Optimal pulse width modulation technique combined with stair phase-coding method for absolute phase retrieval with projector defocusing

The accurate three-dimensional shape measurement of a complex surface is significantly important in industrial testing. However, three-dimensional profilometry by conventional sinusoidal fringe projection using a phase-shifting algorithm performs suboptimally because of the nonlinear intensity response of projectors. To overcome this problem, the present paper proposes using a combined optimizing sinusoidal pulse width modulation (SPWM) technique and stair phase-coding approach to obtain the unwrapped phase. Properly optimizing SPWM with a small degree of a defocusing projector to generate sinusoidal fringe patterns can overcome the undesired harmonics and nonlinear gamma effect. Two groups of four-step phase-shifting fringe patterns are used. One group of the stripes contains four sinusoidal patterns generated by the SPWM technique, which is used to determine the wrapped phase. The other group of stripes contains four sinusoidal patterns with the codeword embedded into the stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of the sinusoidal fringe phase, which is used to determine the fringe order for the phase unwrapping. Moreover, for the defocusing projection, because the frequency of the phase-coding fringe increases, the fringe order decision becomes less reliable. Thus, a self-correction phase unwrapping method is applied for phase retrieval. Experiments were conducted to verify the performance of the proposed method.