A Wavefront Integration Algorithm Based on Radial Basis Function for Off-Axis PMD

Abstract

Sampled points on a measured surface are not evenly spaced on rectangular grids but, rather, have a more general quadrilateral geometry due to the perspective effect of the off-axis configuration, which is extensively utilized in phase measuring deflectometry (PMD). The current procedures for slope-to-wavefront integration results in reconstruction errors, which impact PMD to achieve a higher measurement accuracy. Due to the advantageous properties of the radial basis function (RBF) for irregular sampling and incomplete data, the quadrilateral geometry acquired by a CCD is first realized in this paper using the ray tracing method, which is used to obtain the actual measurement area and sampling interval in off-axis PMD instead of the area defined by the mathematical formula in the past when RBF was used. The RBF integration method is researched in this paper. The simulation and experiment show that RBF is a robust and higher accuracy algorithm for off-axis PMD. We further implement the RBF integration method to measure a crystal transparent element where an off-axis configuration is required.