RE: [ATM] Accuracy of Mahajan's approximation for Strehl ratio

[Michael Peck <mpeck1@ix.netcom.com>]

At 16:22 8/15/05, Koehler, Steve wrote:
> > Maybe. I guess the way to find out is to use a larger FFT. I think I
> > have enough memory to try it, and CPU cycles are cheap.
>
>Another possibility would be to start with very small FFT arrays, and look at
>how the values change as they approach the sizes we typically 
>use.  It is likely

I tried my first idea for refining the FFT based Strehl estimate. For 
the first round I used a 255x255 pupil padded out to 1024x1024 for 
the FFT. Second time around I increased the FFT size to 2048^2. The 
ratio of FFT size to pupil size controls the size of the PSF in the 
simulation: it's about 10 pixels diameter in the first case, 19 in the second.

Here 
<http://home.earthlink.net/~mlpeck54/astro/temppix/strehlvsrms2k.png> 
are the full results. The red dots are for the 2K^2 simulations, the 
green the 1K^2.

Here's a closeup of the diffraction limited regime: 
<http://home.earthlink.net/~mlpeck54/astro/temppix/strehlvsrms_dl2k.png>. 
The points marked with stars are for varying amounts of pure 
spherical aberration. Notice how close those fall to Mahajan's 
approximation at least for RMS <~ 0.2 waves.

Finally, here's 
<http://home.earthlink.net/~mlpeck54/astro/temppix/psf.png> a cross 
section through an unabberated PSF calculated both numerically and 
analytically. The blue dotted curve is the analytical calculation. I 
normalized these to have the same peak values, which I think is OK 
since I'm looking at ratios of quantities. I believe this qualifies 
as sufficient numerical accuracy for our purposes.

I can't imagine where Bob gets the idea that 32K^2 matrixes are 
needed for this kind of computation. That would be massive overkill, 
to put it mildly.

Mike Peck


_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photoblog! http://wildlife-pix.com
Amateur telescope making http://home.earthlink.net/~mlpeck54/astro/astro.html 

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