Analysis of a multi-wavelength multi-camera phase-shifting profilometric system for real-time operation

Real-time accomplishment of a phase-shifting profilometry through simultaneous projection and recording of fringe patterns requires a reliable phase retrieval procedure. In the present work we consider a four-wavelength multi-camera system with four sinusoidal phase gratings for pattern projection that implements a four-step algorithm. Successful operation of the system depends on overcoming two challenges which stem out from the inherent limitations of the phase-shifting algorithm, namely the demand for a sinusoidal fringe profile and the necessity to ensure equal background and contrast of fringes in the recorded fringe patterns. As a first task, we analyze the systematic errors due to the combined influence of the higher harmonics and multi-wavelength illumination in the Fresnel diffraction zone considering the case when the modulation parameters of the four gratings are different. As a second task we simulate the system performance to evaluate the degrading effect of the speckle noise and the spatially varying fringe modulation at non-uniform illumination on the overall accuracy of the profilometric measurement. We consider the case of non-correlated speckle realizations in the recorded fringe patterns due to four-wavelength illumination. Finally, we apply a phase retrieval procedure which includes normalization, background removal and denoising of the recorded fringe patterns to both simulated and measured data obtained for a dome surface.