pollution besides a seeing factor, but this is another topic. But numerical approximation proved again to be a good substitute so I got this fixed. Applied on the mentioned Orion list this added step to the RoT model did not change anything down to a moderate NEML of 4.5 but with lower values of NEML the effects get at least for wide doubles with faint companions quite drastic. With a for suburbs unfortunately usual NEML of 3.5 this gives (with zero obstruction):
SLE832 11.1" +10/11.8mag 150mm instead of 99mm
BAL2147 7.6" +8.7/11.8mag 150mm instead of 113mm
HJ700 11.5" +9.9/11.7mag 140mm instead of 96mm
But there is no change for doubles rather close like for example:
TDS3160 1.5" +9.5/11.7mag 174mm remain.
I will now produce a new spreadsheet for an at the moment final beta version of my RoT model and post it here soon including a list of doubles from the upper part of Eridanus.
Wilfried

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Re: Final steps [Re: WRAK]

I have now uploaded the 3rd version of my RoT model and time will show if this is any good. The answer to the question which aperture is required for resolving unequal doubles with faint companions showed to be quite complex. While the single components of the model are based on more or less educated guesses the parameters are calculated with statistical analysis of limit observations (nonlinear regression). Some guesses were evidently not this good because they did not deliver on the numbers and had to be replaced by better ones - I am sure this process could be repeated several times to get even better results but this may be a task for the future. On the other side it was difficult to get enough solid observations to be able to do solid calculations - my data set is still far too small.
The process of developping the model was quite interesting as I gained a lot of for me new insights:
- Light pollution is for doubles with secondaries brighter than +10mag of no real concern
- For doubles with companions fainter than +11mag the by light pollution reduced telescope magnitude limit plays a significant role at least for wider separations
- The effect of central obstruction on the diffraction pattern seems on first look not this significant - but when calculating for required aperture small differences suddenly become a significant advantage for close doubles of similar brightness. With increasing magnitude difference this advantage gets smaller and results finally in an disadvantage for scopes with CO.
The uploaded spreadsheet is filled with doubles from the upper part of Eridanus. Any response with observations would be apprediated.
Wilfried

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Re: Final steps [Re: WRAK]
#5690268 - 02/20/13 07:10 AM

Wilfried, I will provide some more data points soon - I've had too many other things needing doing to be able to go through observations from recent weeks, some of them likely to be limit or near-limit observations.

I can only agree about light pollution being a limiting factor, especially for small and moderate telescopes, in seeing faint companions. Larger telescopes are less affected for 11th magnitude stars UNLESS very close to much brighter primary stars.

Regarding CO - my current impression is that medium CO (25-35%) is not very helpful for seeing close even pairs, compared to unobstructed apertures. The reduction in disc size is very little. Other factors, such as less good optics, collimation being even slightly off, thermal issues, seem to cause more loss than any gains from reduced disc size. And air turbulence unhelpfully interacts with CO as Danjon and Couder noted long ago.

I've worked out some further questions regarding CO and its interaction with optical quality as well. More on that also after tomorrow, because I'm preparing other material for a presentation that will keep me busy tomorrow.

Thanks for the Eridanus list. I'll look through it as well, and see what I can usefully observe, to add to pairs in Orion and Gemini I've already looked at. Gradually the data points will build up to good numbers.

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Re: Putting the "Rule of Thumb" to test [Re: Asbytec]
#5696159 - 02/23/13 08:23 AM

Quote:

BU 100: Try as I might, I failed to split this double. I even cheated and looked up the Rho and Theta for the companion and still failed. I could, however, see a dim star about 6" arc south of BU 100. I have not looked up that star's magnitude just yet, but I am curious about it. I did spend a lot of time with this first double of the evening, because at mag 11 I really needed to be fully dark adapted to have a chance. Still, no success. At 3.2" sep, it sits very near my 4th diffraction ring (~3.6" arc.)

STT 145: Split. Companion easily seen near PA 340 just outside the first ring at 263x (UO 12mm HD Ortho, 1.6x Barlow.)

A2450: Split. Faint companion easily seen at ~3" arc sep near PA 120 to 130 (south east, anyway.) However, it's PA is listed at 053. I suspect this is incorrect, but I just don't know. If it's correct, then I failed to split it and simply observed another star near PA 130. But, my gut tells me the listing is incorrect. That pair just looked and felt like a double. Stellarium, ironically, shows the companion more south of PA 90, too.

STT 171. Split - maybe. ...

Wilfried and others, the above is quoted from Norme's observations reported 30 January 2013. As I've now caught up with a few of these I thought I'd provide my observing notes, done without benefit of checking what Norme wrote.

The folowing are with my 140mm refractor, seeing started at fairly good, becoming good-plus (7/10) for the more difficult ones. Unfortunately I didn't get to STT 171. These are in Gemini. Night of a 6 day moon recently. Nelm in the observed area was perhaps 4.5, despite moonlight.

For purposes of comparison, I started with STT 140, listed for a mere 117mm aperture - the mag 10.1 companion was seen at 160x, not very difficult; delta-m here is 3.2 mags. I compared it with A2450, same separation, delta-m 3.0, but fainter - mags 8.05 and 11.06. A2450 also showed as a double at 160x - however on the Gemini list it's got 140mm aperture indicated. It was nearly as easy as STT 140 - only the fainter magnitude of the companion made it less obvious.

BU 100 - mags 7.3 and 11.1 at 3.2" (listed for 144mm) was easier - the companion star showed at 100x. It was noticeably easier than A2450, and at 160x the companion was obvious.

STT 145 - mags 7.3 and 9.9 at 1.5" - listed for 147mm aperture. More difficult, but the companion was a just visible speck close to the primary at 160x, and more clear at 230x.

My feeling is that the model used for the Gemini doubles (since revised) was not entirely consistent in predictive capacity; and that exceeding it was not of high difficulty for at least some doubles.

I still have some other pairs, already observed, to provide notes for. And if the weather here ever stops being cloudy I can move on to Eridanus.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#5698452 - 02/24/13 03:24 PM

Quote:

... My feeling is that the model used for the Gemini doubles (since revised) was not entirely consistent in predictive capacity; and that exceeding it was not of high difficulty for at least some doubles...

Fred, you are probably right - it seems that at this stage I had too many underperforming observations in my data set (mostly from Lord's paper) resulting from the use of fixed apertures but meanwhile I have eliminated most of these. The Eridanus list should already do better.
Wilfried

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Re: Putting the "Rule of Thumb" to test [Re: WRAK]
#5749123 - 03/22/13 07:13 AM

As I already posted in the thread "Star pattern for TML test with light pollution" I found a glitch in the last module of the RoT model checking the result against the for resolving of faint companions required telesocpe magnitude limit including the influences of light pollution for NEML below 3.5 as it seems that I have overestimated the influence of light pollution on TML.
I will certainly try to correct this but I have to sample more TML-observations depending on NEML.
As I have only a NEML range 2.5-3.5 available I would appreciate reports from other observers very much. As the advertised magnitudes for faint stars are often not very reliable I recommend the check with http://www.aavso.org/download-apass-data - when restricting the parameter "Radius" to 0.01 you will get most probably only one result and this should be the observed star.
Wilfried

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Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5781195 - 04/06/13 06:50 AM

Foul weather for weeks made not only obervations impossible but stalled also other planned outdoor activities - so I had some time at hand to "play" with numbers.
Target was to gain some impressions how Lord's RoT works compared with the current version of my RoT model. As data set for this investigation I used the set of pairs of the Sissy Haas project and as additional tool I used the AstroPlanner implementation of Lord's algorithm giving not a number but a verbal rating from "UN" for unresolvable to "E" for easy for a given combination of avertised date for the double, telescope aperture, central obstruction size and seeing.

Assuming perfect seeing and zero central obstruction when using the algorithm of Lord's RoT results in a required separation for a split and when you use this result in AstroPlanner you always get a "D" for difficult - I interpret this as comparable with my model approach of a 50% probability for a split meaning a fair chance.
Applied to the Sissy Haas set of doubles and "translated" from separation into aperture you get a set of apertures required for a 50% split probability.

Comparing these results with the results when applying my current RoT model to the same set of doubles gives some interesting insights:
- Lord's RoT is rather conservative when the separation is small - with only few exceptions my RoT requires far smaller apertures with the exception of fainter doubles as the aspect of faintness is not part of Lord's model (a +4/6mag pair gets the rame rating as a +8/10mag one - this I consider a main weakness of Lord's RoT)
- For separations somewhat larger beginning with 3" Lord's RoT is consistenly below the values delivered by my RoT model: The main reason for this is probably the fact that as far as I know Lord had no observation reports available for scopes with apertures smaller than 75mm so his results for larger separations are projections from the other observations with larger apertures and such an approach is prone for desaster. As I have meanwhile with the help of an iris diaphragm a lot of limit observations below 75mm aperture I am quite confident in the numbers of my model
- The combination of somewhat larger separations with not this large difference in brightness of the double star components poses also a problem for the Sissy Haas project because nobody uses scopes with apertures smaller than 50mm so observation reports in this range without the use of aperture masks or iris diaphragm are of no value for the project
- Using the results of my RoT model for the aperture in the AstroPlanner implementation of Lord's RoT gives for separations below 3" separation most of the time "VD" for very difficult oder "ED" for extremely difficult - this may be the other side of the coin regarding available observations: Lord had a lot of observations with apertures above 140mm in his data set while I have only a very limited data set in this range available and especially no own observations. But here I have some plans (see below)
- Things get again very interesting when using the AstroPlanner implementation of Lord's RoT to determine the aperture required for an "XD" (exceedingly difficult) rating - Lord's RoT delivers here extremely optimistic values with in average about 42% smaller apertures as required for a "D" rating. This indicates an extreme wide variation is his data set of observations most probably due to the use of fixed apertures with only a few observations really at the limit and most above. This would also explain the rather pessimistic results for the average "D" rating of Lord's RoT
- In average Lord's "XD" rating corresponds very well with the double standard deviation of 14% for my RoT model meaning reducing the for a 50% chance split required aperture by 28% resulting in a probability of about 3% for a split means once in a while under the very best conditions.

