Analysis algorithm of randomly phase-shifting fringes for reducing high order harmonic error

High-order harmonics and phase shift miscalibration are the two main systematic error sources that affect the accuracy of fringe analysis. To deal with these problems simultaneously, an iterative phase-shifting algorithm based on frequency filtering is proposed. The proposed method filters the high-order harmonics in spectrum domain by using the Butterworth low-pass filter, and then extracts the phase from three frames of randomly phase-shifting fringes by using the least-squares iterative algorithm. Numerical simulation and experimental results show that the proposed method can effectively reduce the ripple caused by high-order harmonics and randomly phase-shifting error and thus can increase the measurement accuracy. The proposed algorithm is suitable for the high-accuracy interferometry and three-dimensional profilometry measurement.