Suppression of spatial nonuniformity and nonlinearity in phase modulation in phase-shifting interferometry

Abstract

In phase shifting interferometers, spatial non-uniformity of the phase modulation often happens in such cases where as aspherical (or spherical) mirror is compared to the corresponding aspherical standard surface which is translated along the optical axis by piezo electric transducer to introduce phase modulation. The amount of phase shift is then different across the observing aperture depending on the gradient of the testing surface. The nonlinear sensitivity of the phase modulator causes a significant errors in measured phase when there is a spatial nonuniformity in phase shift. Many phase measuring algorithms reported to date cannot compensate for the spatial nonuniformity if there is a nonlinear phase shift. It is shown that if we add a new symmetry to the sampling functions of the phase measuring algorithm we can suppress the phase errors caused by the spatial non-uniformity of the phase shift. The new algorithms need at least one more image frame to acquire the symmetry. The lowest-order algorithm compensating for quadratic spatially non-uniform phase modulation consists of six frames.