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WRAK
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Reged: 02/18/12

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Re: Size of spurious disk new [Re: Cotts]
      #5648822 - 01/28/13 05:48 PM

Quote:

...Your graph shows a very small difference in disc size from unobstructed (1.22 units - I assume arcsecs? )...



Dave, no units here - numbers used in the grafic show only a relation. Small numbers in terms of separation translates in noticable numbers in terms of required aperture for splitting a double. Sorry that the image is less than precise - relative number for CO 0.3 is actually 1.1. This means that for a close double for example 0.5" the required aperture for reaching the Rayleigh criterion is 138/0.5=276mm for a refractor and 138/0.5/1.22*1.1 for a reflector with CO of 0.3 giving 249mm and this is certainly a significant difference.
Ed - share your frustration with SCTs concerning double star performance but this is maybe at least on my side also a question of personal preference.
Wilfried


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EdZ
Professor EdZ
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Re: Size of spurious disk new [Re: WRAK]
      #5648902 - 01/28/13 06:27 PM

Quote:

Ed - share your frustration with SCTs concerning double star performance




I certainly have no frustration with SCTs for double star performance. In fact, my C5 was without question one of the best scopes I've ever owned and was an exceptional double star performer. I'd put my C6 near the same.

edz


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fred1871
scholastic sledgehammer


Reged: 03/22/09

Loc: Australia
Re: Size of spurious disk new [Re: EdZ]
      #5649096 - 01/28/13 07:54 PM

Quote:

Quote:

Ed - share your frustration with SCTs concerning double star performance




I certainly have no frustration with SCTs for double star performance. In fact, my C5 was without question one of the best scopes I've ever owned and was an exceptional double star performer. I'd put my C6 near the same.

edz




Ed, is that "exceptional" performance to do with near equal pairs or with significantly uneven pairs? The usual view is that large CO makes an unhelpful difference to close uneven pairs due to more light in the rings. Did your observing experience differ from that?


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fred1871
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Reged: 03/22/09

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Re: Size of spurious disk new [Re: Cotts]
      #5649121 - 01/28/13 08:03 PM

Quote: The data in the WDS which we all use to determine separations only go to 2 significant digits in the separation ranges we are discussing here. Consider a WDS separation given as 1.2" This is a rounded figure and could actually be from 1.15" to 1.24", a range significantly greater than the variances in disc diameter vs. CO in your graph. Noisy data, indeed.

Indeed, quite right. It gets worse - there's some noise in the measures as well, even when quoted to two decimal places. It partly depends on the measuring method. Filar micrometers (the old standard) are typically less accurate than speckle interferometry. Speckle can't be used for everything. Other methods have varying average accuracies - and individual measures ditto. So there's potential "noise" (error bars) there as well. Of course, sometimes by chance noise may tend to cancel; sometimes by chance it's additive. So a series of measures at least allows some refinement. Eventually, the calculation of a grade 1 orbit, can reduce noise to very low levels. And wide pairs likewise can have lower noise levels (easier to measure accurately). And, no, I'm not suggesting big errors (big noise) are common.

And now, back to the main game ....


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

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Re: Size of spurious disk new [Re: EdZ]
      #5649488 - 01/28/13 11:31 PM

"Are we to assume the disk edge cannot be seen beyond a point where the light intensity drop below 50% of peak intensity?"

Even the 28% fall off in the Raleigh limit looks black and the Airy discs overlap by half their diameter. Your own math says a reasonably bright star with a visible disc of 60% the Airy diameter needs 60/50 = 1.2 * the Raleigh limit to see a clean, black space. For a 6" aperture, that increases the separation from 0.9" arc to 1.1" arc even if the first ring remains at 1.2" arc. A dimmer star 40/50 = 0.8 * the Raleigh limit or 0.73" arc for the same split (realizing the potential problems with very dim stars in reality.)

It makes sense cutting the PSF at varying levels of visible threshold might barely change the diameter of the visible disc because the slope of the curve changes little until near the peak. Even if the PSF itself is only 8 to 10% smaller at the base. But this implies bright and dim stars are nearly the same diameter, certainly closer than the significant spread between 1.1" arc and 0.73" arc as suggested above. What magnitude spread would be consistent with a 60% and 40% visible disc diameter? I think that is the question. How can one calculate the (ideal or theoretical) diameter of a spurious disc at some standard threshold of visibility, because that will affect the potential for resolution.

