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The phase-shifting method is widely used in fringe projection profilometry (FPP),The digital light projector (DLP) and charge coupled device (CCD) are generally nonlinear devices.The captured fringes do not have a good sinusoidal property,which leads to errors in the retrieved phase map.The methods to calibrate the nonlinear response of a FPP and compensate for the associated error can be classified into active methods(correction before pattern projection) and passive methods(correction after pattern projection).The basic idea of the active method to precisely obtain the input output relation function of the projector. The passive method compensates the error in phase domain by the post-processing algorithms. Huang et. al. presented the double three-step phase shifting algorithm to reduce the nonlinear phase error by projecting two groups of three-step phase-shifting fringe with an initial phase offset of 60 degree.Subsequently,some scholars improved this method. Zheng et.al. presented a method that combined the two wrapped phases to obtain the combination of the wrapped phase,it is simpler than Huang’s method because only one time phase unwrapping procedure is needed. Lei et. al. combined double-step phase-shifting method and multifrequency temporal phase unwrapping algorithm, proposed a multi-frequency inverse-phase method to realize the 3D shape measurement of the complicated objects. Mao proposed a similar approach.The main difference between Lei and Mao is that the operation order of double-step phase-shifting algorithm for error compensation is different. In Mao’s method,error compensation is performed in the wrapped phase map while it is done with the unwrapped phase map in Lei’s method.This paper compares double-step phase-shifting algorithm, its variational algorithm (Zheng's method, Lei’ s method, Mao's method) and phase shift algorithm with twice the number of steps for nonlinear error compensation, our study finds that these algorithms have similar effect in reducing nonlinear phase error. Phase shift algorithm with twice the number of steps is simpler and more direct than double-step phase-shifting algorithm.In variational algorithm, Zheng’s method reduces the number of phase unwrapping by half compared with traditional double-step phase shifting algorithm,Mao’s method is essentially the same as Lei’s method,it was by introducing multi-frequency temporal phase unwrapping algorithm that Lei and Mao's method can measure the complex object. Experimental results are presented to demonstrate the rationality of this analysis.
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