Three-dimensional profilometry based on two-step generalized phase shift for phase measurement of grating projections

An algorithm is proposed to extract the phase from deformed grating images using a two-step generalized phase-shifting technique for fringe projection profilometry (FPP). This method is based on the principle of the least squares iterative method, which directly extracts unknown phase shift from two deformed grating images that have been modulated by an object and then reconstruct the object wave. Compared to traditional phase-shifting technique, it does not require pre-setting and precise control of the phase shifter, significantly reducing the dependence on the precise calibration of the phase shifter which is particularly beneficial in environments affected by factors such as air turbulence and mechanical vibrations. Moreover, it reduces the number of projected grating images, and increases the measurement speed. Computer simulations and optical experiments demonstrate the effectiveness and correctness of this method.