Re: [ATM] RMS error vs Strehl Ratio

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

Michael Peck wrote:

> 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.
>
Indeed, to three places anyway, the monochromatic Strehl ratio
is 1.000 for quite a bit of the C-F range.


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.
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?

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