It get's complicated because dimmer stars do look smaller, maybe even less than 40% of the Airy disc. A dim star appears as a faint point, not a larger, very dim disc. As I understand taking the eye into account, bright stars (about first magnitude) appear pretty much flat across the central disc while dimmer stars (approaching 6th or 7th magnitude) begin to show some fading near the edge. Dimmer stars, even more so. This fall off is why the Raleigh split works, we can easily see a 28% drop off from the peak. And we can even see the 5% drop off at Dawes giving a dark space.

Now, given even an 8% decrease in the Airy diameter and the fall off from peak intensity, Dawes and Raleigh can both be bested in obstructed scopes (an old Questar ad even prides itself on that fact.) I have matched or beaten the Dawes limit on 7 Tau at it's reported theta, but am not sure how much tighter can be distinctly still be seen as two stars. Surely larger separations that 72 Pegasi at 0.57 or 0.6" arc. I realize we're getting into noise levels, here, and limits of seeing.


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DesertRat
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Re: Size of spurious disk new [Re: fred1871]
      #5649498 - 01/28/13 11:36 PM

Actually the first minimum in an Airy pattern is seen in a close double as it is the defining valley between the spurious disks. Whether or not the CO actually improves detectability (for near equal stars) is tough to say. The numbers say it is so. Seeing however dictates such an overwhelming influence (not to mention other details like eyepieces, visual acuity, etc) that it would be tough to prove.

But if Norme says he has then so much to the good.

The WDS and other catalogues do seem to lack precision. Does anyone know a good source to well defined precise measures for a set of 'popular' doubles? It would have to include orbital elements in some cases, but thats ok.

Glenn


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azure1961p
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Reged: 01/17/09

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Re: Size of spurious disk new [Re: fred1871]
      #5649528 - 01/28/13 11:52 PM

Quote:

Lewis, following Airy (much earlier), gives some of the mathematics in his 1914 paper - along with levels of relative illumination in the diffraction image, etc. Of course, this is for optics without central obstruction.

Norme, the problem of where to slice - that is, what is perceptible to the eye - is I think more of an issue than the nature of the image. EdZ has indicated one aspect of that with his comments on what is seen at varying levels of magnification. In other words - how do you decide/establish "the visual threshold" to know where to slice?




Ahh the slice quandary...

It would seem this becomes a problem not just here with doubles but in resolution limits on a number of fronts, is; planetary contrasts, lines versus disks, light features versus dark and resultant contrast. It would seem when you put the minds microscope up to drawing these finest boundaries and such it hits this ambiguous wall. One you'd normally never find if you never cut the wire that fine.

The slice issue is one of those things that seems to rest quietly till you wake it.

This is a really nice thread. Glad Edz dropped in.

Pete


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Asbytec
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Re: Size of spurious disk new [Re: azure1961p]
      #5649639 - 01/29/13 02:14 AM Attachment (11 downloads)

Pete, apparently this is one of those topics that raises it's ugly head from time to time. I wish I could find the discussion Ed mentioned a few years back. Sorry to have missed it.

Glenn, I'm really curious to know how deep I can get on a split. The challenge is part of the allure of doubles, for me, and the entire journey of discovery has been fascinating. This whole RoT exercise and trying to understand how and why unequal pairs are difficult is so very interesting, too.

I was playing around with the apparent view of 7 Tau (top) and 31 Tau, two very close, nearly equal magnitude, Dawes pairs. The pairs are very close at just over 6th magnitude (approx), too. The sketch below is not far off from actual appearance, to me. I had to make the image small to get the darker space to show accurately as I can. So, 31 Tau is reported at 0.8" (150mm Dawes at 0.8" rounded) arc and 7 Tau at 0.74" arc (0.7" rounded.) So, rounded to one decimal, there is a 0.1" arc difference, otherwise maybe only about 0.06" arc. That's an incredibly tiny amount and still showing some contrast differential (dark, but not black space.)

Still, judging from the difference between the two, I'd bet I could shave off another couple 100th's and get closer to 0.70" arc and still see some contrast fall off between them. Taking the CO into account, Dawes /should/ be closer to 0.77" arc * (1 - 0.28^2) = 0.71" arc (barring aberrations) in 0.28% obstructed 150mm aperture (which is the Sparrow limit for 150mm clear aperture.) So, to me, it seems being able to get closer is a real deal and Wilfried is onto something. A real world observation that seems to agree with the MTF. I find observing something approaching the Sparrow limit fascinating and a challenge worthy of pursuit.

My guess is, accounting for inherent aberration (making close pairs more difficult) and the slightly dimmer pairs observed (making them a tad easier), I might be able to hit about 0.72" arc.

