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fred1871
professor emeritus


Reged: 03/22/09

Loc: Australia
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: WRAK]
      #5616085 - 01/10/13 07:16 PM

Wilfried, you're correct in noting the uneven change in light distribution in the various rings as CO increases. I was careless in the wording. Essentially, the first ring continues to brighten with light transferred from the disc, with increasing CO, but the other rings vary in how much energy is transferred to them individually as CO increases. Nevertheless, total energy transfer increases in proportion to CO.

To look at an aspect of the details of that energy transfer - Rutten and van Venrooij give some overall figures for CO figures of zero, 0.25, and 0.50. The first ring gets 7% of the light with 0 CO, 18% with 0.25 CO, and 35% with 0.50 CO.

The total for the other rings is interesting - 9% for 0 CO, 9% for 0.25 CO, and 17% for 0.50 CO. The changing pattern can be seen in pictorial form in Suiter and other references. I'm also thinking that it's reflected in the contrast transfer graphs that show the effect of different obstruction ratios, as these show some differences in pattern with different obstruction ratios - though that's currently just a speculation on my part.

Lord's table is useful for estimating delta-m limits for different obstruction ratios. In this regard it provides another version of what Treanor did. That Lord thinks Treanor's modification of Rayleigh "was much too optimistic for very unequal pairs resolved using large telescopes" is essentially what Treanor himself said - hence Treanor's dividing line around 15-inches aperture, and recognition that seeing reduces large telescope effectiveness more than small telescope effectiveness.


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Asbytec
Guy in a furry hat
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Reged: 08/08/07

Loc: La Union, PI
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: fred1871]
      #5616647 - 01/11/13 03:53 AM Attachment (20 downloads)

This thread and pursuing difficult doubles has taken me deeper into the diffraction pattern. It's a very interesting subject, a learning experience. Some folks might be embarrassed, but I actually found some answers about what I am seeing at the smallest scales: confusion over where the second and third rings really are and what they look like.

For the longest time, I had wondered what those very thin, fairly bright dancing arcs of light were just outside the first ring. They had not the form of the first ring, nor the visible fourth ring. They are very thin and often just dancing thin arcs of light. I had always thought they might have been some sort of noise in the optic, some blur or artifact of spherical aberration, maybe contributing to some sort of Hairy Disc. So, not recognizing them as part of the pattern (just garbage), I assigned the second ring to the fourth position and assumed the second minimum was further out than it really is.

The second and third ring are extremely hard to see well, any amount of seeing disrupts them easily. The fourth ring, too, because it's broader and somewhat dim. I had only seen them once as distinct rings, the inner second ring slightly brighter than the third (prior to my CO modification.) Anyway, below is somewhat to scale of what an .3D obstructed scope pattern looks like (I am sure you've seen them.)

But, for me, the striking thing was the change in scale I have to adjust to. The rings are so very close together, and not as widely separated as I had thought. When observing a star with less than 2" arc sep, it appeared way too close to the first ring. Now, I know why. This is a learning curve provided by studying difficult double stars, and that's an interesting aspect of this type of observation. So, I discovered I had been mistaken at times. Cool.

Anyway, I think the image below (Aldebaran) is almost to scale. The radii are taken from the following link.
http://www.telescope-optics.net/obstruction.htm


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WRAK
scholastic sledgehammer


Reged: 02/18/12

Re: Refractors vs SCTs and Maks for uneven doubles new [Re: Asbytec]
      #5616709 - 01/11/13 05:28 AM

Norme, the numbers on your image are arcseconds I assume?
A simulation with the AtmosFringe program shows the effect of a smaller Airy disk and a "fatter" first ring due to CO very clearly - but this is still theory. I will try to get an empirical measurement for a 30% obstruction (compared to zero) by an optical labor.
Wilfried


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Asbytec
Guy in a furry hat
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Reged: 08/08/07

Loc: La Union, PI
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: WRAK]
      #5616714 - 01/11/13 05:45 AM

My apologies, yes, in arc seconds. I am trying to get a feel for double separation.

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fred1871
professor emeritus


Reged: 03/22/09

Loc: Australia
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: WRAK]
      #5618269 - 01/12/13 12:09 AM

Wilfried and others - I've posted brief observing notes on two more of the doubles from Wilfried's list of Taurus doubles - the note is in the thread on Taurus doubles.

In both cases the suggested aperture was greater than what I used. So these might help in providing further data points.

I'm still working on making a central obstruction for my refractor, with thin support arms. That will allow comparing unobstructed versus obstructed views with the same optics, eyepiece, observer, seeing....


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WRAK
scholastic sledgehammer


Reged: 02/18/12

Re: Refractors vs SCTs and Maks for uneven doubles new [Re: Gord]
      #5632641 - 01/20/13 04:45 AM Attachment (11 downloads)

After adding some observation reports from Norme and the reflector observations from Lords paper on "Resolving unequal binaries ..." with assumed CO of 28% for 150mm and 33% for 254mm scopes to my data set I modified my RoT model to include the influence of CO. While the statistical quality of the data set is still by far not good enough there is an interesting intermediate result as the uploaded image shows for the example of a fictive double with 1" sep and increasing delta-m starting with m1=5 and m2=6: The reflector with CO33% has an advantage up to a delta-m of 2 and then the reflector takes over. So if your topic are close doubles with small differences in brightness then the reflector is your choice - if you are ready to handle topics like collimation, coma, thermal issues, dew ...
Wilfried


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Asbytec
Guy in a furry hat
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Reged: 08/08/07

Loc: La Union, PI
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: WRAK]
      #5632724 - 01/20/13 08:07 AM

Wilfried, so that's fascinating. For close nearly equal pairs the obstructed aperture has an advantage with 1" sec separation. It's interesting that the change occurs up to about 150mm aperture, that's approximately the aperture where 1" separation roughly equals the Raleigh limit.

