Re: ATM Transverse Aberration or Wavefront Error?

[CZambuto@aol.com]

Scott Rychnovsky asked:

>I have been figuring a 6" F5.5 and am finding it challenging.  One
>difficulty I have is in how to interpret the Foucault test.  I am using a
>version of the TEX program that will calculate the reference paraboloid
>with either Texereau's method or Suiter's method. My understanding is that
>the Tex method minimizes the wavefront error and the Suiter method
>minimizes the transverse aberration.  In a recent set of data the
>(incompletely figured) mirror gave a wavefront error with the Tex method of
>about 1/5, with transverse aberrations max of about 1.5 while the Suiter
>method gave a transverse aberation of 0.87 with a wavefront error of 1/2.5.
>The second analysis would appear to meet the criteria that the transverse
>aberration be less than one, but the wavefront error is unacceptable. My
>question is what am I trying to optimize?

>Ideally the transverse aberration should be <<1 and the wavefront error
>should be 1/(a large number).  Which should take precedence?  Clearly the
>two different analyses are working with the same mirror and the same data,
>and by using one method or the other I can make either criteria look a bit
>better.  The two different analyses may change my impression of when the
>mirror is "good enough".  Which one should I use?

----------------------------------------------

I find that the Tex method, by creating a reference parabola is able to give
much better wavefront numbers, however, personally, I prefer to use Suiter's
typically more difficult criteria (exploratory focus) and get past that. At
any rate, one reason I am responding is I am hearing a combination of
transverse error/wavefront numbers that don't sound right. The Tex method
numbers sound plausible, but the Suiter method (exporatory focus) do not. In
9 years of mirror making I have not seen a combination of .87 TA and 1/2.5
wavefront error. A transverse error of .87 is comfortably within the
Milles-Lacroix envelope, and is usually accompanied by wavefront numbers more
to the tune of 1/5 to 1/10 or so. I am wondering if there is a typo or
miscalculation, or perhaps it is being read wrong. 

I would be interested in seeing the numbers/information you plugged in to get
those results, and check the results with Suiter's data reduction program
"Admir". BTW, Suiter's program "Genmir" gives essentially the same numerical
results as Admir. The Basic listing for Genmir is readily available, having
been written in the TM Magazine article he did (#32).

Now about your question,

Wavefront measurements are derived from a calculation of the deviation in
height of the surface of the mirror, with respect to a given, or chosen
parabola. Transverse aberration is a reference to where the light falls at
the focal plane with respect to the airy disk, whose theoretical diameter has
to do with the focal ratio of your telescope and the wave nature of light.
 So "wavefront" tells you more specifically about the surface of the glass,
and "transverse error" tells you more specifically about what's going on at
the focal plane. Both measurements are valid, however for this method of
testing I believe it most important first to have a transverse error of 1.0,
or one airy disk diameter or less, because that tells you what is happening
at focus. You can have a 1/4 wave mirror that has transverse error of one,
but you can also have a 1/4 wave mirror that is much worse. It depends on the
slope of those 1/4 wavefront errors. -For a nice graphic of how that works,
see "Star Testing Astronomical Telescopes" by HR Suiter, page 7. So get the
T.A. less than one, first. Then worry about how good a wavefront number you
want.

If I remember right, Jean Texereau's criteria at their TM group was to get
the transverse aberration less than one, and a corresponding wavefront of
1/10 or better. If your data reduction numbers are correct, you have further
to go, by that standard. At the telescope maker's workshop I teach, we work
until the TA is .75 or less. At that point we don't care what the wavefront
is (It usually comes in at about 1/10 to 1/15). For the custom refigure jobs
I do, I have a minimum criteria of .5 TA, and usually (on the smaller ones,
especially) get them to around .25 and better. Again, at that point wavefront
doesn't matter. The surface has to be so regular with respect to the parabola
to achieve that kind of transverse error, that corresponding wavefront
numbers, as Suiter says, beyond 1/10 "are probably moonshine".

>PS- My secondary has not come in yet so I have not been able to star test
>the mirror.

That of course, is the final test, and for those who work until their
extral-focal patterns are essentially interchangeable, they don't have to
worry about ANY numbers.

Hope that helps, and again, I'd be very interested to see the measurements
and mask parameters that made those numbers, if for no other reason than that
I might learn something.

Best Wishes,

Carl Zambuto
optician/educator/Director of the Nisqually Valley Telescope Maker's Workshop
Rainier, Wa.