Today I have received the delivery of an iris diaphragm with an inner diameter of 225mm for use with my C925 SCT which means I can then cover the range of 170-225mm (and 235mm without iris) with own limit observations. Below 170mm will not be very useful as then the CO would exceed 50%. But the small gap between 140 to 170mm should pose no serious problem for the validity of the statistical analysis. I can only hope for a good performance of the C925 I did not use so far for double star observing as I do not like the handling, feeling and image quality in terms of crisp spurious disks of this scope this much.
Hope for more clear skies for the rest of the year then.
Wilfried

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Re: Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5815849 - 04/22/13 05:47 PM

The hope for good performance of the C925 did so far not realize - the secondary mirror has somehow gained some freedom for rotation and shifting and therefore collimation is non existent and the star test showed severe distortions of the diffraction pattern. Has to be corrected.
Second mishap was a not this perfect iris diaphragm - changing the aperture required too much force to be useful on a telescope so I had to return it for exchange.
As I do not like the problems with dew on the schmidt plate of the C925 I ordered a Mewlon 210 to have another option - will arrive in a few weeks.
Wilfried

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Re: Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5816342 - 04/22/13 08:49 PM

Wilfried, the rotating secondary on some SCTs is a common issue. Mine did the same - fairly easily solved, as it's just the result of the secondary moving, and rotating in its housing. I re-centered the housing and screwed it tighter; then could re-collimate the secondary, being careful to hold the housing while turning the screws to avoid any slight new rotation.

Nice to be able to afford a Mewlon 210 as an additional telescope.

Dewing? - can be overcome,anyway. The diaphragm, when you get one that works properly, will I expect only be useful for testing limiting magnitudes. Unless your interest is in the effects of enhanced central obstruction, as the CO factor becomes bigger rather quickly as you close the diaphragm. As you've noted, ou can get from the normal 36% obstruction of the C9.25 to 50%, which is very destructive of visual image quality, by stopping down from 235mm to 170mm aperture. I doubt this will be helpful for exceedingly difficult or even very difficult uneven pairs. Indeed, even merely "difficult" uneven pairs may be promoted to "exceedingly difficult" (or impossible) from the enlarged CO.

With my own C9.25 I can get quite good spurious discs, and often get a near match on uneven pairs for what I see with my 140mm refractor. Certainly the refractor gives neater star images - smaller aperture is less seeing-affected, no CO means no detrimental interaction with seeing (as per Couder et Danjon), and no enhancement of diffraction rings - plus the refractor optics are of better quality. So 235mm with CO is similar to 140 without CO, though with a brightness advantage to 235 that does show with fainter secondary stars. The extra ~1.0 magnitude is useful.

It'll be interesting to see what results you get, with the two obstructed telescopes as well as with the diaphragm usage. Problem with the diaphragm on scopes with CO is that you then have two issues - aperture reduction means CO increase, where with the refractor it's simple aperture reduction.

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Re: Putting the "Rule of Thumb" to test - next step [Re: fred1871]
#5819090 - 04/24/13 02:53 AM

I have not yet directly compared the C925 with my 140mm refractor regarding resolving doubles but would expect closer splits and fainter companions with the C925. But may be this is not only a question of reflector with CO vs. reflector but also a question of reflector construction - at least some MAKs seem to do very well with for example Questar 7 comparable with a 6" refractor. Also the Dall-Kirkham design seems to be a candidate for good results - and may be the Schmidt-Cassegrains design is reasonable good for Deep Sky Objects but not this performing with double stars. I think I will let fix my C925 by a profesional and not try to challenge my own limited mechanical ability and then I will see.
Wilfried

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Re: Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5834718 - 05/01/13 04:10 PM

After a few good nights in the last weeks I could expand my data set by about 40 new limit observations between 50 and 140mm. I think this aperture range is now very good covered and with the existing RoT model also quite good defined - the correlation coefficient is still above 0.95. But it is time now to cover also somewhat larger apertures.
Got today the message that my C925 is fixed (secondary mirror secured within the Schmidt plate, Schmidt plate cleaned from the inside, collimation done) and got again (after an inital test after purchase) the very good optical quality of this scope confirmed.
The less than perfect 225mm inner diameter iris diaphragm is returned to the source and I got my money (minus double transport) back but no new iris so far. I hope now again for some clear skies to try the C925 with double stars and will substitute the missing iris with cardboard aperture masks if I have the impression that the C925 is doing a good double star job.
Wilfried

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Re: Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5949160 - 07/01/13 06:44 AM

Paul Rodman has released version 2.1 of his AstroPlanner with an implementation of my current algorithm as one of the new functions. AstroPlanner now offers two additional collumns for double stars:
- One for "Splittable with the selected telescope and location" with content "Yes" for pA (calculated proposed Aperture for a 50% chance for resolving) less or equal the aperture of the selected telescope, "???" for pA larger than telescope aperture but within the standard deviation and "No" for pA above. This is a slightly conservative approach, as a "No" can still mean a small chance for a split if pA is within the 2x standard deviation range
- Second for "Splittable with mm" giving the calculated pA for this double.

The pA algorithm can also be used in the "Select from Catalogue" function with "Splittable with the selected telescope and the selected location" as one of several criterias like mag1, mag2, separation, delta-m, ...

This latter implementation shows drastically how important the topic of TML is in this context as a huge part of the doubles included in the WDS catalogue is very faint and at the same time very wide - so the usual paramters like separation and delta-m are completely to neglect for resolving the companion but only the telescope magnitude limit counts. This works currently good enough for locations with NEML +3.5mag or better but for NEML values significantly worse I have made the error of overestimating the influence of light pollution as already mentioned several times.

Next steps will be the elimination of this TML plunder and the increase of the number of limit observations for apertures > 150mm to get a better statistical significance for this aperture range.

My C925 seems to be in good shape now and the iris diaphragm is already operable.

Wilfried
PS: The selection of the location is necessary for the parameter "average brightness of the sky" resp. NEML
PPS: My relation with AstroPlanner is strictly only as private user contributing some input for additional functions for double star observers like myself

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Re: Putting the "Rule of Thumb" to test - next step [Re: WRAK]
#5949188 - 07/01/13 07:20 AM

That is outstanding, Wilfried! The calculator works really well with my 8 inch--I think it is a very useful tool for those of us who like to observe near the edge.

Edited by Nucleophile (07/01/13 07:21 AM)

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RoT algorithm - CO implementation weakness [Re: Nucleophile]
#5960164 - 07/08/13 08:39 AM

The limit observation results of my recent experiments with an iris diaphragm on the C925 and the resulting very high CO values made me aware that the effects of reduced clear aperture and reduced light energy in the Airy disk need to be taken into account at least for CO >0.3.
One example is the observation of Eps Boo/Izar with a limit aperture of 40mm with zero CO and 120mm with CO 0.75.
The latter corresponds with a clear aperture of ~80mm and taking the reduced light enery in the smaller Airy disk into account gives an equivalent clear aperture of ~40mm.
The calculated pA of the RoT model with 0.75 CO and NEML 3.5 gives 56mm and this is clearly nonsense compared with the effective needed 120mm.
Currently the algorithm calculates only the effects of the reduced size of the Airy disk especially for the separation of more or less equal bright doubles and the negative effects of the changed diffraction pattern for rather unequal doubles.

I will correct this in the next version.
Please notice that this weakness does not show noticeable impact for scopes with CO <0.3 (Newtons and Maks) while values for scopes with CO >0.3 (especially SCTs) might be a bit on the optimistic side but still within the standard deviaton range.
So as practically nobody is using scopes with CO >0.4 for double star observing the results of the pA calculator should still be of good use.
Wilfried

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Re: RoT algorithm - CO implementation weakness [Re: WRAK]
#5960400 - 07/08/13 11:55 AM

Keep up the good work!

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Effects of CO on Resolving Unequal Binaries [Re: Nucleophile]

My recent experiments with cental obstructions larger than 0.4 show a drastic effect regarding resolving unequal doubles - the energy transfer from the Airy disk to the diffraction rings of the primary rises progressive and at the same time the energy loss in the Airy Disk of the secondary does the same. So the secondary gets quickly lost in the otherwise optical impressive diffraction pattern of the primary. A first look at the numbers suggest that the resolving power of scopes with CO correspond to that of scopes without CO calculated according corresponding to the reduced surface for wide doubles where the resolving power corresponds with the telescope magnitude limit and for close doubles with less than ~10" separation also reduced energy in the Airy disk relative to the by CO reduced size of the Airy disk.
Examples:
- Already mentioned Izar with an equivalent of 40mm refractor to 120mm reflector with CO 0.75
- STF2011 2" +7.93/10.23mag with an equivalent of 90mm refractor to 160mm reflector with CO 0.56
- STF2029 6.2" +7.95/9.62mag with an equivalent of 65mm refractor to 130mm reflector with CO 0.69.

