Re: [ATM] Is this Sphere good enough?

[Jim Burrows <burrjaw@earthlink.net>]

At 2004-08-18 20:30 +0200, Vladimir Galogaza wrote:

>The Strehl ratio is  "the ratio of the light intensity at the peak of the 
>diffraction pattern of an
>aberrated image to that at the peak of an aberration free image".

The Strehl ratio, using Vladimir's quoted definition, can be calculated 
exactly using Eq. (4.6) in "ATM math".  In fact, the early versions of 
Sixtests did this by numerical integration.

The input to the expression is the "wavefront phase error".  Since 
wavefront phase error is twice surface profile error (divided by wavelength 
assumption), the equation can be written in terms of surface error.

The next step is "ATM math"'s Section 5.3 which derives the Maréchal 
approximation for Strehl ratio (SR) in terms of surface RMS error.  Also 
Mahajan's (guessed) approximation is quoted and turns out to be better 
than, both for large errors (Maréchal goes negative) and comparisons with 
integrated SR values as above or a few aberrations for which an exact SR 
has been obtained.  When the author of Sixtests became aware of the Mahajan 
expression, he decided it was much easier numerically to calculate the RMS, 
then use that expression to get the SR.

Finally, the parabolic reference has disappeared.  We can now evaluate 
total telescopic systems using RMS based on this relationship to SR which 
is widely accepted as the best single-value criterion. In particular, 
primary mirrors whose reference, as part of a multi-mirror system based on 
geometric optics, is a non-parabolic conic surface (cassegrain or Schmidt) 
or even non-conic (RC cass).

         -- Jim Burrows
         -- mailto://burrjaw@earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84)  

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