Joint least-squares algorithm correcting phase-shift errors and detector nonlinearity simultaneously in phase-shifting interferometry

Phase-shifting interferometry may suffer from the errors caused by the miscalibration of the phase shifter and the nonlinearity of the detector simultaneously. These errors are not easy to eliminate because they are generally coupled with each other in interferograms. For solving this issue, we suggest a joint least-squares phase-shifting algorithm. It allows one to decouple these errors through an alternate least-squares fitting procedure, thus accurately estimating phases, phase shifts, and coefficients of the detector response simultaneously. The converging condition of this algorithm, associated with the uniqueness of the equation solution and anti-aliasing phase shifting, is discussed. Experimental results demonstrate that this proposed algorithm is helpful for improving phase-measuring accuracy in phase-shifting interferometry.