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

Loc: La Union, PI
Re: Size of spurious disk new [Re: azure1961p]
      #5650326 - 01/29/13 01:31 PM

You may be right, Pete, it's a complicated topic. Maybe Wilfried can just use the 50% figures in the chart he posted above. Maybe Treanor ran into the same problem and simply chose a cut off. But the figures are still a tiny bit smaller suggesting a tiny bit more resolution.

One thing becoming somewhat apparent to me is, when the conditions warrant - when all induced aberrations are minimal, those scales can make a tiny difference. You can push just a little deeper, maybe to the point where the size of the spurious disc will either make or break a tight split.

For example, I would never think of calling a split on 72 Pegasi at 0.56" arc. I called one on 7 Tau at 0.74" arc. And there is the slightest hint of a possible, barely detectable, tiniest hint (you get the point) of a very faint dark space on STT 517 at 0.67" arc. Not enough to call a split, but just enough to make you wonder. That seems unprecedented in theory and in practice.

So, there is probably no definite point where a split becomes non resolution, except for the Sparrow limit in concept, in theory, and maybe in practice. But, what is the Sparrow limit, 107/D is all scopes? There is probably a more gradual change up to the point where contrast is truly flat across the peaks. So, what is that point?

Point being, I think Wilfried asked a fascinating question that could use a good answer. I wish I had one for him. I do think about it a lot, and I do push my scope to those limits to see.


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

Loc: La Union, PI
Re: Size of spurious disk new [Re: Asbytec]
      #5650383 - 01/29/13 01:54 PM

Quote:

I wish I had one for him.




Maybe I do. I'd have to dig up and verify my work, but at one point I calculated my own scope to have a high frequency resolution similar to a 6.4" clear aperture. Then, at lower frequencies larger than the first ring, I calculated it's mid range contrast transfer to be close to a 4.3" clear aperture. (I think I even included some aberration, Strehl 0.95 for my scope and assumed a Strehl 0.98 for the clear aperture.)

Now, since unequal pairs with separations within the frequency range corresponding to the first three or four rings seem to behave like planetary contrast at the same scale, so this treatment might be applicable to unequal pairs, too. After all, it is diffraction contrast that makes either difficult.

So, for tight pairs, treat an obstructed scope just like a slightly larger clear aperture. Conversely, for mid range frequencies out to about 3x or 4x Raleigh, treat an obstructed scope like a smaller aperture. A good figure can be calculated, for perfect or aberrant apertures, and the size of the spurious disc might be implicit in the answer.


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: Asbytec]
      #5650689 - 01/29/13 04:27 PM

Ed, thanks for the posted links - I will go through them in the next days and will probably take the liberty to add some of the reported splits to my so far rather small data set of limit observations for my RoT project.
Wilfried


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DesertRat
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Reged: 06/18/06

Loc: Valley of the Sun
Re: Size of spurious disk new [Re: fred1871]
      #5650819 - 01/29/13 05:44 PM

Fred said:
Quote:

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.




Thanks Fred! You jogged my memory into recalling the orbit grades. Interestingly Castor has a grade of '3' which was one I had interest in as I captured it as a test two years ago in computing plate scale. I realize a wider separation would be beneficial, but most binaries with good grades are very close doubles.

As far as the size of the spurious disk, one can calculate that assuming it is defined as something like full width half max. Using the wave eqn solution (no aberratons) with a possible obstruction, its not difficult to do. And it appears further up in this thread someone already did that calculation.

However the visual appearance I believe would be larger than that. If you were to use an insane amount of magnification, and had seeing of the gods, I suspect you would measure it out to something closer to the intensity of the first bright ring, or closer to 20% of the central max. But the flaw there is that the perception would be quite sensitive to the magnitude of the star. Bright stars would 'measure' quite a bit larger than faint stars.

Glenn


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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: DesertRat]
      #5651347 - 01/29/13 11:10 PM

Glenn, my thoughts were to forget the spurious disc and simply go with line pairs. Calculate the maximum line pairs at either Dawes or Abbe limit, as modified by (1 - co^2), then calculate the clear aperture required to attain that spacial frequency. That clear aperture and the obstructed aperture should have the same maximum spacial frequency. So, you could treat resolution of close pairs the same way applying different apertures.

You can even apply aberration to the calculation using very good Strehl of 0.98 for the refractor and 0.95 for the obstructed scope. Using line pairs implies the spurious disc size. That would work for maximum spacial frequencies, in terms of getting an figure.

I don't remember how to treat lower frequencies. I may have determined the aberrant contrast transfer for both at lower frequencies, then applied the (D - co) rule of thumb to come up with a percentage of the clear aperture required. Its basically what we do we we say a 150mm - 42mm = 109mm clear aperture, then apply the a reasonable Strehl to both (instead of referring to "perfect" apertures like MTF does.) This should be more realistic, despite the non linear eyeball function.