But this approach seems only valid for really large CO's as the same calculation would give for a 235mm SCT with CO 0,38 an equivalent of a 213mm refractor but this is certainly far too optimistic. For CO less 0.4 seems the equivalent diameter calculated only with the energy loss without relation to the size of the airy disk more appropriate. This would give for the C925 an equivalent of 185mm - for my feeling still a tad too optimistic.
What I still think is that reflectors with CO significantly smaller than 0.3 (Newtons and Maks) have an advantage for resolving equal bright doubles and not this much troubles with moderate delta-m's.
Further investigation needed.
Wilfried
PS: Spreadsheet with simple algorithm for calculating equivalent apertures for download available (based on numerical approximation for size of Airy disk and energy loss depending on size of CO)

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Re: Effects of CO on Resolving Unequal Binaries [Re: WRAK]
#5968059 - 07/12/13 08:22 PM

Quote:

PS: Spreadsheet with simple algorithm for calculating equivalent apertures for download available (based on numerical approximation for size of Airy disk and energy loss depending on size of CO)

Thanks, Wilfried.

I am putting the finishing touches on a calculator I have developed for my 15"---will post the results to this forum as soon as I refine a few parameters.

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RoT Check against TML [Re: Nucleophile]
#5973571 - 07/16/13 04:55 AM

Quote:

My current RoT model includes a final step checking the magnitude of the secondary against the (with the most simple approach 2.7+5*LOG10(D_mm) calculated) TML of a scope with the proposed aperture pA of the calculator including the effects of light pollution (calculation somewhat more complicated).

I thought this a clever approach to avoid crass errors with unrealistic pAs especially for wide doubles with very faint companions.
As I made some plunder here with overestimating the effect of light pollution on TML I looked for ways to do a better job but progress was slow. For example a small project for getting TML observations with different amounts of light pollution got stuck due to the lack of for this purpose usable open clusters currently in my field of view - but I am still interested in this question and will continue to investigate this topic.

My research for other approaches in this field resulted in the insight that the topic TML itself is more complex than I anticipated - even very sophisticated models like this calculator http://www.cruxis.com/scope/limitingmagnitude.htm based on the work of Bradley Schaefer http://adsabs.harvard.edu/full/1990PASP..102..212S deliver results with errors too large for my requirements thus creating huge erratic pA values I wanted to avoid from the very beginning.

So I decided to change my approach - I will simply add fictive bogus double in to my data set of limit observations with large separations above 10" and faint companions with magnitudes at the observed TML values of different aperture sizes and let do the program for statistical analysis do the final work while I concentrate on the structure of the RoT model.
Maybe there will be then with specific parameters occasionally an unrealistic small pA with a TML below the magnitude of the secondary but I will try to make the probability for such a result very low.

After some more research and consideration I came to the conclusion that the concept of checking the for light pollution corrected telescope magnitude limit of the proposed aperture against the magnitude of the secondary especially for wide doubles is not this bad as I thought lately.
My error was to consider the concept of TML as an analytical one giving a "true" value for resolving faintest stars possible with a given aperture - and this is certainly not the case even if you try hard as for example Schaefer did as in the end besides the influence of all other factors the collecting of photons in a given situation remains a random process.
If we therefore consider TML as statistical concept we can relax a bit and stick with the concept of probability used already in the base RoT model. So I need a TML formula as simple and reliable as possible comparable for example with the Dawes criterion for resolving close equal binaries (is the currently used TML=2.7+5*LOG10[D_mm] good enough?) and a similar reliable algorithm for considering the effects of light pollution and central obstruction.

This means I will stick with the existing structure of the RoT model but consider the TML concept no longer as analytical but statistical one.
Wilfried

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Re: RoT Check against TML [Re: WRAK]

This topic begins to develop momentum as working with rather faint doubles made me aware that the current version of the RoT model is based on limit observations mostly up to +12mag for the companion and therefore not a really challenge in terms of RoT.
Thus the current algorithm results in an error for doubles with primaries fainter than +14mag as in my struggle to adapt best to the existing observations with not so obvious influences of the value for M1 I came to a rather not so clever formula including a limit for M1<14mag. This limit was not mentioned so far as I simply forgot about it.
Now that I was reminded of it I made a small change that at least no error results but the limit as such remains - I would now even go so far that values of M1>12.5 are not handled this well but I simply do not have enough observations in this range to check this possibility against reality. I could try to change this limitation of the current model but I am not sure if there is any interest for a RoT for doubles fainter than this.
Then there is generelly the topic of wide doubles - if wide enough all other parameters should be of no influence but the magnitude of the companion in relation to TML. The question remains how gracious this change of the rules can be implemented with increasing separation. This topic requires certainly more investigation.

I have now implemented the above mentioned new algorithm for calculating the influence of light pollution in terms of NEML (including in this implementation the extinction due to the altitude of the object) and have uploaded the updated version of the RoT model filled with wide and faint doubles in Oph between 15 and 50 arcsecs separation and up to +15mag for the companion and would be happy to get any responses how this works compared with reality as I have the feeling that I have maybe now under the influence of Schaefers work a tad unterestimated the effects of light pollution.
The model works still in the mode that the larger proposed aperture "wins" - either depending on separation, delta-m, M1, M2, CO and NEML or TML driven.
Wilfried

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Overdue analysis of the RoT behavior [Re: WRAK]
#6039565 - 08/22/13 04:03 AM

The current algorithm works with the parameters separation in arcseconds, difference of magnitudes delta_m, magnitude of primary m1 and secondary m2, size of central obstruction CO in terms of % of aperture diameter, light pollution in terms of Naked Eye Magnitude Limit NEML (in the field of view as opposed to the usual definition in zenith) and Telescope Magnitude Limit TML (again in the field of view and not zenith).
Result of the algorithm is the proposed aperture in mm for resolving a double with the given parameters with a standard deviation of 14%. This standard deviation covers all kind of errors in the advertised data as well as in the observation notes and all other influencing parameters not included in the algorithm with the exception of seeing: reasonable fair seeing is assumed as essential for resolving of even not this difficult binaries with resolving meaning getting an image with clear indication of position and separation of the secondary without any doubt.
While it is not feasable to show the interaction between all of these parameters in simple graphs it is possible to show the influence of a single parameter with fixed values for the other parameters to gain some impression how the algorithm works.
I will try this in my next posts.
Wilfried

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Re: Overdue analysis of the RoT behavior [Re: WRAK]

The first component of the RoT model deals with separation - this is the trodden path of Dawes criterion modified with CO size according to diffraction theory, but the effects of the factor CO will be discussed separately.
The basic relation between separation and aperture is an exponential increase of aperture with decreasing separation.
The graph shows this relation with m1=4, m2=6, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
It is certainly possible to "beat" Dawes but the standard deviation of 14% (result of statistical analysis of my data set of limit observations) means that a resolution with an aperture more than 28% smaller than the calculated proposed aperture has a probability of less than 5% and requires therefore rather very favorable conditions and especially excellent seeing.

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Re: Overdue analysis of the RoT behavior [Re: WRAK]

The second component of the RoT model deals with the magnitude difference between primary and secondary - this is the starting point for our discussion regarding resolving unequal doubles.
The basic relation between delta_m and aperture is a moderate exponential increase of aperture with increasing delta_m. For higher values of delta_m an influence of CO is assumed, but the factor CO will be discussed separately later.
The graph shows this relation with sep=3.3, m1=5, m2=6-13.5, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
This also shows one of the current weaknesses of my data set: too few limit observations with apertures larger than 140mm. My C925 is more or less of no use for this task as the reduction of the aperture leads to unreasonable high CO values so I depend on reports of other observers.

Forgot to mention: Delta_M of less than 1 is considered equal bright.

Edited by WRAK (08/24/13 05:50 AM)

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Re: Overdue analysis of the RoT behavior [Re: WRAK]
#6042458 - 08/23/13 08:51 PM

Excellent work, Wilfried. I cannot wait to try your RoT in the coming months.

