Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry

A novel fast convergent algorithm to extract arbitrary unknown phase shifts in generalized phase-shifting interferometry (PSI) is proposed and verified by a series of computer simulations. In this algorithm an error function is introduced and then the unknown phase shifts are found by an iterative tangent approach. In combination with the statistical method, this algorithm can give the most exact results in the fewest iteration steps. It can be used for generalized PSI of arbitrary frames for both smooth and diffusing objects and can usually reach the exact phase shifts with only four or five iterations for three- or four-frame PSI.