Complementary double pulse-width-modulation for 3D shape measurement of complex surfaces

Pulse-width modulation has the advantages of fast projection speed and high precision. However, when it is used to measure the three-dimensional (3D) shape of complex surfaces, it suffers from harmonic interference caused by slight defocusing and is sensitive to pixel oversaturation. To achieve high-speed and accurate 3D measurement of complex surfaces using this method, in this paper, a complementary double pulse-width-modulation (CDPWM) is proposed and used to generate ideal phase-shift fringe patterns. In our method, a triangular carrier signal with a zero phase is first used to generate a set of double pulse-width-modulation (DPWM) patterns, and then a triangular carrier signal with a phase of π/2 is used to generate another set of DPWM patterns. Then, the CDPWM is obtained by fusing these two sets of DPWM patterns. We demonstrate that CDPWM can tremendously suppress harmonic interference so that in practical applications, a smaller defocus can be used to robustly reconstruct complex surfaces. Moreover, it is proved that the patterns corresponding to the π/2 phase are the compensation patterns of the patterns corresponding to the zero phase, which enables CDPWM to eliminate or reduce the pixel oversaturation effect caused by a surface with a high dynamic range. Through experiments on simulated and real data, the proposed method is shown to substantially improve the phase quality and measurement accuracy over a wide range of fringe periods (e.g., from 18 to 912 pixels), especially when the defocus level is low. Different camera exposure times are used to demonstrate the robustness of the proposed method to oversaturated pixels. Furthermore, we measured a set of ice surfaces and a metal surface containing both low- and high-reflection areas. The projector was set to a slight defocus, which better preserved the binary characteristics of the patterns it projected. The measurement results proved our method can significantly improve the measurement accuracy of surfaces with complex reflection characteristics.