A monocular deflectometric system comprises a camera and a screen that collaboratively facilitate the reconstruction of a specular surface under test (SUT). This paper presents a methodology for solving the slope distribution of the SUT utilizing pose estimation derived from reflections, based on vision ray calibration (VRC). Initially recorded by the camera, an assisted flat mirror in different postures reflects the patterns displayed by a screen maintained in a constant posture. The system undergoes a calibration based on the VRC to ascertain the vision ray distribution of the camera and the spatial relationship between the camera and the screen. Subsequently, the camera records the reflected patterns by the SUT, which remains in a constant posture while the screen is adjusted to multiple postures. Utilizing the VRC, the vision ray distribution among several postures of the screen and the SUT is calibrated. Following this, an iterative integrated calibration is performed, employing the calibration results from the preceding separate calibrations as initial parameters. The integrated calibration amalgamates the cost functions from the separate calibrations with the intersection of lines in Plücker space. Ultimately, the results from the integrated calibration yield the slope distribution of the SUT, enabling an integral reconstruction. In both the numeric simulations and actual measurements, the integrated calibration significantly enhances the accuracy of the reconstructions when compared to the reconstructions with the separate calibrations.

Phase measuring deflectometry (PMD) plays a more and more significant role in the measurement of specular surfaces. However, most of the deflectometric methods are only suitable for continuous specular surfaces, but not for the discontinuous surfaces. In this work , with the hardware of stereoscopic PMD, a mechanism is introduced that a specular surface can be reconstructed iteratively with the pre-known coordinate of a reflecting point. Based on the mechanism and the excellent local properties of the B-spline surface, a reconstruction method suitable for the both kinds of specular surfaces is proposed. Meanwhile, to resist the noise of the single point, this work mathematically analyses the mechanism of the method. With the mathematical conclusion, the sparse point cloud solved by stereoscopic PMD is employed to scale the B-spline surface s, improving the accuracy of reconstruction. Simulated and actual experiments are carried out and the results show high accuracy and robustness of the PMD system and the reconstruction method.