Quasi-pointwise two-step phase-shifting profilometry with the fringe parameters estimated statistically

Fringe projection profilometry is a popularly used three-dimensional measurement technique in which phase-measuring algorithms based on two-step phase shifting are usually used because of their best tradeoff between measurement resolution and speed. Most two-step phase-shifting algorithms involve neighboring or other spatial operations, thus having degraded accuracies at edges and discontinuities of the measured object surface. Pointwise two-step algorithms enable overcoming this issue. With them, however, the offsets of the dynamic ranges of the projector and camera are usually improperly overlooked or inaccurately estimated, thus inducing errors in their measurement results. For solving this problem, this paper suggests a quasi-pointwise two-step phase-shifting algorithm for fringe projection profilometry. This algorithm models the captured fringe patterns practically by taking the offsets of the dynamic ranges of the projector and camera into account, and estimates the fringe parameters from the statistics of fringe intensities. As a result, we can calculate fringe phases in a pointwise way from two fringe patterns having a phase difference of π/2 radians. The simulation and experimental results demonstrate that the proposed method has a relatively low level of errors in measuring object surfaces having isolated regions and discontinuities.