Compound phase-stepping algorithm by Lissajous figures technique and iterative least-squares fitting

Many algorithms for the phase-stepping (or phase-shifting) interferometry have been developed for last decade. In recent years, some algorithms are becoming more and more attractive to practical measurement because the phase steps can be calculated through fringe data itself and the calculation of phase distribution is insensitive to phase-stepping errors. A compound phase-stepping algorithm by Lissajous figures technique and iterative least-squares fitting method is proposed in this paper. The calculation of phase distribution-is composed of two parts for analysis of real interferograms. First,calculate the initial phase steps by utilizing Lissajous figures and ellipse fitting. Second, calculate the exact phase distribution by solving the coupled equations obtained through the spatial least-squares fitting and the serial least-squares fitting. The iterative method with the initial phase steps obtained from the first part is applied to the second part. An optical disk has been measured to verify the performance of the new algorithm. The experimental results show that the new algorithm is insensitive to phase-stepping errors and phase steps can be automatically calibrated on line.