Steve,
> I had assumed that the test got more difficult because of the
absolute deviation from a sphere (tens of waves in this case) rather
than the f-ratio per se. Is a 1-meter F:3.6 harder than a .5 meter F:3.6?
Yes, the 1-meter interferogram will have the double fringe density.
> Is there an kind of interferometer that would be more suited my
> testing case?
Yes, but it's extremely expensive. I think the best test is a Fizeau
interferometer. It's a null test exactly on the optical axis, but only
for a ring-shaped zone. By moving the reference sphere along the
optical axis this zone can be moved in or out. Several interferograms
of different zones can later be stitched together by software. Look
for "Verifire Asphere" on the Zygo Website. US patents 6781700,
6879402 and 6972849. The mathematics are described in the paper
"Interferometric Measurement of Rotationally Symmetric Aspheric
Surfaces" by Michael F. Kuechel. I spent a few days with this
mathematical derivation until I fully understood how it works. This
paper is available on the Zygo website.
> Is there a good book or introduction to interferometery I should
read to get a working understanding of this process?
-- Daniel Malacara, Optical Shop Testing
-- Malacara + Servin, Interferogram Analysis for Optical Testing
-- My website is neither a good book nor an introduction. It's more a
collection of ideas, formulas and calculations. May be you find it
helpful:
http://www.astro-electronic.de/faq3.htm
Michael