Pixel-Wise Phase Unwrapping With Adaptive Reference Phase Estimation for 3-D Shape Measurement

Abstract

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.