Fringe projection profilometry has been widely applied to three-dimensional measurement. However, the nonlinear effect of the projector leads to errors in the unwrapped phase in the phase-shift method. In this paper, we propose a direct gamma estimation method. Theoretical derivation shows that the gamma factor is related to the three-step phase-shifted fringe patterns and the ideal unwrapped phase. The unwrapped phase after Gaussian low-pass filtering is taken as the initial estimate of the ideal unwrapped phase. We correct those abnormal values after calculating the gamma factor. The corrected gamma factor is used to inverse gamma correct the captured fringe patterns, and then the gamma-corrected unwrapped phase is obtained by phase demodulation and phase untangling from the inverse gamma corrected fringe patterns. Then we perform iterative operations on the gamma factor and ideal unwrapped phase. We consider the gamma-corrected unwrapped phase as the new ideal unwrapped phase, recalculate and update the new gamma factor until the gamma factor converges to a stable, desired state. Our method only needs to project and collect three frames of fringe pattern, which meets the high-speed measurements requirement. The experimental result of the face mask demonstrates that our method can effectively reduce the nonlinear phase errors.
To unwrap the wrapping phase from phase measuring profilometry in 3D surface measurement, many spatial and temporal phase retrieval methods have been presented. However, spatial phase retrieval method often leads to errors because of discontinuous morphology, noise and fringe undersampling. Temporal phase retrieval method can solve this problem. But the method needs multiple frames of fringe images which would take much time. We proposed a novel absolute phase measurement method with few-patterns to overcome this problem. The proposed method combines an object reflectivity correction and a half-period gray-coded phase unwrapping algorithm. One group of precoded three-step phase-shifting fringe patterns are used to determine the wrapped phase, divide the region, and correct the surface reflectivity of the tested object, a frame of half-period gray-coded pattern is used to determine the fringe order. The proposed method can obtain a large number of codewords for fringe order without decreasing the intensity level for each stair. The result shows that our half-period gray-level coding (HGC) method is robust and efficient.
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