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Rayleigh and Dawes mystery

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#1 WRAK

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Posted 08 January 2013 - 08:45 AM

There exist many solid papers on the topic of Rayleigh and Dawes and other criterions for splitting equal +6mag brigth doubles with some allowance for a somewhat fainter companion depending on the location of the companion in the diffration pattern and also a lot of solid papers on diffraction theory explaining that the size of the Airy disk depends not only on the diameter of a scope but also on the size of central obstruction - very often both topics are discussed in the same paper.
Yet until now I found no paper concerning the resulting consequences for all these criterions - if the size of the Airy disk (the distance of the first minimum from the center of the spurious disk) depends on the size of CO then also these criterions are influenced.
For example Rayleigh requests sitting the secondary in the first minimum calculated with 1.22 for zero CO but with a CO of 33% the first minimum sits at 1.098 (value according to Chris Lords paper on splitting unequal doubles) and then the Rayleigh criterion should be calculated accordingly giving then 124/D_mm instead of the usual 138/D_mm. The same relation should then also be valid for Dawes etc.
What did I miss here?
Wilfried

#2 Asbytec

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Posted 08 January 2013 - 10:37 AM

I think you are correct in principle if not in definition. I'd like to hear more discussion, too.

I have adjusted my Airy disc to 0.84" arc and expected Dawes limit to 0.72" arc based on D/(1 - o^2). I am pretty sure I successfully observed 7 Tau at 0.74" arc (reported) as a "Dawes split." There was a contrast difference between the peaks, how much is anyone's guess. It certainly was not the classic black space, however.

The spacial frequency conversion comes from the link below (bottom.)
http://www.telescope...obstruction.htm

#3 WRAK

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Posted 08 January 2013 - 12:44 PM

My calculation approach would give Dawes 0.7" for your scope - may be a bit more challenging. Question remains why should this consequence not have been discussed elsewhere already long ago?
MfG Wilfried

#4 Asbytec

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Posted 08 January 2013 - 09:29 PM

Well, not sure why this does not seem to be common knowledge or applied to observation. If your calculations are correct, I can already imagine how difficult reaching 0.7" arc will be. Maybe 0.72" as well. Would like to try, though.

#5 WRAK

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Posted 09 January 2013 - 08:29 AM

The resulting effect of the shrinking size of the Airy disk due to CO for Rayleigh or other criterions depending on the diffraction pattern seems obvious - may be too obvious to be true and only the experts like our Prof. EdZ know why this is not the case. So we have to wait for an expert to explain this.
Meanwhile I have made an aperture mask for my 80mm refraktor with a central obstruction of about 30% - if theory works this should make an 8 from an elongation and a clear split from an 8. Next clear sky ...
Wilfried

#6 Asbytec

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Posted 09 January 2013 - 09:19 AM

I've lined up some of your Tau list in ascending order of required aperture for the next clear night. I will work from 140mm to 160mm RoT apertures to see if I can get a steady Airy disc instead of a fleeting flash of light.

Our own Mr. Cotts is getting a 200 TEC Mak for doubles, I am sure he might be interested in the subject of how well they perform on them compared to his 6" refractor. I am interested, too.

I wish someone would pick up on this topic and run with it. It's right at the heart of what I am discovering about my own scope. And double stars seem to be a good way to probe the limits of Dawes and Raleigh as well as probing the effects of a CO and residual spherical aberration (common to APOs, too, I believe.)

#7 WRAK

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Posted 09 January 2013 - 10:45 AM

Looking forward to your report, should give some clues about the validity of my RoT model.
Please check your NEML at this session.
Wilfried






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