Three-flat test solutions based on simple mirror symmetry

In interferometric surface and wavefront metrology, three-flat tests are the archetypes of measurement procedures to separate errors in the interferometer reference wavefront from errors due to the test part surface, so-called absolute tests. What is believed to be a new class of solutions of the three-flat problem for circular flats is described in terms of functions that are symmetric or antisymmetric with respect to reflections at a single line passing through the center of the flat surfaces. The new solutions are simpler and easier to calculate than the known solutions based on twofold mirror symmetry or rotation symmetry. Strategies for effective azimuthal averaging and a method for determining the averaging error are also discussed.