Re: [ATM] RMS error vs Strehl Ratio

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

At 09:19 8/12/05, Richard F.L.R. Snashall wrote:

>>What are you questioning? To an excellent approximation for a 
>>nearly diffraction limited wavefront
>>
>>Strehl = exp(-(2*pi*RMS)^2)     [Mahajan's approximation]
>>


>The strict monotonicity of the function you mentioned implies that
>a valley in the RMS error will be exactly at a peak in the Strehl
>ratio -- monochromaticly.  However, based upon the design I supplied,
>it would appear that the same is, then, not true polychromaticly.

I was going to annoy the list with a bunch of ascii math showing that 
there would be a monotonic relationship between polychromatic RMS and 
polychromatic Strehl provided the monochromatic RMS is small enough 
at all wavelengths of interest, and also that these quantities are 
defined the way I think they are and actually calculated accurately. 
I've seen enough funny results from the major optical design programs 
not to take those last two assumptions for granted.

Anyway I suspect the monotonic relationship is breaking down in your 
case because the RMS errors get large within the wavelength range of interest.

>How can I have confidence that finding the best system via RMS error
>minimization will yield the best system in terms of Strehl ratio?
>Is it relevant, i.e.: is one a more important consideration than
>the other?

Well, if you point your theoretical refractor at a theoretical star 
what do you theoretically see? Not a RMS wavefront error. You see a 
PSF. To the extent that the Strehl ratio gives you a meaningful 
indication of the quality of that PSF I'd think that would be what 
you want to use. Of course since you're far from diffraction limited 
over part of the wavelength range specified in your design perhaps 
neither quantity is quite right.

Mike Peck



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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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