General phase-stepping algorithm using Lissajous figures technique

Many phase-stepping algorithms have been developed for last decade. Some of them may be more attractive to practical measurements because of the insensitivity to phase-stepping errors. But it should be noticed that all existing phase-stepping algorithm need to know or calculate the phase steps. Why cannot we extract the measured phase without knowing or calculating phase steps? A new phase-stepping algorithm is proposed by our group. The algorithm can be implemented without knowing or calculating the phase steps. Actually, the new algorithm gives important improvements for the algorithms developed by C.T.Farrell and M.A.player. Based on using Lissajous figures and ellipse fitting, the new algorithm introduces a simple transform for the intensity of the interferograms. New phase extraction expressions are derived. The simulating results indicate that the new algorithm is insensitive to phase-stepping errors and the accuracy of the new algorithm is only limited by the computation truncation errors.