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Re: Overdue analysis of the RoT behavior [Re: Asbytec]

The third component of the RoT model deals with the magnitude of the primary.
The basic relation between m1 and aperture is a moderate more or less linear increase of aperture with increasing magnitude but only if separation requires this.
For wide pairs the increase of m1 is no issue - only the telescope magnitude limit could be a topic in this regard but this is anyway handled with the magnitude of the secondary, so there is no need to deal with TML here.
The graph shows this relation with sep=2, m1=4-12.5, delta_m=2.5, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
The impact of the TML check for M2 would be effective for M1=12 and 12.5 as with the delta_m of 2.5 we reach already larger values than the TML for the resulting pA - but the graph does not show this effect as the TML check will be discussed separately.
Note: M1 less than 6 is considered to be no issue and +12.5mag is considered to be the upper limit for useful results

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Re: Overdue analysis of the RoT behavior [Re: WRAK]

The fourth component of the RoT model deals with the magnitude of the secondary.
The basic relation between m2 and aperture is a moderate more or less linear increase of aperture with increasing magnitude - this time interestingly without relation to separation. Don't remenber the details but it seems that for this component there was no statistical relevance of separation.
The telescope magnitude limit is certainly a topic for increasing values of M2 and this will be handled in the next step.
The graph shows this relation with sep=5, delta_m=2, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
Note: M2 larger 9 is considered to be the critical value with which M2 is beginning to influence the proposed aperture

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Re: Overdue analysis of the RoT behavior [Re: WRAK]

As the TML check is so far the last step next comes the influence of light pollution.
The fifth component of the RoT model deals with this factor in terms of naked eye magnitude limit NEML (in the field of view in contrary to the usual approach relating to zenith means also including extinction).
In the very beginning of this RoT discussion I thought light pollution a serious impact for resolving doubles - meanwhile I see this rather relaxed. The influence of LP on resolving doubles seems rather moderate.
The basic relation between NEML and aperture is therefore a very moderate more or less linear increase of aperture with decreasing values of NEML.
The graph shows this relation with sep=2, m1=7, m2=10, CO=0 and NEML=2-6.5. I don't have many actual observations with comparable parameter values in my data set but it is clear that the difference between a very dark and a heavily light polluted sky is only about a few mm in aperture, may be up to one aperture class.
Note: It is assumed that +6.5mag is the best possible value for NEML (being aware that this is depending on personal acuity) and Light Pollution is considered to be of impact only for doubles with secondaries fainter than +9mag

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Re: Overdue analysis of the RoT behavior [Re: WRAK]

Next comes the sixth factor: telescope magnitude limit TML - for close pairs this is not really an issue as the other parameters do their job but for wide pairs TML becomes the limit for resolving.
The influence of TML was for some time rather difficult for me as I assumed this to be a given technical parameter mentioned in the specs for scopes - so it took me some time to realise that TML is also a statistical concept with high impact not only of seeing but also of personal acuity and a lot of other factors.
There is a list of TML observations in the paper of Schaefer on the topic of creating a TML model - the variation is enorm and can not be explained fully despite the relatively high number of parameters in the model.
Next issue is the from Schaefer not even considered rather inadequate precision regarding reported magnitudes for fainter stars - so it does not make much sense to try own TML limit observations for this porpose (but I will stay on this topic as I consider it still interesting).
In the end I adopted the often used simple and probably somewhat inprecise formula TML=2.7+5*LOG10(D_mm) as average value with a standard deviation hopefully similar to the 14% of my RoT algorithm.
To consider the most obvious side effects I included of the influence of light pollution (here comes NEML again) with values according to the model of Schaefer and a modification for CO reduced apterture.
The TML check is applied after the use of the RoT algorithm with the so far discussed parameters and if M2 is fainter than the calculated TML for the size of the proposed aperture then the pA is increased to match this value.
The results seem so far realistic if sometimes a bit optimistic.
The graph shows the few examples in my data set of limit observations of TML checks with a positive result - all with separation larger than 10" and rather high values for M2 else rather different parameters.The "x" marks again the aperture according to the observation reports

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Re: Overdue analysis of the RoT behavior [Re: WRAK]
#6048313 - 08/27/13 07:59 AM

Wilfried, I applaud your work and wish you continued success toward a very difficult goal.

Norme

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Re: Overdue analysis of the RoT behavior [Re: Asbytec]

Finally the seventh factor: size of Central obstruction CO.
The RoT model does not have a separate module for CO as it is included in the first module for separation (giving some benefit due to the smaller size of the Airy disk) and in the second module for Delta_M (negative influence for larger values of delta_m) but maybe an additinal separate CO module is necessary.
I have selected by random observations from my list sorted by size of CO shown in the graph below - while this seems to work fine for CO up to 0.35 all observations with larger CO show crass errors in the calculated proposed aperture. This may not be such a problem as CO larger 0.4 is no real issue but I would prefer a better behavior of the RoT model even for extreme values of CO especially in the range 0.3-0.4.
My problem here is that I have not enough observations with large apertures with many different sizes of CO. My own approach with an iris for a C925 only demonstrates the drastic negative effect of really large CO but only with smaller apertures.
What I would need is a systematic setup starting with a small CO of 0.2 or even smaller with slowly increasing sizes of CO.
To some degree I hope I can this do with an already ordered 8" f/22.5 scope with CO 0.25 but the date of delivery has slipped for several month's.
If this does not bring enough useful data material I may have to buy a ~f/10 Newton but I don't like the idea to have to handle such a large tube - so I would appreciate it very much if somebody with this kind of equipment would contribute limit observations by changing size of CO up (and maybe aperture down as alternative approach) to the limit of resolving doubles with the help of masks.

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Re: Overdue analysis of the RoT behavior [Re: WRAK]
#6061773 - 09/03/13 10:10 PM

Wilfried, the CO size ties in nicely with the discussion elsewhere about how good are reflectors for double stars. Looking at this graph, I notice bars for 235mm aperture, although CO is given there as 0.38, and Celestron say 0.36 for the C9.25.

But, taking the bars as given - it appears the 235mm SCT is equivalent to a 155mm aperture, in terms presumably of resolving large-delta-m doubles. Yes? Obviously it's not about light gathering, as obstructed 235mm collects more light than unobstructed 155mm; and likewise outperforms it on equal pairs.

As a generalised equivalent I find it interesting because my own comparisons of my two telescopes, unobstructed 140mm, obstructed 235mm, suggests the SCT is slightly better (but only slightly better) for large delta-m pairs, assuming the secondary star does not fall on the first diffraction ring, and if delta-m is very large, that it doesn't fall on the 2nd or 3rd rings.

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Re: Overdue analysis of the RoT behavior [Re: fred1871]
#6062103 - 09/04/13 03:32 AM

Fred, while your impression that the C925 might be compared with a 155mm refractor in terms of performance for resolving doubles may be correct this relation is not the topic of the graph above. This graph illustrates how utterly wrong the RoT algorithm works for CO 0.35 or larger. In the short term this means that the RoT only works for CO up to 0.35 - this is no problem for most scopes but I will try to correct this if possible.
Regarding obstruction of C925 - specs give 85mm for the secondary mirror but including mounting the CO is exactly 90mm. This means 90/235 = 0.383 CO. But I fear there is more to consider with SCTs (in comparison with other types of reflectors - as for example the Schaefer TML calculator does). Ed Wiley is happy to get with his C11 results down to Rayleigh with video - I assume then this would be impossible for visual observing.
Back to the topic RoT: I have far too few limit observations in this aperture range and it will be difficult to get much more because you can not reduce the aperture without getting absurd high CO - and when you can not reduce the aperture you never know if an observation is actually on the limit.
Only possibility would be a large Newton with small CO as a start and masks for reducing aperture as well as increasing CO to maintain a given ratio - may be a bit cumbersome but it could be done.
Wilfried

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Overall RoT Performance [Re: WRAK]

Trying to get an overall picture I applied die current RoT algorithm on my full data set of ~380 limit observations (excluding all observations with CO larger 0.4 and obviously underperforming ones).
This data set includes also the about 130 ones I used for creating the current RoT algorithm with statistical analysis but ~250 observations are "new" ones.
A small part of the observations is sourced from published papers and books and also from observations posted on this board (thanks to Fred, Norme, Roberto, Mark, Ed, Sasa, Tom, Dave, EdZ ...) but most observations are my own made mostly with refractors using aperture masks or iris diaphragms - so there is a bias towards smaller apertures.
It would certainly be possible to redo the statistical analysis with the now much larger data set to get higher statistical significance for the parameters but I tend to wait until I have more observations with apertures larger than 140mm. I want also to find a solution for the larger CO values.
Meanwhile the results are not this bad as you can see from the graph - the blue line shows the actual reported apertures and the red line shows the proposed aperture calculated with the RoT algorithm.
Wilfried

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Re: Overall RoT Performance [Re: WRAK]
#6062268 - 09/04/13 08:15 AM

Excellent work Wilfried and all credit to you! I'm more than happy to keep feeding data to refine the model. Fit looks excellent and aperture coverage is very good for the instruments available to the typical observer. Moreover, if your exercise also leads to better understanding from newbies (like me) to what can be expected from a typical instrument and their local conditions, the exercise is worth while in itself!

Thank you for your efforts and for sharing it with us.

Roberto

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Re: Overdue analysis of the RoT behavior [Re: WRAK]
#6063476 - 09/04/13 10:20 PM

Quote:

Fred, while your impression that the C925 might be compared with a 155mm refractor in terms of performance for resolving doubles may be correct this relation is not the topic of the graph above. This graph illustrates how utterly wrong the RoT algorithm works for CO 0.35 or larger. In the short term this means that the RoT only works for CO up to 0.35 - this is no problem for most scopes but I will try to correct this if possible.
Regarding obstruction of C925 - specs give 85mm for the secondary mirror but including mounting the CO is exactly 90mm. This means 90/235 = 0.383 CO. But I fear there is more to consider with SCTs (in comparison with other types of reflectors - as for example the Schaefer TML calculator does). Ed Wiley is happy to get with his C11 results down to Rayleigh with video - I assume then this would be impossible for visual observing.
Back to the topic RoT: I have far too few limit observations in this aperture range and it will be difficult to get much more because you can not reduce the aperture without getting absurd high CO - and when you can not reduce the aperture you never know if an observation is actually on the limit.
Only possibility would be a large Newton with small CO as a start and masks for reducing aperture as well as increasing CO to maintain a given ratio - may be a bit cumbersome but it could be done.
Wilfried

Wilfried, thanks for the clarification. And I'll re-measure my SCT obstruction

Limit observations - agreed, difficult without aperture masks or similar. And with an SCT I agree they don't help. Your suggestion about Newtonians with small CO is a good one; and in the case of larger Newtonians, off-axis aperture masks (no CO) could be used to simulate small telescopes. However, even with a fixed aperture, a large enough number of observations of many doubles might approximate to limit observations for some of them.