For example, with 5/6 mag pair at 1" arc separation, the required obstructed aperture looks to be about 102mm while unobstructed aperture seems to require closer to 115mm. An 0.33D obstructed 102mm scope has an Airy disc approximately 138/102 = 1.3" arc in radius and a Dawes limit at 116/102 = 1.1" arc. Reduced for the CO by about (1-o^2) ~ 89%, Raleigh limit is 1.2" arc and Dawes is 1.0" arc with a perfect aperture. The first ring is near 1.8" arc.

So, these appear to be Dawes splits a 102mm clear aperture is incapable of.

What's interesting is how this changes with the magnitude of the companion. For example, a 350mm scope has a Raleigh limit of 126/350 = 0.4" arc and a Dawes limit ~ 0.3" arc. It is certainly capable of a tighter split, but it's first ring lies at about 1.16 * 550 * 0.206/D = 183/350 = 0.5" arc. A second ring is at 2.73 * 550 * 0.206/D = 309/350 ~ 0.9" arc. So, it appears for 1" arc split, the (brighter) rings begin to interfere with the faint companion in an obstructed aperture.

Surely, at an intermediate aperture (about 180mm), the brighter first ring would interfere at 1" arc with a somewhat brighter companion. That seems to occur near delta Mag of about 3 or so. In this zone, it appears the dimmer ring structure of a clear aperture allows easier detection in smaller scopes.

As delta Mag falls, we need a larger obstructed scope for the same 1" arc split. Presumably, this is because the outer diffraction ring brightness is less, due to the reduced angular diameter of the Diffraction pattern, and possibly equaling the apparent "brightness" of a smaller clear aperture with fainter (if larger) ring structure. In other words, for a 1" split, the scope needs it's first or second ring to be within that 1" angular radius at larger delta mag, a clear aperture can manage it with less energy in those same rings.

Interesting. Excuse the math and thinking out loud. I'm still absorbing what this graph might be telling us.


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fred1871
professor emeritus


Reged: 03/22/09

Loc: Australia
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: WRAK]
      #5633879 - 01/20/13 08:20 PM

A very interesting graph, Wilfried. I'm a little surprised that the turnover point is at delta-m of 2 magnitudes - I'd have expected somewhere closer to 1 magnitude, at least for telescopes with larger (33% diameter) central obstructions.

A question - why have you set the CO for 254mm at 33% ? This would be unusual for a Newtonian unless of short focal ratio. Lord's 10 1/4-inch reflector mentioned in his paper is of long focal ratio, therefore is likely to have a smaller CO.

More thoughts when I've studied the graph further. Though I suspect there are issues it'll show with regard to the 1" separation, related to varying apertures; rings differentially affect different apertures for the same separation (does the secondary star fall on a ring or a space for a given aperture). I read Norme's comments as partly relating to this.

And I now have some more observations of difficult doubles; data on those soon.


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Asbytec
Guy in a furry hat
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Reged: 08/08/07

Loc: La Union, PI
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: fred1871]
      #5633928 - 01/20/13 09:06 PM

Fred, it is an interesting question. I failed to split an unequal pair (BU1040) where the companion was 3.5" arc as sat on my 4th ring. Curiously, the 4th ring was certainly not visible, so it appears there is more at work than the visual threshold. Also, at each minimum there is a bit of destructive interference occurring from the primary. I wonder if it affects the companion's brightness. Something causes the MTF beyond the first ring to have a constant slope, it's not lumpy at each ring's spacial frequency.

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azure1961p
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Reged: 01/17/09

Loc: USA
Re: Refractors vs SCTs and Maks for uneven doubles new [Re: Asbytec]
      #5634199 - 01/21/13 12:12 AM

Very nice work Wilfreid. The shift in scope design advantage is curious and compelling particularly as I've been reading along as this has developed. Great work by all parties involved.

Pete


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WRAK
scholastic sledgehammer


Reged: 02/18/12

Re: Refractors vs SCTs and Maks for uneven doubles new [Re: fred1871]
      #5634432 - 01/21/13 07:40 AM

Quote:

... A question - why have you set the CO for 254mm at 33% ? This would be unusual for a Newtonian unless of short focal ratio. Lord's 10 1/4-inch reflector mentioned in his paper is of long focal ratio, therefore is likely to have a smaller CO...



Fred, the advertised data of this mixed bag of observations point rather to the mid of the last century and these are probably not Lord's own observations but some from the Lewis collection. Another hint are 254mm = 10" aperture. But this would maybe even the more suggest a smaller CO. The reason why I assumed despite this a rather large CO is the heavy overperformance for very close equal bright doubles in relation to the Dawes criterion even when modified for CO. May be the unknown observer even used a trick described by Taylor in Argyle's book on "Observing ..." - intentionally increasing the CO for a better chance to split very close equal bright doubles.
Wilfried


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Asbytec
Guy in a furry hat
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Reged: 08/08/07

Loc: La Union, PI
Re: Refractors vs SCTs and Maks for uneven doubles [Re: WRAK]
      #5634523 - 01/21/13 09:03 AM

STT 517AB, a very close, 7th magnitude pair.
http://www.cloudynights.com/ubbthreads/showflat.php?Cat=0&Number=5634514&...


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