Enhanced high dynamic range 3D shape measurement based on generalized   phase-shifting algorithm
  It is a challenge for Phase Measurement Profilometry (PMP) to measure objects with a large range of reflectivity variation across the surface. 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 3D shape measurement method without changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval when any of the regular fringe patterns are saturated. But Jiang's method still has some drawbacks: (1) The phases in saturated pixels are respectively estimated by different formulas for different cases. It is shortage of an universal formula; (2) it cannot be extended to four-step phase-shifting algorithm because inverted fringe patterns are the repetition of regular fringe patterns; (3) only three unsaturated intensity values at every pixel of fringe patterns are chosen for phase demodulation, lying idle the other unsaturated ones. We proposed a method for enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm, which combines the complementary technique of inverted and regular fringe patterns with generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely regular and 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 by 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 Jiang's method, which demonstrate that the proposed method not only expands the scope of Jiang's method, but also improves the measurement accuracy. 
Minmin Wang, Guangliang Du, Canlin Zhou, Chaorui Zhang, Shuchun Si,   Hui Li, Zhenkun Lei, YanJie Li
cs.CV physics.optics