Re: [ATM] RMS error vs Strehl Ratio

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

At 09:12 8/11/05, Richard F.L.R. Snashall wrote:
>When I first started learning design, I quickly accepted that
>RMS wavefront error and Strehl Ratio were correlated, and even
>that an equation approximated the relationship between the two.
>
>However, I have come across something that makes me start to
>question what is going on.

What are you questioning? To an excellent approximation for a nearly 
diffraction limited wavefront

Strehl = exp(-(2*pi*RMS)^2)     [Mahajan's approximation]

where RMS is the root mean square wavefront error in waves at some 
wavelength lambda. OSLO returns RMS wavefront errors and Strehl 
ratios satisfying this formula to 4 digits or so if you have it 
calculate monochromatic quantities. And if you ask it to focus for 
best monochromatic error it will adjust the focus by an additional 
-0.127mm, where the monochromatic RMS OPD is 0.

Presumably it is calculating some weighted mean RMS error for 
polychromatic quantities - I notice you have 11 wavelengths being 
evaluated in your design with varying weights applied to each. 
Presumably also it's calculating a polychromatic Strehl ratio as a 
weighted mean of monochromatic Strehl ratios. I'm just guessing about 
that though. You could check it easily enough if you think it's worth 
the trouble. That's going to give a different number than applying 
Mahajan's formula to the "polychromatic RMS" obviously enough.

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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