Single frame digital phase-shift fringe projection profilometry based on symmetry transform

To solve the problem of large filtering error of the fundamental frequency in the composite Fourier transform profilometry and shorten the measurement time needed in the phase shifting profilometry, a symmetrical transformation method (STM) for measuring the three-dimensional (3D) contour of objects is proposed. Only one composite grating is projected on the object in the STM. The grating is composed of overlapping two orthogonal sinusoidal fringe patterns with a pi/2 phase difference and different frequencies. The two sinusoidal deformed patterns with a pi/2 phase difference are demodulated from the deformed composite pattern reflected on the surface of an object. The other two patterns can be obtained through a symmetric transformation with sub-pixel precision. Based on the captured and calculated fringe patterns, the fast reconstruction of the 3D shape of the objects could be achieved. The STM has broad application prospects in the real-time 3D measurement field due to its single-shot feature.