Suppression of fundamental-frequency phase errors in phase-shifting interferometry

I develop and test several new phase-shifting formulas for a Fizeau interferometer, using a spherical cavity of high NA. The associated phase-shift miscalibrations provide a useful range for testing phase-shift error compensation experimentally. After removing the "double-frequency" cyclic phase variation from the error-fringe pattern by well-known methods, the residual phase oscillations occur mainly at 1 and 3 times the fringe frequency. The latter can be addressed by the theory of characteristic polynomials; the former cannot, but is removed by a variation on known averaging methods, and allows empirical optimization of phase-reconstruction performance, which can then be analyzed with characteristic polynomials again.