Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing

Three-dimensional profilometry by sinusoidal fringe projection using phase-shifting algorithms is usually distorted by the nonlinear intensity response of commercial video projectors. To overcome this problem, several methods including sinusoidal pulse width modulation (SPWM) were proposed to generate sinusoidal fringe patterns with binary ones by defocusing the project to some certain extent. However, the residual errors are usually nonnegligible for highly accurate measurement fields, especially when the defocusing level is insufficient. In this work, we propose two novel methods to further improve the defocusing technique. We find that by properly optimizing SPWM patterns according to some criteria, and combining SPWM technique with four-step phase-shifting algorithm, the dominant undesired harmonics will have no impact on the phase obtained. We also propose a new sinusoidal fringe generation technique called tripolar SPWM, which can generate ideal sinusoidal fringe patterns with a very small degree of defocusing. Simulations and experiments are presented to verify the performance of these two proposed techniques.