I've recently made a long list of some of the more difficult doubles that I've successfully observed with the 140mm refractor. Most of these are not "limit" observations; some of them possibly are. A number of patterns emerged. One is, that for 140mm, a pair where the delta-m is twice the separation (say, 4.0 magnitudes at 2.0") is reasonably difficult, and needs fairly good seeing conditions. It might be glimpsed with unsteady seeing, but becomes very certain in steadier conditions.

A small number of very uneven doubles, much more difficult than that, have also been successfully observed. A point of interest is that a subset of these are pairs where the separation numbers cluster around Rayleigh - in other words, where the separation coincides with the first dark interspace between disc and first bright diffraction ring. For the 140mm refractor, that's around 1.0" - separations listed in the range 0.9" to 1.1".

The much-discussed 42 Ori falls into that category. I did manage to see it as double, with 140mm, but it was about as hard as any pair I've succeeded with. The separation at present is likely 1.0" - a slowly closing pair, the last measure some years ago, as I said in a note on CN some time ago. Delta-m is 2.9 magnitudes. With 42 Ori, the separation is near 1/3 rather than 1/2 the delta-m number. I'll put my data list in another note, and also describe pairs where the separation approximates to the first bright ring.

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Re: Overdue analysis of the RoT behavior [Re: fred1871]
#6063902 - 09/05/13 08:12 AM

Fred, I always appreciate your expertise. I want to reply, but will be away for a while. More later, would love to continue the discussion and observe as well.

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Re: Overall RoT Performance [Re: WRAK]
#6065392 - 09/05/13 11:20 PM

Wilfried, as promised, here are some lists of doubles that I've seen as definite but difficult splits with my 140mm refractor.

The first list, pairs around 1.0" (about Rayleigh for 140mm), are examples of doing better than I'd expected. The delta-m figures for these range from 1.6 to 3.0. And, yes, the dm1.6 pair was the (relatively) easiest; the pairs around dm 2.5-3.0 noticeably a lot harder, even in Pickering 8 (about as good as it got).

55 Leo 6.0, 9.0 1.1" dm3.0
15 Boo (KUI 66) 5.44, 8.43 1.0" dm3.0
BU 13 Ori 7.57, 9.22 1.0" dm1.65
HEI 670 Ori 5.97, 8.36 1.1" dm2.4
BU 314 Lep 5.9, 7.5 0.9" dm1.6
42 Ori (DA 4) 4.6, 7.5 1.0" dm2.9
Upsilon Gru (BU 773) 5.70, 8.24 0.9" dm2.54
BU 603 Leo 5.97, 8.53 1.0" dm2.6

Minimum magnification needed for these was in the 250x-400x range. 250x was enough for BU 314; 400x for certainty with 42 Ori, and Upsilon Gruis. 285x showed various others.

That first list is not a result of deliberately targeting Rayleigh; it showed this pattern when I've later gone through the last couple of years of observing notes. Now, I'll look for other doubles that fit this pattern - larger delta-m, and falling in the first dark space.

Second list, doubles where the 2ndry star falls on or about the first bright ring. Again, culled after the event from a couple of years' observing. The standout here is a dm 2.85 pair (BU 1190); otherwise, dm is generally 2.0 to 2.5. Without the diffraction ring I'd expect to have found doubles split with dm 3.5 to 4 at this separation, because these are wider (1.3"-1.6") than the first list (0.9"-1.1").

near or on 1st bright ring
BU 1190 Ori 6.95, 9.81 1.4" dm2.85
STT 145 Gem 7.3, 9.9 1.5" dm2.6
BU 91 Tau 8.1, 10.6 1.5" dm2.5
47 Tau (BU 547) 5.05, 7.32 1.2" dm2.27
Theta Gru 4.45, 6.60 1.5" dm2.15
BU 281 Psc 7.4, 9.4 1.6" dm2.0
BAS 3 Tau 6.16, 8.2 1.3" dm2.0
BU 1089 Oph 6.57, 8.98 1.5" dm2.4

The easiest of these were, unsurprisingly, BAS 3 and BU 281 (160x); the hardest was BU 1190 (285x).
I now plan to try various pairs around 1.3"-1.4" with larger delta-m. One I did attempt, unsuccesfully the first time (I'll get back to it), was HO 389 Boo - 1.6" at delta-m of 3.5 (mags 7.0, 10.5).

I also have examples of pairs wider than the first diffraction ring, with larger delta-m. The second dark interspace for 140mm is ~1.83"; the 2nd bright diffraction ring centred at 2.2". Here are some pairs separated 1.7" to 2.0", with delta-m of 3 or more.

A 146 Vir 7.31, 10.77 1.7" dm3.5
RST 690 Cir 6.7, 9.8 2.0" dm3.1
BU 15 Ori 7.44, 11.6 2.0" dm4.15
Kui 17 Tau 4.26, 7.85 1.8" dm3.6
STF 562 Tau 6.82, 9.94 1.9" dm3.1

These required varying magnifications, typically 230x-285x, though when seeing was best some were visible at 160x.

I should mention that the magnifications are only indicative. I don't always work through a full series of magnifications to discover the minimum required; and seeing conditions affect that as well - some pairs are not possible in less good seeing; some require less power in better seeing. The toughest ones, such as 42 Ori, did require higher powers, after trying less; usually 400x was needed there.

Anyway, I thought this emerging pattern might be of some general interest, as well as providing some more data points for the RoT endeavours.

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Re: Overall RoT Performance [Re: fred1871]
#6065537 - 09/06/13 02:50 AM

Thanks Fred, will go through your list for inclusion in my data set and give you feedback with calculated RoT values.
42 Ori was also for me one of the most difficult observations with 140mm but I go never above x280 magnification because the seeing in my location is rarely better than Pickering ~7 - so all I got was a very pointed elongation with a clear indication of separation and position.
Wilfried

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Re: Overall RoT Performance [Re: WRAK]
#6066803 - 09/06/13 08:32 PM

Wilfried, part of my intention in providing the lists (above) was to document finding that the first bright diffraction ring does appear to have a noticeable effect on pairs of larger delta-m. This is a long-attested belief among observers; and I was not surprised to find my data collection confirming it.

But it does suggest certain complications in developing an RoT. In particular, that the delta-m versus separation factors are bumpy rather than smooth, as a result of diffraction ring interference with visibility at certain light levels. It's one of several matters I plan to look at further while I'm collecting data on difficult doubles. And for enhanced ring effects, I have an SCT of large CO. I'll have to use it more often.

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Re: Overdue analysis of the RoT behavior [Re: Asbytec]
#6066807 - 09/06/13 08:33 PM

Norme, will be glad to see you return when you can. Useful thoughts you offer.

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Re: Overall RoT Performance [Re: fred1871]
#6068940 - 09/08/13 05:53 AM

Quote:

...

The first list, pairs around 1.0" (about Rayleigh for 140mm), are examples of doing better than I'd expected. The delta-m figures for these range from 1.6 to 3.0. And, yes, the dm1.6 pair was the (relatively) easiest; the pairs around dm 2.5-3.0 noticeably a lot harder, even in Pickering 8 (about as good as it got).

55 Leo 6.0, 9.0 1.1" dm3.0 -> pA 158mm
15 Boo (KUI 66) 5.44, 8.43 1.0" dm3.0 -> pA 169mm
BU 13 Ori 7.57, 9.22 1.0" dm1.65 -> pA 149mm
HEI 670 Ori 5.97, 8.36 1.1" dm2.4 -> pA 137mm
BU 314 Lep 5.9, 7.5 0.9" dm1.6 -> pA 145mm
42 Ori (DA 4) 4.6, 7.5 1.0" dm2.9 -> pA 152mm
Upsilon Gru (BU 773) 5.70, 8.24 0.9" dm2.54 -> pA 170mm
BU 603 Leo 5.97, 8.53 1.0" dm2.6 -> pA 155mm

-> According to the pA numbers 15 Boo and Ups Gru should have been the most difficult but all observations are within a reasonable pA range

...
Second list, doubles where the 2ndry star falls on or about the first bright ring. Again, culled after the event from a couple of years' observing. The standout here is a dm 2.85 pair (BU 1190); otherwise, dm is generally 2.0 to 2.5. Without the diffraction ring I'd expect to have found doubles split with dm 3.5 to 4 at this separation, because these are wider (1.3"-1.6") than the first list (0.9"-1.1").

near or on 1st bright ring
BU 1190 Ori 6.95, 9.81 1.4" dm2.85 -> pA 148mm
STT 145 Gem 7.3, 9.9 1.5" dm2.6 -> pA 138mm
BU 91 Tau 8.1, 10.6 1.5" dm2.5 -> pA 150mm
47 Tau (BU 547) 5.05, 7.32 1.2" dm2.27 -> pA 124mm
Theta Gru 4.45, 6.60 1.5" dm2.15 -> pA 99mm
BU 281 Psc 7.4, 9.4 1.6" dm2.0 -> 110mm
BAS 3 Tau 6.16, 8.2 1.3" dm2.0 -> 120mm
BU 1089 Oph 6.57, 8.98 1.5" dm2.4 -> 116mm

-> most of these pairs should have been rather easy and be possible with smaller apertures

The easiest of these were, unsurprisingly, BAS 3 and BU 281 (160x); the hardest was BU 1190 (285x).
...
I also have examples of pairs wider than the first diffraction ring, with larger delta-m. The second dark interspace for 140mm is ~1.83"; the 2nd bright diffraction ring centred at 2.2". Here are some pairs separated 1.7" to 2.0", with delta-m of 3 or more.

