Improved least-squares method for phase-to-height relationship in fringe projection profilometry

Abstract

Background: The height estimating function is very important for three-dimensional (3-D) measurement systems based on a digital light processing (DLP) projector and a camera. Sinusoidal fringe patterns of the projector are projected onto an object, and the phase of the measuring point is calculated from the camera image. Generally, the least-squares method (LSM) and look-up table(LUT) method are typically used to obtain the phase-to-height relationship. Results: The merit of LSM is that one equation is obtained from geometric analysis, but it has difficulty incorporating lens distortion. The LUT method can obtain an exact model that includes lens distortion, but the amount of memory needed increases with the number of pixels because each model is obtained at each pixel. This paper compares for these two methods and proposes an improved LSM using LUT. Conclusions: The proposed method has one equation like the case of LSM, but the modeling result is better than LSM because lens distortion is fully considered.