[ATM] Re: Aplantic Gregorian

[Jim Burrows <burrjaw@earthlink.net>]

At 2004-11-30 01:18 +0000, Richard F.L.R. Snashall wrote:

>I infer you are describing fifth and higher order terms.  Correct?

It's more than that - no polynomial fit involved.  There's two surfaces to 
satisfy two conditions for an aplanatic system:  axial stigmatism (no 
spherical aberration) and the optical sine condition (no coma).  Born and 
Wolf use these two conditions to set up a pair of differential equations 
for the primary and secondary profiles.  Given your desired 3 Cassegrain 
(or Gregorian) parameters, of which there are several sets - the one I use 
is d=primary-secondary separation, s'=secondary-image distance, and 
EFL=effective focal length - you can integrate the differential equations 
numerically and find the RMS difference between the true surfaces and the 
actual surfaces.  Or, given primary and secondary surfaces, do an iteration 
to find the best-fit 3 parameters and the system RMS.

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

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