A 146 Vir 7.31, 10.77 1.7" dm3.5 -> pA 164mm
RST 690 Cir 6.7, 9.8 2.0" dm3.1 -> pA 121mm
BU 15 Ori 7.44, 11.6 2.0" dm4.15 -> pA 188mm
Kui 17 Tau 4.26, 7.85 1.8" dm3.6 -> pA 118mm
STF 562 Tau 6.82, 9.94 1.9" dm3.1 -> pA 129mm

-> A146 might have been a bit of a challenge but certainly doable and BU15 is an extraordinary observation with 140mm - congratulation. The other pairs should have been rather easy

These required varying magnifications, typically 230x-285x, though when seeing was best some were visible at 160x.

...

Fred, thanks for these report - I have added all these observations to my data set. Interesting the range from pA 99mm to pA 188mm given your impression that all of these doubles were on the 140mm limit. May be you can revisit some of these doubles with seemingly extreme low or high values if you find a difference how difficult resolution is.
Wilfried

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Re: Overall RoT Performance [Re: WRAK]
#6070466 - 09/08/13 11:47 PM

Wilfried, thanks for running the RoT numbers on these doubles. More of a mix than I'd originally thought, although I could see that some were less difficult than others at the time of observation. In particular, some of the "1st bright ring" pairs I suspected were very much subject to seeing conditions. There I'll stay with BU 1190 as being of high difficulty; BU 91 on the numbers is similar, but on the night, conditions made it slightly less difficult.

Generally, I thought the first list was a good listing of "limit" observations, though as usual the seeing conditions at the time will affect what happens. However I'll stay with my estimation that 42 Ori and Upsilon Gruis were the two most difficult pairs for 140mm. Both required 8/10 seeing, with any significant unsteadiness they became uncertain. In the case of Upsilon Gru, I had observed it with a 7-inch (178mm) refractor years ago, and thought it fairly difficult then - requiring 330x for certainty on a quite steady night. I was surprised that the 140mm managed it - the same night I had looked at Theta Gruis, and noticed it was straightforward, so I tried nearby Upsilon, knowing it was a lot tighter and had larger delta-m. Theta I agree is not a "limit" example for 140mm.

The third list - BU 15 in Orion was difficult, but I'm wondering if we have a too-faint magnitude for the secondary. And, looking up Burnham's own catalog, I confirmed that he discovered it with his 6-inch refractor; and the separation record suggest it hasn't changed since his time, although the PA is slowly changing. Burnham also lists a mix of magnitude estimates for the secondary star, three of the four being brighter than the number currently listed. So it might be not as tough as the numbers suggest. Maybe 11.6 is a typo for 10.6?
A146 Vir is I'd say pretty much a "limit" observation for 140mm, and there I think the numbers are accurate.

I am planning to re-visit various of these in the future. Some of them I'll try again with 140mm, others I want to attempt with the SCT (235mm) to see how the bigger aperture plus large CO affect the view. I don't have enough comparisons available yet, for doubles that were difficult for 140mm.

I'll add a couple more observation results here. One that surprised me, though the numbers appear to be fine, is BU 1052 Ori - mags 6.68 and 8.22, at 0.6" (!!) - seen elongated at 400x with 140mm in 8/10 seeing.

Another - I've looked at 46 Virginis (AGC 5) with both telescopes, and it was marginal/uncertain in both, not helped by the seeing on those nights. I'm planning to re-visit 46 Vir - mags 6.18, 8.78 at 0.7". Delta-m of 2.6 makes it tough. It appears to be a very long-period binary, that's been closing, more rapidly in recent times. The small number of measures I have on hand give 1.3" in 1876 (discovery), 1.1" in 1970, 0.8" in 1991, 0.7" in 2005. The PA is slowly increasing. So on the measures recorded, it's not likely any wider than 0.7" at present. It's also on the Haas project list, where successful observations with 7-inch and 8-inch scopes are listed.

Overall, one of my intentions for the three lists was to see if there was a pattern that reflected the reduced visibility effect in the area of the first bright ring. Although that shows, I'll need to find some pairs of greater delta-m where the secondary is on the ring. As well, more observations for all three categories would be useful; that means making lists of further unequal doubles at various separations and concentrating on those. And I'll hope that I don't get too many Gamma Equulei type conundrums as a result.

Edited by fred1871 (09/09/13 12:44 AM)

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Re: Overall RoT Performance [Re: fred1871]
#6070734 - 09/09/13 06:29 AM

Fred, the first ring for a 140mm scope should be around 1.35". Here is a list with doubles with separations 1.3-1.4" and delta_m's larger 2 up to 4:
ID Name RA Dec M1 M2 Delta_M Con
WDS04209+1352 BAS3, BD+13 00665 04h 20m 52,7s +13:51:52,1 6,16 8,2 2,04 Tau
WDS02037+2556 STF208, IDS01580+2527, BDS1074, ADS1631, BD+25 00341 02h 03m 39,3s +25:56:07,6 5,82 7,87 2,05 Ari
WDS12136-3348 HWE72, IDS12084-3314, CD-33 08257 12h 13m 36,8s -33:47:34,6 6,48 8,55 2,07 Hya
WDS16200-6439 I15, IDS16107-6424, CP-64 03442 16h 20m 00,5s -64:38:55,7 6,84 8,95 2,11 TrA
WDS07310-0210 A1967, IDS07259-0157, ADS6147, BD-01 01745 07h 30m 59,1s -02:09:53,4 7,2 9,33 2,13 Mon
WDS17406-3539 DAW148, IDS17339-3535, CD-35 11803 17h 40m 36,5s -35:38:53,5 7,82 9,96 2,14 Sco
WDS19134-1427 BU138, IDS19078-1437, BDS9106, ADS12168, BD-14 05333 19h 13m 25,8s -14:26:49,3 7,81 9,96 2,15 Sgr
WDS21555+6519 STT457, IDS21529+6450, BDS11391, ADS15467, BD+64 01607 21h 55m 31,0s +65:19:14,9 6,01 8,17 2,16 Cep
WDS04294+2433 LEI4 04h 29m 23,7s +24:32:59,9 7,55 9,77 2,22 Tau
WDS19313-0207 D20, IDS19260-0220, BDS9365, ADS12538, BD-02 05024 19h 31m 15,8s -02:06:36,7 7,22 9,58 2,36 Aql
WDS17557-3034 I1011, IDS17493-3033, CD-30 14939 17h 55m 45,0s -30:34:18,0 7,63 10 2,37 Sco
WDS20229+4259 HO128, IDS20195+4240, BDS10180, ADS13786, BD+42 03721 20h 22m 55,5s +42:59:00,4 6,41 8,82 2,41 Cyg
WDS22139+7228 A895, IDS22119+7158, BDS13616, ADS15781, BD+71 01116 22h 13m 52,3s +72:27:55,2 7,91 10,36 2,45 Cep
WDS16413+3136 STF2084, IDS16375+3147, BDS7717, ADS10157, BD+31 02884 16h 41m 17,5s +31:36:07,0 2,95 5,4 2,45 Her
WDS11073-4238 HJ4409, IDS11027-4206, CD-41 06343 11h 07m 16,7s -42:38:19,3 5,24 7,73 2,49 Cen
WDS05145-1823 B1943, IDS05101-1830, BD-18 01035 05h 14m 29,0s -18:23:06,4 7,86 10,4 2,54 Lep
WDS06344+0318 A2673, IDS06291+0323, ADS5202, BD+03 01304 06h 34m 21,7s +03:18:23,3 7,44 9,99 2,55 Mon
WDS01036+6104 BU396, IDS00575+6032, BDS543, ADS868, BD+60 00157 01h 03m 37,0s +61:04:29,4 6,06 8,62 2,56 Cas
WDS03421-1709 HU436, IDS03375-1728, BDS1830, ADS2706, BD-17 00715 03h 42m 04,1s -17:08:45,3 7,84 10,41 2,57 Eri
WDS23288-0050 A896, IDS23236-0123, BDS13647, ADS16781, BD-01 04440 23h 28m 46,2s -00:50:08,2 7,98 10,59 2,61 Psc
WDS13544+2955 STT272, IDS13499+3024, BDS6671, ADS9051, BD+30 02461 13h 54m 25,5s +29:54:56,3 7,56 10,18 2,62 CVn
WDS07378-0236 A534 07h 37m 48,9s -02:35:49,4 7,94 10,61 2,67 Mon
WDS04312-7838 I472, IDS04364-7850, CP-78 00145 04h 31m 09,9s -78:37:58,6 7,96 10,67 2,71 Men
WDS19535+2405 DJU4, IDS19492+2349, BD+23 03820 19h 53m 27,7s +24:04:46,6 4,63 7,37 2,74 Vul
WDS15166-6054 B1777, IDS15085-6032, CP-60 05698 15h 16m 36,7s -60:54:14,4 5,79 8,55 2,76 Cir
WDS23208-5018 RST5560, IDS23152-5051, CD-50 13948 23h 20m 50,1s -50:18:23,0 6,15 8,93 2,78 Gru
WDS05574+0002 BU1190, IDS05523+0001, BDS3069, ADS4542, BD+00 01227 05h 57m 25,3s +00:01:39,1 6,95 9,81 2,86 Ori
WDS03428+0754 STT61, IDS03374+0735, BDS1828, ADS2709, BD+07 00537 03h 42m 45,9s +07:54:10,6 7,77 10,63 2,86 Tau
WDS05528-3832 I16, IDS05494-3833, CD-38 02270 05h 52m 47,7s -38:31:33,6 6,88 9,76 2,88 Col
WDS01125+0228 STT27, BDS643, BD+01 00223 01h 12m 30,6s +02:28:17,6 6,54 9,5 2,96 Cet
WDS13101+3830 BU608, IDS13051+3904, BDS6410, ADS8805, BD+39 02611 13h 09m 42,0s +38:32:01,9 6,26 9,23 2,97 CVn
WDS23244+1429 BU719, IDS23194+1356, BDS12346, ADS16735, BD+13 05105 23h 24m 23,9s +14:28:44,9 7,65 10,68 3,03 Peg
WDS07059-0101 CRJ1 07h 05m 52,8s -01:01:13,6 5,98 9,11 3,13 Mon
WDS06544+2110 STT160, IDS06484+2117, BDS3681, ADS5553, BD+21 01426 06h 54m 21,3s +21:09:40,8 6,66 9,92 3,26 Gem
WDS17039+1941 BU822, IDS16595+1950, BDS7847, ADS10323, BD+19 03218 17h 03m 52,7s +19:41:25,8 6,58 9,89 3,31 Her
WDS03346-3152 B53, IDS03306-3213, CD-32 01358 03h 34m 33,6s -31:52:29,3 6,6 9,93 3,33 For
WDS19502-1000 RST4643, IDS19447-1016, BD-10 05195 19h 50m 09,8s -10:00:25,7 6,91 10,26 3,35 Aql
WDS04339-0644 BU881, IDS04290-0657, BDS2268, ADS3305, BD-07 00838 04h 33m 54,7s -06:44:20,1 5,72 9,19 3,47 Eri
WDS03027-0741 BU11, IDS02578-0805, BDS1549, ADS2312, BD-08 00568 03h 02m 42,3s -07:41:07,7 5,4 8,9 3,5 Eri
WDS13328+2421 A567, IDS13281+2452, BDS6523, ADS8937, BD+25 02643 13h 32m 48,2s +24:20:48,3 6,21 9,71 3,5 Com
WDS17420+1557 BU1251, IDS17375+1600, BDS8120, ADS10723, BD+16 03256 17h 41m 58,6s +15:57:07,8 5,59 9,38 3,79 Her
WDS09087-0835 KUI38, IDS09038-0811, BD-08 02588 09h 08m 42,2s -08:35:22,2 5,6 9,47 3,87 Hya
WDS23190-0937 HO199, IDS23138-1010, BDS12289, ADS16671, BD-10 06094 23h 18m 57,6s -09:36:38,6 5 9 4 Aqr
All these doubles should be doable with 140mm but some may be already rather difficult (pA up to 180mm).
Wilfried
PS: Did not check if any of these doubles were already in your observation reports

