Direct gamma estimation method in Fringe projection profilometry

Abstract

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.