airy versus FWHM for nyquist sampling [ap-ug] Re: ML8300 First light


Jun 26, 2009

 


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#45903 Jun 26, 2009

-----Original Message----- >From: chris1011@...

>Sent: Jun 26, 2009 11:07 AM

>To: ap-ug@yahoogroups.com

>Subject: Re: one other thing to add Re: [ap-ug] Re: ML8300 First light

>

>In a message dated 6/26/2009 11:56:36 AM Central Daylight Time,

>strehl983@... writes:

>

>

>> chris1011@... wrote:

>> >

>> > Yes it's true. A 2" F9 produces exactly the same size Airy disc as a 12"

>>

>> > F9, in microns. Arc sec per pixel has nothing to do with Airy disc size.

>> >

>>

>> Rolando, I think the confusion is because you are speaking in terms of

>> linear resolution and others are thinking in terms of angular?

>>

>

>The term resolution never came up. I only discussed in terms of sampling

>the smallest size Airy disc produced by an optical system. It does not matter

>what the aperture is, the smallest size Airy disc is ideally sampled by an

>F-ratio that is similar to the pixel size. So, for an F9 scope, which has an

>Airy disc approximately 12 microns diameter, a 9 micron pixel size will

>produce a fairly nice round image, not terribly undersampled and not

>oversampled. As an extreme example, if you shoot with an F2.5 focal ratio and a 12

>micron chip, you will find the stars to be little square pixels, so I would say

>it was undersampled.

>

>However, there is a limit because of the atmosphere. So as you exceed 12"

>aperture, you can use faster focal ratio optics and not get little square

>stars 1 pixel diameter. The atmosphere will limit you to around 1.2 arc sec and

>you will get round stars, larger than theoretical.

>

>Rolando





this reminds me of something I finally learned about two years ago relating to Nyquist sampling. I've been told for years that you want to sample at twice the frequency you intend to reproduce. On the other hand I was in a lecture from Dr. Terry Lomheim of The Aerospace Corporation in early 2007 where he was discussing critical sampling, aliasing and beating.



When he described critical sampling he mentioned that it takes 4.88 pixels to cover the Airy diameter. Duh? I thought I had been told 2 pixels, so what gives?



well it turns out that the 2 pixels are for the FWHM (full width half max): in other words the value at the sampling "edge" is not zero but half of the peak value. For the Airy diameter it is from null to null (zero value to zero value) of the J1 Bessel function. Ok so that works out to be (if you look up the values of the Bessel) just another way to describe the same energy distribution.



So by way of analogy, you can measure a horse different ways; you can measure how high to the shoulders or the ears or even the length of the legs. You get a different numerical answer but it is still the same horse you are describing.



So the comment about you needing 4.88 pixels to critically sample an Airy diameter is the same as saying you need 2 pixels to sample FWHM of the same diffraction limited optical blur.



anyway it seems germane to this discussion so I thought I'd mention it in case anyone else had that confusion I had until early 2007.



here's a bit on it from Wikipedia

en.wikipedia.org/wiki/Airy_disk





rdc



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