North is left and west is bottom. Seeing was exceptional at about 9/10 on average.

Edited by Asbytec (01/29/13 02:54 AM)


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: Asbytec]
      #5649688 - 01/29/13 04:20 AM

For evidence regarding the performance of refractors and reflectors for splitting equal bright doubles I prefer again sticking to the numbers. Lord lists in his paper (to be found still under http://web.archive.org/web/20111203102746/http://www.brayebrookobservatory.or... ) single observations with 3 and 6" refractor and 6 and 10" reflector. While the advertised data in these reports for magnitudes is obsolete the data given for separation seems quite OK even if meanwhile WDS lists other separations due to orbits.
In relation to Dawes the 3" refractor shows for equal bright doubles one result with a 0.98 ratio and the 6" refractor shows 3 results with 0.92 ratio. For the 6" reflector Lord lists 2 results with a ratio of 0.79 and two with 0.92 and for the 10" reflector we find two results with a ratio of 0.87.
So at least this source gives evidence in favour of reflectors. There are hopefully other sources with better evidence for this topic and may be to the contrary - would be glad to know them but please do not refer to old threads that can no longer be found.
Wilfried


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fred1871
scholastic sledgehammer


Reged: 03/22/09

Loc: Australia
Re: Size of spurious disk new [Re: DesertRat]
      #5649693 - 01/29/13 04:25 AM

Quote: The WDS and other catalogues do seem to lack precision. Does anyone know a good source to well defined precise measures for a set of 'popular' doubles? It would have to include orbital elements in some cases, but thats ok.

Glenn


Glenn, the best prospect for highest accuracy measures is recent speckle measures of doubles. There are science papers, some available online, that discuss the improved level of accuracy attainable.

Otherwise, the 6th Orbit Catalog, same site as the WDS, the USNO astrometry section. Orbits with a "grade 1" rating are likely to be very accurate. Quite a few grade 2 orbits are of high standard too for getting high accuracy separations.

The WDS is a collecting house. Data will vary in accuracy, being collected from multiple sources, with varying levels of accuracy. It's the best single databasae for doubles. Of course there are errors, and the keepers of the WDS are open to being advised of these. But some data collected is of necessity going to be less accurate, or have errors.

If you look at some of the orbit plots in the 6th Orbit Catalog, especially with lower-graded orbits, say grade 3 and 4, you'll often find quite large error lines marked for some measures. It can even happen with grade 1 and 2 orbits - some data points don't fit the pattern of a large number of others so they're effectively rejected in determining the orbit.

Hope this helps.


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fred1871
scholastic sledgehammer


Reged: 03/22/09

Loc: Australia
Re: Size of spurious disk new [Re: WRAK]
      #5649696 - 01/29/13 04:31 AM

Wilfried, I may have overlooked it, but does Lord give a description in his paper you're referring to of what he means by "resolved"? The term is, as we've seen in these forums, often used with different meanings - separated, notched, elongated, not quite round, etc.

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

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Re: Size of spurious disk new [Re: Cotts]
      #5649723 - 01/29/13 06:00 AM

Quote:

Your graph shows a very small difference in disc size from unobstructed (1.22 units - I assume arcsecs? ) to about 1.16 units in a 30% obstructed scope.




Dave, those figures are not arc seconds, but the constant used to determine the angular size with the wavelength and the aperture. The Airy disc in a 30% obstructed scope is indeed (1.11 * 550 * .206) = 126/D radius in arc seconds - not 138/D. It's the difference between 0.92" and 0.84" for a 150mm clear and obstructed aperture, respectively.

The additional diffraction effects can be approximated using (1 - co^2.) So, in an obstructed aperture, the Airy disc is smaller with added diffraction by a factor of (1 - co^2), but also dimmer and smaller due to both diffraction and obscuration by a factor of (1 - co^2)^2 normalized to 1. It is the reason a 30% obstructed scope puts 68% of the light into the disc and 32% into the rings: the rings are brighter and the disc is dimmer and smaller.

Now, is that significant? In good seeing, cooled, perfectly collimated, and with a reasonably good Strehl (=/> 0.95) I am convinced (real world observation) it is.

It allows an obstructed scope to resolve closer pairs and still maintain some contrast between peaks. But, it also hampers unequal pairs with greater separations, complicated by the fact the second ring is a full magnitude dimmer in a moderately obstructed scope just as Treanor's chart above shows. The chart also shows how the disc shrinks in angular size at 50% intensity, and Treanor thought it to be significant.


