[Raytrace] A real world application

[Michael Peck]

At 01:19 12/21/2001 -0500, Peter Chen wrote:
>          The primary being spherical, the best that can be done in a two 
> mirror system is to make a inverse Dall-Kirkham (or Pressman-Carmichael, 
> Rutten's terminology).  The secondary is a convex spheroid.  This is a 
> zero field system.  The image is a spot only on the optical axis.  I've 
> added a diagonal flat for finding a target in the field.

Someone corrected me once for inadvertently anglicizing this name, so I'll 
do the same. It's Pressmann-Camichel. Wilson calls these spherical primary 
telescopes; for some reason he decided not to give the designers credit (or 
blame) for this one.

>         The system requirements are as follows:
>Primary - 20 in diameter, 76 in. ROC, sphere
>Secondary - 4 in diameter (to reduce fabrication cost, actually any size 
>up to 6 inch is ok)
>Diagonal flat -  to be located 2 inch in front of primary, for ease of 
>mounting
>Focus  - 13 in. above optical axis (to accommodate focuser)

This is actually a more difficult design (and probably fabrication) problem 
than you may have thought. It's also probably outside the scope of ATM 
projects, but since there doesn't seem to be much list traffic right now 
any question has to be considered "frequently asked."

>The problems are:
>    1.  It doesn't focus to a spot, even on axis.   The secondary roc 
> doesn't seem quite right.
>     2.   I have no idea how difficult it would be to make a spheroid with 
> a conic constant of 8.959129.  Is that realistic?  How does one test such 
> a piece?   (note:  The piece will be concave.  We replicate with it and 
> get the convex part).
>
>:  Does anyone have any suggestions?

Personally I prefer to use a spreadsheet for preliminary cassegrain design, 
then fiddle it in OSLO as needed. The version of my cassegrain design 
spreadsheet on my web page doesn't do spherical primaries, but I added a 
line to my local copy.

I see two likely errors in your layout. First, it appears you made your 
secondary a flat. I reverse engineered your probable intended configuration 
and came up with a secondary radius of curvature of -472.89mm, which 
produces a system focal ratio of f/10.35 or a secondary magnification of 
-5.447. The second probable error I see is that my spreadsheet returns a 
conic constant of 7.086, which is still highly oblate.

Plugging those numbers into OSLO I still get lousy results: after 
refocusing I get a P-V error of over 2.7 waves. What gives? Well, I solved 
to eliminate 3rd order spherical aberration, but this system has a huge 
amount of residual 5th and even 7th order spherical. In order to get good 
performance you're going to have to make your secondary a higher order asphere.

OSLO has several ways to set up a general high order aspheric surface. I 
picked the simplest one, which it calls a "standard asphere." I don't know 
how to solve for higher order aspheric coefficients by hand, so I used 
OSLO's default optimization method (they call it GENII) and defined the 
secondary conic constant and 6th and 8th order aspheric coefficients as 
variables. Here's the system specification that OSLO returns (I've omitted 
the tertiary flat):


*LENS DATA
No name
  SRF      RADIUS      THICKNESS   APERTURE RADIUS       GLASS  SPE  NOTE
  OBJ       --        1.0000e+20    1.0000e+14             AIR

  AST  -1.9304e+03   -772.160000    254.000000 AS      REFLECT

   2   -472.890000    772.160000 P   50.800772 S       REFLECT   *

   3        --        279.408778 S   13.501962 S           AIR

   4        --            --          0.005258 S           AIR

  IMS       --            --          0.005258 S

*CONIC AND POLYNOMIAL ASPHERIC DATA
  SRF        CC          AD          AE          AF          AG
   2       7.092349      --     -9.6589e-14 -1.2996e-17      --

As specified OSLO tells me P-V error is about 0.004 wave. You could 
actually, probably, get away with a 6th order asphere, but P-V would only 
be about 0.11 wave.

I don't think many ATMs would care to tackle a fairly steeply curved convex 
oblate spheroid with an 8th order correction. Depending on what kind of 
resources you have available at NASA you might be able to make one, but I 
doubt the opticians who work on it would thank you.

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