Holistic form reconstruction based on a nonlinear 3D zonal grid model in stereoscopic deflectrometry

Phase measuring deflectrometry (PMD) is extensively used to measure the specular surfaces. Stereo-PMD can address the height-slope ambiguity problem, but it remains the error propagation and accumulation in traditional stepwise reconstruction, which involves slope estimation followed by slope integration. Furthermore, while the zonal method is widely used in slope integration due to its superior spatial resolution, the employed regular linear two-dimensional (2D) grid is often inadequate for actual irregular slope samplings. In this work, based on stereo-PMD, by replacing relative height with absolute height, a nonlinear three-dimensional (3D) grid model is proposed to shorten the error propagation chain and overcome the limitations of irregular grid data. The reconstruction method using this model only consists of two nonlinear optimizations. The results indicate an enhanced low-order accuracy and noise robustness when compared with the traditional stepwise stereo-PMD method.