Least-squares calibration method for fringe projection profilometry

This paper presents a novel calibration approach for determining the mapping relationship between the depth map and the phase difference in fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and hence perfectly describes the mapping between the depth map and the phase-difference distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. A least-squares estimation algorithm with linear computation is deduced to retrieve the related parameters and to reconstruct the mapping function. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.