Phase measuring deflectometry (PMD) is an effective technique for three-dimensional measurement of specular surfaces. However, the ambiguity of monoscopic PMD and the time-consuming searching process of stereoscopic PMD are challenges for specular surface reconstruction. To solve it, we propose an iterative reconstruction algorithm for the stereoscopic phase measuring deflectometry system free of the time-consuming searching process for each pixel. An arbitrary seed point on the specular surface is accurately obtained via a coarse-to-fine optimization means without any other expensive and complicate auxiliaries. Then, a plane with the height of seed point is set as the initial surface form for the iteration, in which the pinhole model is used to find the linear relation to update the surface form. The converging height is the output as the final result. Simulations and experiments verify the feasibility and efficiency of our proposed method based on the stereoscopic phase measuring deflectometry system. The accuracy and robustness are comprehensively evaluated as well.

Calibration is a critical step for the phase measuring deflectometry system. Existing calibration methods are mainly optimizing the calibration parameters with respect to the 2D re-projection error criterion. However, such a procedure cannot reduce metric errors in the practical application. Therefore, an accurate and practical calibration method is proposed. In which, conventional calibration means is first applied for the primary calibration. Then, a precise square planar mirror is used for the optimization of system calibration parameters. All the intrinsic and extrinsic parameters are considered as a global multi-objective optimization problem. Three metric error criteria are introduced to evaluate the 3D reconstruction accuracy of the reference mirror. Compared with classical calibration means, which apply the parameter optimization in 2D image space to minimize the re-projection errors, the proposed optimization approach is executed in 3D space directly. An experiment and comparison are conducted to verify that the proposed optimal calibration approach can effectively reduce the system deviation and to improve the system measurement accuracy.

In phase-measurement profilometry (PMP), the gamma effect can cause severe nonlinear distortion of the phase pattern (i.e., water ripples on the surface profile). Gamma correction is an effective method to eliminate the gamma effects of commercial projectors. However, projector defocusing on the suppression of higher harmonics inevitably results in an estimated gamma deviation from the true value. In this study, gamma mapping is constructed using the duty ratio (DR) to code the chord distribution of the simulated distorted phase while considering projector defocusing. With the known gamma mapping, the accurate gamma is calculated by DR coding of the actual distorted phase under projector defocusing. Simulated experiments verified that the relative errors of the gamma calculated by the proposed method under different degrees of defocus were less than 3.5%. Furthermore, the experimental results demonstrate that the proposed gamma calculation method is robust to the defocus effect of the projector and that a smoother surface can be reconstructed after gamma correction.