Phase-height relationship by plane analysis in 3D shape measurement using fringe pattern projector

In a three-dimensional(3-D) measurement system based on a digital light processing (DLP) projector and a camera, a height estimating function is proposed based on geometric analysis. 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. 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 modeling errors for the given x-z plane are within ±0.1 mm. The model for the entire working space can be represented by several plane models because all the x-z plane models along the y-axis are nearly the same. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement.