Enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm

Measuring objects with large reflectivity variations across their surface is one of the open challenges in phase measurement profilometry (PMP). Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to phase fluctuations and errors. Jiang et al. proposed a high dynamic range real-time three-dimensional (3D) shape measurement method (Jiang et al., 2016) [17] that does not require changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval whenever any of the regular fringe patterns are saturated. Nonetheless, Jiang's method has some drawbacks: (1) the phases of saturated pixels are estimated by different formulas on a case by case basis; in other words, the method lacks a universal formula; (2) it cannot be extended to the four step phase-shifting algorithm, because inverted fringe patterns are the repetition of regular fringe patterns; (3) for every pixel in the fringe patterns, only three unsaturated intensity values can be chosen for phase demodulation, leaving the other unsaturated ones idle. We propose a method to enhance high dynamic range 3D shape measurement based on a generalized phase-shifting algorithm, which combines the complementary techniques of inverted and regular fringe patterns with a generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely the regular and the inverted fringe patterns, are projected and collected. Then, all unsaturated intensity values at the same camera pixel from two sets of fringe patterns are selected and employed to retrieve the phase using a generalized phase-shifting algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Jiang's method, demonstrating that our method not only expands the scope of Jiang's method, but also improves measurement accuracy.