A General Reconstruction Framework for Deflectometric Measurement Based on Nonuniform B-Splines

Abstract

Phase measuring deflectometry (PMD) is a powerful tool well suited for precision measurement of optical surfaces. However, accurate and efficient surface reconstruction from gradients is challenging for the PMD. Because most reconstruction algorithms are not well adapted to complex surface forms with local undulations, and a large number of tedious operations are demanded for calculating the ray intersections. Besides, the format of the reconstructed data is usually not compatible to the machine tools and additional format conversion is required, which increases the computational effort and lengthens the error propagation chain. Therefore, a general reconstruction framework is proposed for the deflectometric measurement based on the non-uniform B-spline (NUBS), which embeds the NUBS into the PMD framework to enhance the local representativity. The correspondences between the points on the screen, camera and workpiece can be established by the parameter mapping instead of by the ray intersections. Simulations and experiments prove the effectiveness of the proposed method, and the measurement accuracy can achieve a level of one hundred nanometers in practice.