LAUSR

Phase-shifting algorithms are widely used for optical metrology that extract the phase from several fringe patterns with phase shifts. However, accurate phase shifts are always the crucial premise to guarantee the accuracy of phase extraction, and phase shift errors are usually the major error source. This article proposes an efficient half-period phase histogram equalization (HPHE) method to handle the phase shift errors in phase-shifting algorithms, which does not estimate any parameters and only require processing one half-period phase. Through analysis, we know that the period of the phase errors is half that of the wrapped phase, and the period of its histogram is $\pi $ in phase domain. Therefore, we can obtain the half-period phase ranging from 0 to $\pi $ by computing the remainder of the original phase. Then we directly apply histogram equalization on the distorted half-period phase to estimate the corrected half-period phase, then we can obtain the corrected whole-period phase. Some simulations and experiments have been conducted for three-, four-, and five-step phase-shifting algorithms, and their results indicate that the HPHE method can effectively reduce the phase errors and performs much better than the whole-period phase histogram equalization (WPHE) method.