Somehow you have to work in the lessor peak intensity of the obstructed scope (causing more light in the rings) using a approximation of (1 - co^2)^2 to determine their Strehl-like number and effective contrast transfer. The clear aperture definitely has the advantage here, so it can be smaller and perform as well.

Measuring them at insane magnifications would work, too. Dave mentioned that above. He seemed disinclined to do so because of the difficulties in getting 800x on a good night. He may have a point, and it would require calibration and some special equipment. It might be subject to errors, too. It could be done, but it might be done on paper, as well.


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: Asbytec]
      #5652854 - 01/30/13 05:44 PM

According to the topic of this thread all observation reports were with may be one exception for equal doubles - certainly all interesting regarding the size of the spurious disk but to my regret of no use for the RoT project.
Wilfried


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azure1961p
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Reged: 01/17/09

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Re: Size of spurious disk new [Re: WRAK]
      #5653428 - 01/30/13 11:35 PM

Did Edz ever weigh on the queries you guys made?

Pete


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: azure1961p]
      #5653545 - 01/31/13 02:35 AM

Sorry, no weigh intended.
Wilfried


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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: azure1961p]
      #5653681 - 01/31/13 06:37 AM

Quote:

Did Edz ever weigh on the queries you guys made?

Pete




what queries?


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: EdZ]
      #5661894 - 02/04/13 02:24 PM

Back to the topic of this thread - the size of the spurious disk. Rereading the strong arguments of Taylor for the use of reflectors for double star observing I found no reason to doubt his measurement even if some of his reported observations shows extreme Dawes ratios down to 0.5 (without considering the effects of CO - Taylor mentions the use of artificial high COs for resolving extremely tight doubles).
At the same time I do not see any reason to question the observations of EdZ.
Referring to the numbers given for the size of the spurious disk in the already posted table of Chris Lord I get a relation of 42% of the Airy disk for non obstructed scopes. While Lord explains very well how he calculated the other numbers in his table he did this regrettable not for his numbers for the size of the spurious disk.
But may be the size of the spurious disk lies in the eye of the observer?
Wilfried


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fred1871
scholastic sledgehammer


Reged: 03/22/09

Loc: Australia
Re: Size of spurious disk new [Re: WRAK]
      #5662741 - 02/05/13 12:16 AM

A comment regarding Taylor - yes, he mentions using very large CO ratios, but indicates that none of the results he reports made use of that technique. Rather, it was with the 12.5-inch reflector in normal mode, with its normal small CO.

Quote:
But may be the size of the spurious disk lies in the eye of the observer?
I've been saying this for some time now, in various versions, and I've noticed some others expressing a similar view.

How the eye sees what's there is interactive with the diffraction image, affected by seeing, CO effects, optical aberrations, and the quality of the eye along with the observer's ability to see (a skill improved by experience/practise).


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Size of spurious disk new [Re: EdZ]
      #5884117 - 05/25/13 02:39 PM Attachment (4 downloads)

Quote:

... in Lord's table ... edge of disk center is another point that needs discussion. He seems to have chosen an arbitrary point, that at which the light is 50% or one half of the peak intensity.
... Are we to assume the disk edge cannot be seen beyond a point where the light intensity drop below 50% of peak intensity? Or is this simply an arbitrary point? I think it is just an easily identified arbitrary point used forr consistency
...
edz




Had to reactivate this thread for good reasons. Any approach for calculating the size of the spurious disk has to make assumptions regarding the visual theshold or use such a parameter as part of the calculation.
50% of the intensity seems an assumption very far away from reasonable to me - as we can see with good enough seeing conditions the first diffraction ring (or even more) of bright stars and as we know according to diffraction theory the energy resting in the first diffraction ring the visual threshold has to be less than 10% for scopes without CO.
But if you have a look at graphs of the diffraction pattern (like for example from http://micro.magnet.fsu.edu/optics/lightandcolor/images/diffractionfigure3.jpg) you see instantly that this small gap between spurious disk and first ring is certainly not what you see in the scope where the dark space between spurious disk and first ring seems much larger. But despite this I still think that the size of the spurious disk is at least for refractors much larger than 50% of the Airy disk (for brighter stars).
Have also searched my observation notes for dark space at Rayleigh for my 140mm refractor means 1" separation - found only one for the equal faint pair HO22 1" +8.5/8.64mag. All other observations at this separation range (not many as I have not this many nights with fair seeing) were notched rods at best and all positive obervations below 1" were with overlapping spurious disks from rods to eggs (considered positive resolutions when still allowing successfully to estimate the position of the companion).
Wilfried


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