Three-Flat Test Solutions based on Simple Mirror Symmetry
Three-flat tests are the archetypes of measurement procedures used in interferometric surface and wavefront metrology to separate errors in the interferometer reference wavefront from errors due to the tests part surface, so-called absolute tests. A new class of solutions for the three-flat problem for circular flats is described in terms of functions that are symmetric or anti-symmetric with respect to reflections at a single vertical line through the center of the flat surfaces. The new solutions are simpler, and easier to calculate than the known solutions based on two-fold mirror symmetry or rotation symmetry. Strategies for effective determinations of azimuthal wavefront averages are also discussed.