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

[Peter John Smith]

> At 07:22 PM 1/17/02 -0500, John Francis wrote:
> >Has anyone modeled a mirror profile using Zernike polynomials for input
into
> >a raytrace program? What I would like to do is use the actual test
results
> >from a mirror profile analysis and use this to evaluate the system Strehl
> >ratio of a final "as built" TCT.

And John Upton replied :-
>
>      I haven't seen any response to this part of your post last week.  I
> have never tried to do this, so I cannot help in that respect.  I am
> intrigued by the concept, though.
>
>      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 did not reply originally because I have never entered Zernikes in Zemax
and from that simulated performance.  So, no, I dont have much to offer
here.

In theory Zemax can do it but there are many problems.

Mainly the fact that Zemax comes in Standard, Advanced and More advanced
(called by other names) with extra capabilities.  For the first you only
need to part with an arm.  The next costs an arm and a leg and the more
advanced requires even more intimate sacrifice.  Luckily I got in very early
before prices really skyrocketed.- and then the Australian dollar was worth
a lot more too.

If anyone reads a rave review about some special feature of Zemax beware -
dont go out and blindly purchase because the chances are it will only be
available in the advanced editions and you had better look at the price
first.

Entry of a surface as Zernikes was only available in the more advanced
editions but this may have changed now.

Anyway, no, I cannot help although I can in theory do it.  What I need is a
good tutorial with examples on how to use this feasture of  Zemax..  I am
waiting.

Zemax also allows one to enter custom surfaces in a variety of other ways.
Apart from the more normal conics and Even and Odd Aspheres,  with you can
enter surfaces by entering linear polynomial coefficients but that is is
very awkward because it is messy to get and enter the required coefficients.
Another option is to enter nodes representing departure measurements which
is far more user friendly.  I have dabbled with this but found that with the
number of nodes (its a cubic spline) limited to 8  on a radius there is
limited control - especially at the edges because you do not have control of
the edge slope and you cannot see the mirror shape without plotting out
surface heights from another portion of the program.  So you do not get
visual feedback on the shape you are entering.  Its right at the nodes but
not always in between and the slope on the edge is out of control.

Anyway, to get back to Zernikes.  I dont understand them enough and I simply
dont have the need or incentive to rectify this lamentable position.  Again,
any information on this I am willing to absorb as long as it is not too
complex.

It is not too difficult (but messy) to compute predicted Strehl from a
surface profile.

If one knows departure from the ideal shape - eg a paraboloid in a Newt. -
one knows the departure from a spherical wavefront of the reflected rays.

>From this one can compute the RMS deviation and finally apply a simple
formular to compute Strehl.

I think one of Jim Burrows programs may allow you to enter departures into a
file which will then do some of these calculations.  It does not handle
Zernikes (I dont think) but it may be a more practical approach.


Coincidentally I have done something along these lines.

Although it does not do it via Zernikes I have written a program which
allows one to draw on screen a mirror profile via mouse representing
departures from any target conic.  It uses 20 nodes to a clamped cubic
spline fit across a radius plus two outside the edge so the edge slope can
be better defined.  The initial aim of the program was to then simulate
Ronchi, Wire and Foucault (geometric only - I am not up to proper
diffraction calcs) but I subsequently added an analysis feature which does
the RMS and Strehl calculations for the target conic plus departures.   This
seems to work well.

Like many things I do this grew like topsy as I added interesting bits and
pieces and there are various bugs although it is close to release as long as
people are willing to put up with some idiosynchrosies.  The next step,
partly finished, is to add a Foucault reduction section so the derived
surface shape can then be directly used to generate Ronchi and Strehl info.
Its partly done but I have had to call it quits for now and tidy up what is
finished rather than dabble with the Foucault interface to the rest of the
program.

Maybe I can arrange release of this soon if people are interested but I am
rather strapped for time right now.

Sorry if this did not answer the original question and strayed far from
raytracing into the testing area.  Hope some is of interest.

Peter Smith.