Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry

Phase-shifting fringe projection profilometry usually suffers from the errors induced by illumination fluctuations. As a result, ripple-like artifacts that have the same periods as fringes appear on the phase map. Because the illumination fluctuations cannot be simply modeled using fringe harmonics, their induced errors are difficult to remove by use of a phase-shifting algorithm. To solve this problem, this paper suggests a least-squares method constrained by phase smoothness. This method calculates fringe phases using the generalized phase-shifting algorithm and estimates coefficients related to illumination fluctuation by use of smoothed phase map. Alternately implementing these two steps enables one to eliminate effects of illumination fluctuations on the measurement results. Experimental results demonstrate that this proposed algorithm is helpful for improving measurement accuracy.