Vision-Ray-Calibration-Based Monocular Deflectometry by Poses Estimation from Reflections

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.