<title>Susceptibility of error-compensating algorithms to random noise and nonlinear phase modulations in phase-shifting interferometry</title>

Abstract

In phase shifting interferometry, many error-compensating algorithms have been reported. Such algorithms suppress systematic errors caused by nonlinear sensitivities of the phase shifter and nonsinusoidal waveforms of the signal. However, in a Fizeau interferometer where both error sources are equally dominant, the most common group of the algorithms produces errors comparable to those produced by discrete Fourier algorithms which have no capability to compensate for phase-shift errors. It is shown that if an algorithm has an extended immunity to nonlinear phase shift, it can suppress the effects of both error sources simultaneously and yield much smaller errors. When a phase-shifting algorithm is designed to compensate for the systematic phase-shift errors, it becomes more susceptible to random noise. The susceptibility of phase shifting algorithms to random noise is analyzed with respect to their immunity to phase-shift errors. It is shown that for the most common algorithms for nonlinear phase shift, random errors increase as the number of samples becomes large. This class of algorithms has an optimum number of samples for minimizing the random errors, which is not observed in the Fourier algorithms. However, for the new algorithms with an extended immunity to nonlinear phase shift, random errors decrease as the number of samples increases.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.