Least-squares algorithm for phase-stepping interferometry with an unknown relative step

A pointwise least-squares phase-stepping algorithm with an unknown relative phase step is proposed. In phase-stepping interferometry the recorded temporal intensity sequence is a discrete sinusoidal signal biased by a direct-current component. Its value at a certain time can be predicted from its three past samples by use of a recursive formula. Based on this linear prediction property, an unbiased least-squares estimator is deduced to determine the relative phase step from a sequence of intensity values, and the result is used to evaluate the phase value. The validity and performance of this algorithm are verified by computer simulations.