Linear error analysis of differential phase shifting algorithms

An important process in optical metrology is the determination of the difference between test and reference states. Direct calculation of the optical phase difference encoded in two fringe patterns can be done by using differential phase shifting algorithms (DPSAs). If the phase difference does not reach a complete period, DPSAs provide directly its continuous values and the known limitations of the unwrapping stage are avoided. This work presents a generic design protocol of DPSAs obtained by a least squares fitting that combines phase shifting algorithms (PSAs) in a suitable non-linear way. Results are also provided that quantitatively characterize the effect on some representative DPSAs by the main systematic error sources. The goodness of the analyzed DPSAs is contrasted with the experimental results for wavefront distortion evaluation using phase-shifted Mach–Zehnder fringe patterns.