Re: ATM Strehl

["James W. Burrows" <burrjaw@earthlink.net>]

At 17:07 2002-01-02 +0000, Richard F.L.R. Snashall wrote:

>If you need a reference, Born and Wolf, chapter 9.1, equation 24.

That's the Maréchal approximation, which underestimates the Strehl ratio 
(in fact, goes negative for large RMS).  It's also in Suiter, p. 238, Eq. 
(13.1).  Further down on the same page in Suiter is the Mahajan 
approximation, Eq. (13.2).  It's much better, although a slight 
overestimate, good enough that I decided to use it rather than the messy 
integration of the Strehl ratio definition in earlier versions of Sixtests.

I've tried for quite a while to find an exact expression for the Strehl 
ratio of a sphere with no success.  Thinking that Mahajan might give a 
hint, I got a copy of his paper (V. N. Mahajan, "Strehl ratio for primary 
aberrations...", J. Opt. Soc. Am., 72(9), Sept 1982, p. 1258-1266).  Nope, 
the formula was just a fortunate guess: "Since S1 (Maréchal) underestimates 
the Strehl ratio, exp(-s˛), which, for small s, is greater than S1 by 
approximately s^4/4, should approximate the Strehl ratio better."

         -- Jim Burrows
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