Re: [ATM] Foucault and diffraction

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

At 11:55 1/16/05, Richard F.L.R. Snashall wrote:



>Hmmm... I wonder how this relates to Born & Wolf's 20% (Strehl 0.8) measure:
>
>                  +/- 0.5 * (f#)^2 * lambda

You can get that from geometry. Suppose you have a paraboloid with radius 
of curvature R on one diameter and R-dR on another 90° in azimuth away. 
Then the sagittae are

y^2/(2R)

y^2/(2(R-dR)) ~= y^2*(1+dR/R)/(2R)

making the P-V astigmatism at the surface.

r^2*dR/(2R^2) = dR/(32 F^2)

The tolerance must come from setting the wavefront error equal to 1/4 wave, 
which is slightly too stringent. According to Wilson the tolerance for 
astigmatism is about 1/3 wave PV (for 0.8 Strehl).

For investigating diffraction effects the easiest thing to do is download 
one of the FFT based simulations of knife edge (and similar) tests. Jim 
Burrows' DIFFRACT is the easiest to find and use. I've written a little 
foucault simulator and so has Steve Koehler and probably some others have 
as well. It's fairly straightforward with readily available efficient FFT 
routines and a bare minimum of knowledge of the underlying physics.

Mike Peck


_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photography page http://home.netcom.com/~mpeck1/index.html
Amateur telescope making http://home.netcom.com/~mpeck1/astro/astro.html 

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