[Raytrace] Zernike Polynomial Modeling (Was: Re: TCT (Tilted Component Telescope) designs

[Michael Peck]

At 12:14 1/28/2002 -0600, John D. Upton wrote:

>     Has anyone of this list done this before?  It would seem the ultimate 
> way to assess the potential performance of a mirror (short of using it 
> under near-perfect seeing conditions).  The real problem in attempting 
> this would be the data reduction from Foucault (or Gaviola caustic, etc.) 
> test data to a set of polynomial coefficients to enter into OSLO.
>
>     What analysis tools might be available to help transform test 
> measurements into polynomial coefficients?

I know two different ways to extract Zernike polynomial fits from Foucault 
test data. I'd even be happy to tell you how to do it, but the methods 
don't exactly lend themselves to ascii math and the limitations of a 
mailing list. There's nothing particularly difficult or mysterious about it 
though -- although there is a certain amount of number crunching involved. 
I didn't know the latest version of Sixtests provides Zernike polynomial 
output. I suspect that its output can probably be entered without 
modification into OSLO LT, but I'll have to check it out.

The free version of OSLO is pretty limited as to how you can specify a 
surface. It only recognizes the radially symmetric polynomials, so you'll 
only be able to use part of the information from an interferogram that 
includes measurements of astigmatism and other non-symmetric aberrations. 
It appears that the coefficients OSLO expects are relative to the surface 
in whatever units of measure you're using. I think interferograms will 
typically give Zernike coefficients in waves on the wavefront, so you'd 
need to multiply by the wavelength and divide by two (for a mirror - and 
possibly reverse the sign) to enter into OSLO.

When you do a Zernike analysis of a wavefront in OSLO it returns 
coefficients in waves, so its output convention differs from its input 
convention. In general usage conventions for Zernike polynomials aren't 
well standardized, so transferring values from one program to another may 
well lead to nasty surprises. I've occasionally encountered optical designs 
that include high order aspheres, but Zernike polynomials never seem to be 
used for that purpose. The only situation where you're likely to encounter 
them is if you have actual test data.

I'm going to include one sample here. This has 20nm RMS of the Zernike 
polynomial equivalent of 9th order spherical aberration, on top of the 
250mm f/6 paraboloid that we've been using as our "standard" newtonian 
mirror. The coefficient value I entered is AS5 = 10^-6*sqrt(11)*20. If you 
do a wavefront analysis of this you'll see that the RMS wavefront error is 
just over .07 waves and the Strehl ratio is 0.8, while P-V is over 0.4 - 
this is evaluated at 550nm.

***** 250mm f/6 newt with added Zernike asphere *****
*LENS DATA
Newtonian 250mm f/6
  SRF      RADIUS      THICKNESS   APERTURE RADIUS       GLASS  SPE  NOTE
  OBJ       --        1.0000e+20    1.5709e+18             AIR

  AST  -3.0000e+03   -1.5000e+03 S  125.000000 AS      REFLECT   *

   2        --            --         23.563883 S           AIR

  IMS       --            --         23.563883 S

*CONIC AND POLYNOMIAL ASPHERIC DATA
  SRF        CC          AD          AE          AF          AG
   1      -1.000000      --          --          --          --

*ASPHERIC SURFACE DATA
   1   ASP ZSR    5 - SYMMETRIC ZERNIKE SAG
       AS0        --     AS1        --     AS2        --     AS3        --
       AS4        --     AS5    6.6330e-05

********

Mike Peck

_________________

Michael Peck
email mpeck1@ix.netcom.com
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