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RoT Gracious Behavior Analysis [Re: WRAK]

I know that there has to be some bumpy behavior of the current algorithm as I use several logical switches to set the different parts of the model in action (for M1>6, M2>9, ...). To check this assumption I made a set of fictive observations with incremental changes for all involved parameters. The result can be seen in the graph with to my surprise only - to my surprise there is only one real bump to see and this occurs when the M1>6 switch gets active. Will have to make this smoother in a next version.
Wilfried

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Re: Overall RoT Performance [Re: WRAK]
#6072480 - 09/10/13 01:17 AM

Wilfried, that's quite a list of doubles around 1.3"-1.4". Some of them I'll ignore - they're too far north to be above my horizon, ever, where I live at present; and some others have declinations that will keep them too low in the sky. That still leaves quite a few.

A comment on two of them. First, RST 5560 in Grus (23208-5018). It's part of the easy pair, DUN 248 - I have notes on the Rossiter pair from 7-inch refractor days; it wasn't too hard with that telescope, seen double at 180x, despite delta-m of 2.8 at 1.3". I'll try it again with the 140mm.

The other, HO 199 (23190-0937) is on my list to observe, and if clouds had stayed away a couple of nights ago I'd have tried it already. The delta-m is 4.0 at a listed 1.4" - problem is it's a 1962 measure, and nothing newer is listed, so this is a neglected pair. The photometry is old as well, single-decimal magnitudes. The WDS summary indicates a changing PA, 57 degrees in 78 years - extrapolating (linear) suggests ~37 degrees less, so ~130; separation may have slightly increased, but the change 0.2" is within possible errors of measurement and rounding. It'll be interesting to check it. Hipparcos appears to list it as single (hence no 1991 measure) and gives ~5.00 as the V magnitude. Because there are 14 measures listed I'd expect this to be a genuine pair. The possibility exists of course that it may have taken to rapid change between 1962 and 1991, but with a parallax of 13mas it'll be 250 ly away, so rapid change is less likely - 1.4" is a big orbit at that distance (projected 100+ AU separation). Not impossible, of course - depends on which part of the orbit it's in, and line of sight angle.

Again, thanks for the list - I can see a few objects not on my current lists, and several others I need to re-visit.

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
#6121395 - 10/06/13 10:07 PM

Quote:

I've had the experience of observing a double star that another experienced observer could not see, same time, same telescope, same eyepiece. The two of us looking alternately. To me the companion was fairly obvious; to him it was invisible, then after "look in this position" it was "maybe I can see it". So we have the observer factor as well. Some observers will need a bigger telescope, or higher power, or more practice on doubles.

this is perhaps the most important and fundamental point.

observer aside, wilfried's comment that different rules have to be applied in different contexts (the rayleigh criterion with this pair, some other criterion with that pair) is just a statement of the blind man and elephant problem: there's a complex landscape of visual targets, which present very different resolution problems to the eye. one size rule can't fit all.

i have never understood the claim that a resolution rule or resolution limit of any kind can "tell me whether i can resolve a binary or not", when the only way to know if you can resolve a binary or not is to try.

one way to understand the problem is that any "rule of thumb" is actually going to suggest to you *how to look*. an experienced observer uses different observing strategies or tricks depending on the visual challenge, and presumably the quality and degree of the challenge is all that a rule of thumb can tell you. thus, a rule such as "in this situation, use the rayleigh criterion" is not how observers think: the operative rule is more like "in this situation, use averted vision" or "move attention around the object, and let seeing help your acuity" or "pile on the magnification". experienced observers don't really need these kinds of rules, because judgment integrates rules into insight.

if i remember correctly, this thread began from a "rule of thumb" that i suggested, and if i remember correctly it was just the resolution limit (whichever of the many resolution limits you prefer) multiplied by any magnitude difference greater than 1. (the various studies i have looked at suggest a better rule is the resolution limit multiplied by half the magnitude difference; a magnitude difference of 3.0 means resolution should be expected at 1.5 times the resolution limit of a matched pair.) in practice, i use rules such as this basically to interpret catalog data and decide how long i will persist in the attempt.

the underlying problem is that the catalog data are variously unreliable, especially for the infrequently measured ("neglected") doubles. that embarks us on the search for a rule of thumb for when to use the rule of thumb.

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Re: Putting the "Rule of Thumb" to test [Re: drollere]
#6121787 - 10/07/13 06:54 AM

Bruce, nice to hear from you again.
Since this thread started we have discussed most of the existing concepts for a RoT for resolving unequal binaries - and more or less dismissed all of them, especially the deterministic ones for reasons you mention and others as well.

The current state of affairs is a probability model based on statistical analysis (least square nonlinear regression) of a data set of limit observations.
The current model uses the following parameters: separation, delta_m, magnitude of primary, magnitude of secondary, central obstruction, degree of light pollution in terms of Naked Eye Magnitude Limit and a final check against Telescope Magnitude Limit.

Result is a proposed aperture for a fair 50% chance for resolution with the assumption of reasonable good seeing and average personal acuity.
The advantage of this approach is then a known standard deviation allowing calculation of probabilities for smaller or larger apertures.

