Full-field 3D shape measurement of discontinuous specular objects by direct phase measuring deflectometry

With the advent of intelligent manufacturing, phase measuring deflectometry (PMD) has been widely studied for the measurement of the three-dimensional (3D) shape of specular objects. However, existing PMDs cannot measure objects having discontinuous specular surfaces. This paper presents a new direct PMD (DPMD) method that measures the full-field 3D shape of complicated specular objects. A mathematical model is derived to directly relate an absolute phase map to depth data, instead of the gradient. Two relevant parameters are calibrated using a machine vision-based method. On the basis of the derived model, a full-field 3D measuring system was developed. The accuracy of the system was evaluated using a mirror with known positions along an accurate translating stage. The 3D shape of a monolithic multi-mirror array having multiple specular surfaces was measured. Experimental results show that the proposed DPMD method can obtain the full-field 3D shape of specular objects having isolated and/or discontinuous surfaces accurately and effectively.