Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N greater than or equal to 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations. (C) 2004 Optical Society of America