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EdZ
Professor EdZ
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Reged: 02/15/02

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Re: Size of spurious disk new [Re: Asbytec]
      #5649738 - 01/29/13 06:21 AM

Quote:

please do not refer to old threads that can no longer be found.




actually, these old threads are very easily found with just a minor effort. search on key words

Limits of C5
observations of 52 Ori at 1.1" and other 1" to 1.5" pairs including fainter pairs.

data for 52 Ori = 1.08"

Magnitude, Color and Obstruction affect resolution

look for links in these threads to other relevant threads

Dawes Limit vs Resolution

Evidence of overlap appearance in obstructed scope
observation of Zeta Cancri at 1 arcsec using C5, clearly shows that 16Cnc visible disk is not less than 50% of Airy disk.


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

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Re: Size of spurious disk new [Re: EdZ]
      #5649745 - 01/29/13 06:28 AM

Thanks, Ed, "spurious disc" and a few other key words did not bring anything up within the first 10 pages.

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EdZ
Professor EdZ
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Reged: 02/15/02

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Re: Size of spurious disk new [Re: Asbytec]
      #5649759 - 01/29/13 06:56 AM

What is the formula for spurious disk size?

For this I seaarched on the word resolution
for the previous set I ssearched on the word limits
both under my name - open ended date


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EdZ
Professor EdZ
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Reged: 02/15/02

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Re: Size of spurious disk new [Re: EdZ]
      #5649787 - 01/29/13 07:22 AM

Porrima at 1.0 arcsec in a C5 - strongly ooverlapped

edz


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: fred1871]
      #5649792 - 01/29/13 07:28 AM

Quote:

Wilfried, I may have overlooked it, but does Lord give a description in his paper you're referring to of what he means by "resolved"? The term is, as we've seen in these forums, often used with different meanings - separated, notched, elongated, not quite round, etc.



Certainly a good question - Lord refers basically to Dawes, but also to Rayleigh, Sparrow etc. but does not give any definition what is to be considered as resolved. As Lord is using historical material from the Lewis collection of observations this question cannot be answered with any confidence as there are too many people involved - we can only trust in the seriosity of the observers.
Interesting also the last page of his paper I have overlooked until now, would have spared me some own calculations: The statement "Resolution of equal binaries may be marginally improved by introducing a central obstruction" is on top of a table with a calculation of the influence of a CO on the Rayleigh criterion.
Wilfried


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Cotts
Just Wondering
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Reged: 10/10/05

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Re: Size of spurious disk new [Re: Asbytec]
      #5649802 - 01/29/13 07:42 AM

Norme, if I see pairs such as in your illustrations I call them a split and move on.

I use Dawes and Rayleigh to select pairs for viewing - my new 8" TEC Mak-Cass will be examining lots of pairs from 0.4" to 1.0" because it's theoretical limit for splitting/resolving/dividing close pairs is around 0.6"...

And I'm jealous of your Pickering 9/10 seeing......

Dave


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

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Re: Size of spurious disk new [Re: Cotts]
      #5649826 - 01/29/13 08:11 AM

Dave, I fell into some great seeing during retirement, something not common during my professional career, and often so very thankful. It has allowed me to push the limits in ways I've never imagined. Without getting too religious, sometimes I look up and just thank God for the blessing. Few things are more beautiful than a well behaved Airy pattern.

Ed, having read some of the posts...I see where you mention more than once about the Airy disc size. In fact, "Although it could be a lifelong study, I wonder just at what point or how abruptly a transition from 'smaller disks' to 'more difficult to see' does occur? These thoughts need to go in the other thread when I get time." If you had not done so, now is the time.

I wish I could find that article, this seems to be discussed over and again. Anyway, Wilfried is looking for a way to figure the visible disc size, what would be the best way to attack that on paper, first? I used what I understood your article on resolution to mean: 50% Airy disc diameter and extrapolating down to limiting magnitude. Maybe that is not exactly the right method.

Fred mentioned slicing the PSF is too subjective or would be for different observers, but it might be a start.

Well, got some observing to so...back later. Cheers.


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azure1961p
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Re: Size of spurious disk new [Re: Asbytec]
      #5650044 - 01/29/13 10:57 AM

I think part of the reason the slicing of the pie so to speak or lined boundary between value and another creates a quandary is that no line or slice can exist. Between values it would seem the lines, slices or limits are soft edged with a null zone of sorts. Within this grey area you could put varying perception between different observers and such so this zone is a grey area of averages.

Just a thought.

Pete


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