Inertia alignment of phase-shifting algorithms for high-numerical-aperture spherical testing in Fizeau interferometry

In Fizeau interferometry for high-numerical-aperture spherical surface tests, the mechanical phase shift becomes spatially nonuniform within the observation aperture. We divided the aperture into annular regions and calculated the object phase using several algorithms designed for different phase shifts. The division substantially decreased the nonuniformity; however, it caused bias errors at the regional boundaries in the measured phase. The error is due to the different error coefficients of the algorithms for the phase-shift nonlinearity. A convolution technique that modifies a sampling window to align the error coefficients of a set of algorithms is proposed. The technique is experimentally shown to minimize phase measurement errors.