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

Phase measuring deflectometry (PMD) is a powerful tool well suited for the precision measurement of optical surfaces. However, accurate and efficient surface reconstruction from gradients is challenging for PMD. Because most reconstruction algorithms are not well adapted to complex surface forms with local undulations, a large number of tedious operations are demanded for calculating the ray intersections. Besides, the format of the reconstructed data is usually not compatible with 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 nonuniform 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 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 100 nm in practice.