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

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

At 14:39 8/15/05, you wrote:
>Hi Michael,
>
>I think I sensed your reluctance to burden  atm public
>with mathematics except if they explicitly  "ask for it".
>Therefore I am sending my questionnaire off - list.

Vladimir:

I'm a little reluctant to burden the list with ASCII math mostly 
because it's hard to read. If email software could translate LaTeX 
I'd happily annoy the list any time the urge struck me. Anyway I'm 
sending this back to the list even though it's at the outer limits of 
relevance to ATMing.


> >I created 1000 random wavefronts where both
> >the aberration content and the total RMS wavefront error varied
> >randomly.
>
>1) Why randomly ?
>2) I thought that aberration content and total RMS wavefront error are
>synonyms.

The RMS wavefront error is just a summary quality measure. It doesn't 
tell you anything about the details of how your optical system 
departs from reality. I created random wavefronts because it's more 
general than some special case, like for example looking at varying 
amounts of spherical aberration or some other specific defect.

One question that's somewhat interesting, perhaps even to some ATMs, 
is do the details of departures from perfection matter? The answer is 
clearly yes if the RMS error is large enough, which is something you 
can infer from the scatter in the Strehl-RMS relationship as RMS gets large.

>3) Why you say that SR is "estimated". What kind of approximation is
>     this estimation based on?
>    (Can we estimate one approximation with another?)
>

I used "estimate" to convey that I was using physical and numerical 
approximations to make the calculation, namely (a) Fraunhofer 
diffraction theory and (b) Discrete Fourier transforms to approximate 
the mathematics contained within (a).

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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