What criteria is used to judge the quality of an airy disk pattern?
In what sense? In the case of telescope systems, the "best" Airy disk is one that cannot be improved further with lens design and construction, and the system is said to be diffraction-limited. Fainter stars will seem to be tiny points, compared to bright stars, but that's just because the intensity of the whole of the disk is low. Theoretically, the size of the Airy disk produced by a telescope is the same for stars of all intensities.
If you're talking about the pattern of rings around the disk, I believe that the standard (if there is such a beast) is that the quality of the Airy pattern is the highest when the disk contains the bulk of the light, the minima appear as dark rings, and the diffraction pattern is symmetrical, and the intensity of the rings falls off with distance from the disk. Are there numbers to quantify "quality" in this sense? I have no idea, but there are probably ATM forums where you could get more information than you need.
I don't think that there's a quantitative way to describe the quality of an airy disk. I was asking for when I'm in the lab and trying to optimize a system to give me the "best" airy disk. Thanks for the advice, it is helpful.
Presumably you mean how is the point spread function of an optical instrument evaluated? The Airy disk represents the aberration-free diffraction limit for optical imaging, and so deviations from the real PSF from an Airy disk pattern is the quantitative measure of instrument quality. For more exotic optical measurements (near field methods, for example), different criteria are used.
That's a slightly different question- are you asking how to align optical devices?
Well, aligning the system is part of the task that I'm assigned to do, but not necessarily what I am asking about. My goal is to understand how an obscuration affects the airy disk pattern.
That's also a different question: where is the obscuration? If the obscuration is in the exit pupil (like a support spider), the effect is straightforward to understand. If the obscuration is located arbitrarily in the optical path, the effect can be much more complex.
It's going to be a circular obscuration in the exit pupil (pretty mundane, I know...but it's the assignment).
I expect to see the radius of the Airy disk decrease and its principle maximum decrease value and the secondary maxima increase in value...as for the support struts, I'm not sure what I'll see but it'll be a learning experience.
The point-spread function is the Fourier transform of the field in the exit pupil- for an unobscured circular pupil, the PSF is an Airy function. Adding an obscuration is straightforward- a sum (or difference) of 'circle functions', and taking the Fourier transform of two functions added together is equally straightforward.
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