An iterative algorithm for interferograms with random phase shifts and high-order harmonics

Random phase shifts and high-order harmonics are common sources of systematic errors in phase-shifting interferometry. An iteration algorithm based on the least-squares method is proposed to deal with these problems simultaneously. Only 2p+1 randomly phase-shifted interferograms are needed to extract phase information and phase shifts accurately and eliminate the effects of harmonics up to the pth order. Simulations show that our method exhibits higher precision than Wang's method and the 6A-frame algorithm if the interferograms have random phase shifts and high-order harmonics. It converges with almost the same accuracy of about 0.005 rad when the RMS of random phase shifts is less than 0.6. Experiment shows that the proposed method eliminates the modulation with three times the fringe frequency by compensating for the effects of the second-order and third-order harmonics.