ATM Fold Flat Flatness

[Anthony Stillman <atmer@flash.net>]

In some off list correspondence the issue of fold flat flatness has arisen.
The common wisdom is that such flats should be exceptional.  For example,
in issue number 32 (Spring 1988) of "Telescope Making", in an article
written by Robert E. Cox, entitled "Portability Is a Folded Refractor", the
third paragraph reads:

"The solution is a simple one: fold the optical path between the objective
and its focal plane with mirrors.  It is important that the folding flats
must be of a very high quality.  Furthermore, it is advisable that the tilt
of the flat to a beam of light from the objective be kept to a minimum.
The more oblique it is, the more sensitive the system becomes to small
residual curvature in the flat."

As I wrote, the common wisdom, but is it so.  An extraordinarily difficult
person, albeit brilliant optical engineer, told me a few years ago that it
wasn't.   To clear this up in my head I've been running some OSLO LT models.

Clearly, residual power in a tilted fold flat will induce astigmatism.
Further, it's clear that the more oblique the tilt, the more stig will be
introduced.  And, so what.  Does it really matter enough to fork over a
couple hundred dollars for a 1/20 wave flat?

For the purpose of this post I've confined my examination to a typical
visual ATM instrument.  Namely, a newtonian with an 8 inch f/8 paraboloidal
primary  and a 1.57 inch diagonal 8 inches from the focal plane.  A field
angle of 17.5 arc minutes was chosen, as in an ideal system, this gives a
full field peak to valley wavefront error of about 1/2 wave and a
corresponding RMS wavefront error of about 1/10 wave.  Further, I've
limited the flat's failing to power.  That is, given it a finite radius.

It's difficult to describe the system impact with just a few numbers, but
the following table does give a feel for it.


                 on-axis           full field        Strehl
                 P-V     RMS       P-V     RMS
perfect flat     0.00    0.00      0.50    0.10       1.00

1/4 wave cave    0.13    0.03      0.56    0.11       0.97
1/4 wave vex     0.13    0.03      0.49    0.10       0.97

1/2 wave cave    0.25    0.06      0.63    0.13       0.88
1/2 wave vex     0.25    0.06      0.48    0.10       0.88

1 wave cave      0.50    0.11      0.87    0.17       0.61
1 wave vex       0.51    0.11      0.57    0.13       0.61

The peak to valley and RMS values are in waves.


The first conclusion I draw from this is that a quarter wave of sag across
the minor axis of a diagonal can be tolerated.  The second conclusion is
that if you have a chose between a flat that's a bit of concave and a flat
that's a bit convex, go with the one that's vex.

I know all of this may be seem like blasphemy to some.  A decade ago I
would have said as much (uh, did).  And, there's more to a flat's flatness
than just an absence of power.  Higher order aberrations and surface
smoothness come to mind.  Both will be fodder for further examination.

Anthony


The included excerpt written by Robert E. Cox is copyrighted by Kalmbach
Publishing Company 1987.  Its inclusion is in compliance with the copyright
act of 1976.

PS  At present, I am some thirty e-mails behind in both on and off list
communication.  There are people I have yet to thank for help and ideas,
and there are quires to which I intend to respond.  To those concerned,
please forgive my tardiness.  But, uh, my dog ate my computer.  Yea, that's
it.  It fell in the creek and then my dog ate it.