Efficient Half-period Phase Histogram Equalization for General Phase-shifting Algorithms with Phase-shift Errors

• Published in: IEEE transactions on instrumentation and measurement Vol. 71; p. 1
• Main Authors: Wang, Yuwei, Zhu, Haojie, Wang, Yu, Chen, Xiangcheng, Wang, Yajun
• Format: Journal Article
• Language: English
• Published: New York IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Diffraction patterns; Equalization; Errors; half-period phase; histogram equalization; Histograms; optical metrology; Phase shift; phase-shift errors; Phase-shifting algorithms
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2022.3212743

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 paper proposes an efficient half-period phase histogram equalization (HPHE) method to handle the phase-shift errors in phase-shifting algorithms, which doesn't 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 π in phase domain. Therefore, we can obtain the half-period phase ranging from 0 to π 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.