Hybrid Method for Phase-Height Relationship in 3D Shape Measurement using Fringe Pattern Projection

A height estimating function is proposed based on geometric analysis for a three-dimensional (3-D) measurement system using a digital light processing (DLP) projector and a camera. The proposed 3-D shape measurement method is a hybrid method that combines the geometric parameter measuring method and the least squares method. This method uses the phase-to-height relationship for one line by plane analysis, and the related parameters are estimated using the least squares method. The proposed method has one function per image line instead of one function per image pixel. Sinusoidal fringe patterns of the projector are projected on the object, and the phase of the measuring point is calculated from the camera image. Then, the relationship between the phase by fringe patterns and the height of the measuring point is described as a parameter of the horizontal coordinate on the image plane. Thus, the 3-D shape of the object can be obtained. Our experiments show that the error of the modeling function is within +/- 0.1 mm when the x-z working range is 100x50 mm. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement using the geometric relationship between the projector and camera.