This approach allows to cover all other factors not included in the algorithm per probability - errors in advertised data, variations of seeing, acuity, experience and so an. So far the results are promising especially in the aperture range from 30 to 140mm I could cover with my own equipment using iris diaphragms.
Current weak points are larger apertures and larger values of CO but I have plans to cover at least the range up to 200mm also myself soon.
Wilfried

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RoT and glare [Re: WRAK]
#6188005 - 11/11/13 04:45 AM

My recent attention to the topic of aerosol diffusion (low transparency due to haze) with the effect of enhancing the halo around brighter stars made me aware that I have so far ignored the effect of glare on resolving unequal doubles. This was more or less intentional as I think the number of doubles in this category is rather small and resolving of such doubles is less a question of aperture but used methods like for example occultation.
A minimum size of aperture is certainly needed depending on the usual parameters like separation, magnitude of the secondary and delta_m but may be some extra mm in aperture are needed to have a better chance seeing the companion through the halo. Only if the companion is fainter than the halo even with perfect transparency then resolution with direct vision might be impossible.
Will consider to add a glare module to the RoT algorithm.
Wilfried

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RoT Field Test [Re: WRAK]

The recent RoT "discussion" with Bruce motivated me to post my current set of limit observations to make it public use for RoT field tests.

In total there are now about 300 observations made by me with an iris on my 140mm refractor to be able to change the aperture on the fly. To this set I added about 150 observations found in books and on this board (observer given in parantheses after the name of the object) with fixed apertures but with descriptions proposing limit or near limit observations.

As benchmark I added the results of my current RoT algorithm based on statistical analysis of a small subset (about 20%) of the current base plus a number of observations listed by Lord in his paper on resolving unequal binaries meanwhile eliminated from the data set because considered not this reliable for my purpose.

With the small data set my RoT had a correlation coefficient of 0.932 and a standard deviation of ~14mm and as we have now a much larger data set we can consider this also as good field test for it - with the full current data set the correlation coefficient is 0.913 and standard deviation is ~19mm. This means that there is some degradation to notice indicating that there is room for improvement but this I knew from the very beginning as the first data set for statistical analysis was far too small and the model itself contains some known shortcomings.

I intend to do statistical analysis again with the meanwhile much larger data set but want also to wait for another scope giving me the opportunity to cover the range of apertures up to 200mm myself also with variable aperture.

Finally I want to stress the fact that this data set (while it may include some errors unavoidable with such a number of observations) is the only one I know consisting mainly of "real" limit observations done with variable aperture and is thus a perfect base for field tests for any other RoT concepts. Feel free to do your own calculations.
Wilfried

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Putting the RoT to test – state of affairs [Re: WRAK]
#6431723 - 03/27/14 05:29 AM

Current state of affairs:
- Mr. Royce has now started the production of my 8" DK scope. This means that from about mid summer I should be able to cover the aperture range up to 202mm myself. After a sufficient number of observations in the range 150 to 200mm aperture (with a reasonable range of central obstruction between 0.25 to 0.33) I will then redo the statistical analysis with some adaptions of the model structure. Looking forward to it
- I have started now to repeat sessions several times if possible (though I had few opportunities to do so lately) to get a wider range of limit observations to cover better the spread reality of required minimum apertures for resolving a given double. This also means that I no longer consider a small standard deviation as quality parameter for my RoT algorithm – to target is not to get it as small as possible but as realistic as possible
- A realistic target seems to be to that the RoT value minus the 3-fold standard deviation should be the "competitive" lowest possible value for ideal conditions with nearly 100% of all observations above this value. For the simple case of equal bright doubles up to +6mag we have found by experiment this "hard" limit of resolution defined as observation with confident correct estimation of the position angle to be at about 0.5 Rayleigh or 0.6 Dawes criterion. This means that the standard deviation should be around 14-16% to match this range. A RoT value of for example 100mm would then mean that the realistic lowest required aperture assuming perfect conditions would then be 60mm and that even under not this good conditions 140mm should be enough (but with unavoidable possibility of non resolution with really bad conditions)
- I am now aware of an unavoidable bias in my data set as the registered observations in the upper range of used apertures by me plus the addition of difficult "third party" observations with fixed apertures tend to reduce the recorded spread compared to reality. I have currently no idea how to handle this and tend to ignore it – with a reasonable large total number of limit observations this effect will hopefully be neglectable
- It is certainly no longer correct to assume a symmetrical deviation around a RoT mean value as the negative deviation is definitely limited by laws of optics while the positive deviation is defined by seeing conditions and basically open ended as there are situations where no amount of aperture will allow resolution. But as working hypothesis it might be sufficient to stay with the assumption of a symmetrical standard deviation to avoid too much complexity in the RoT model
- But important to note: This asymmetry seems to get stronger with increasing faintness of the companion – a tad of haze in combinaiton with some light pollution is enough to eliminate a faint star against the background, so the threshold for non resolution is for faint stars much lower than for bright ones. Thus I have started to record the current telescope magnitude limit at the beginning of each session in the field of my target area on a regular base. If my current TML is for example +11.8mag for my 140mm refractor it is futile to try to resolve a companion of +12mag regardless separation. Next day with for example TML of +12.2mag I might at least try if wide enough. So far no idea how to handle this.
Wilfried

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Reged: 02/02/10

Loc: sebastopol, california
Re: Putting the RoT to test – state of affairs [Re: WRAK]
#6433559 - 03/28/14 12:07 AM

wilfried, i hope your new royce scope is everything you expect. i found i had to make several "improvements" to mine in order to get it operating effectively.

i will say, the effect of the first magnitude ring shrinking in diameter with a fainter star (smaller airy disk) appears most clearly in my royce DK, so i'll be curious if you notice it -- del CYG is a really unmistakable example of it.

i think i commented in another thread on your RoT analysis, but i'll mention again that a correlation coefficient gives you no information on the validity of a level sensitive prediction, because you can simply double or triple all the predicted scores and get exactly the same correlation with the observations you want to predict.

the problem with the TML is interesting, because it is really a visual and not an instrument parameter. for example, the standard calculation for it requires you to put in your pupil aperture PA and your naked eye magnitude limit, which is just assumed in the aperture based formula:

2.61 + 5*log(D) ... is really .... NEML - 5*log(PA) + 5*log(D)

in particular, i am unsure how aperture interacts with a physiological limit like this, because the physiological limit being predicted here is your averted vision (rod) threshold, whereas the limit of interest to a double star astronomer is the foveal threshold, and not just for detection but for small interval angular resolution. this means the other complicating factor is magnification, which reduces image brightness as it increases angular scale.

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6433752 - 03/28/14 06:31 AM

Quote:

... the problem with the TML is interesting, because it is really a visual and not an instrument parameter. for example, the standard calculation for it requires you to put in your pupil aperture PA and your naked eye magnitude limit, which is just assumed in the aperture based formula:

2.61 + 5*log(D) ... is really .... NEML - 5*log(PA) + 5*log(D) ...

Bruce, this is an interesting topic indeed and there is more in it but NEML, PA and D because with the same values for these parameters I get different "current" (means observed) magnitude limits. This might be also a problem with the reliability of advertised magnitudes for faint stars but mainly I think this has to do with transparency. A tad of haze has as far as I have observed no real effect on NEML (at least it would be hard to measure) but certainly an effect on the telescope magnitude limit as haze leads to some spread of the light of the star and the given brightness is then related to an area instead of a single point.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6433774 - 03/28/14 07:06 AM

Quote:

... i think i commented in another thread on your RoT analysis, but i'll mention again that a correlation coefficient gives you no information on the validity of a level sensitive prediction, because you can simply double or triple all the predicted scores and get exactly the same correlation with the observations you want to predict. ...

Bruce, yes that's correct ... but then the standard deviation as the second quality parameter will explode. If the model with the best correlation coefficient has also the smallest standard deviation it is at least from a statistical point of view to prefer.
Wilfried

 Post Extras:
WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6436023 - 03/29/14 12:35 PM

Quote:

wilfried, i hope your new royce scope is everything you expect. i found i had to make several "improvements" to mine in order to get it operating effectively.

i will say, the effect of the first magnitude ring shrinking in diameter with a fainter star (smaller airy disk) appears most clearly in my royce DK, so i'll be curious if you notice it -- del CYG is a really unmistakable example of it...

Hope for the best regarding the 8" DK and will have a look at Del Cyg with it to check this impression.

Wilfried

 Post Extras:
WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: WRAK]

My data set of limit observations has now grown to ~620 lines - to my regret still most of the observations below 140mm as my 8" Royce DK is still in production (will hopefully come in time for the observations of Delta Cyg to countercheck Bruce's impression regarding seemingly different diameter of first ring of primary and secondary).

Statistical analysis without changing the structure of the model resulted in somewhat different parameter values but else rather similar results compared with the analysis with about only ~130 limit observations. But the overall statistical quality of the model got somewhat worse with a correlation coefficient of now only 0.914 compared to earlier ~0.945. This seems a confirmation of my impression that several components of the model have to be enhanced to get better results.

Attached is a graph showing the relation between used apertures and proposed apertures - up to 140mm this seems rather straight forward. With 140mm we come into the realm of fixed apertures with enlarged spread due to the fact that we have to accept observations being on the "limit" because we have this impression but no proof for it.
We see the same effect with 150mm - here additonally with one obviously extreme overperforming observation.
Especially "off" are my own seriously underperforming 235mm observations. This might have several reasons working in combination:
- model does not work really good with large CO (in this case 0.38) as I know already
- seeing in my locations is usually not good enough to come near the optical potential of this scope (had it tested in an optical labor with a very good 0.95 Strehl result)
- collimation might be an issue as I have never seeing good enough to secure perfect collimation
- I do not like this scope very much for observing of close doubles so my own performance might be questionable here.

Overall I think this result is a good argument for my impression that fixed aperture observations are no good base for any serious conclusions regarding aperture limits for resolving doubles.
Wilfried

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