Self-calibration of in situ monoscopic deflectometric measurement in precision optical manufacturing.

Accurate in situ measurement of complex optical surfaces is desired for precision manufacturing, and deflectometry is a promising measuring method. However, deflectometry's measurement accuracy depends heavily on the geometric calibration's reliability. Existing calibration methods suffer from the limitations of low efficiency, complicated operations, and expensive equipment. Therefore, a self-calibration method is proposed for the monoscopic deflectometry in order to determine the the camera and screen positions. A flat mirror without markers, rather than high-precision metrological instruments, is employed to assist with the self-calibration work, and a re-projection model is adopted in order to trace the rays from the screen to the camera. Numerical optimization is performed on the global parameters-including the camera intrinsic parameters, the screen intrinsic parameters, and the geometric transformations-in order to improve the geometric calibration's reliability. This self-calibration method only requires that four images be captured, hereby reducing the operating complexity and improving the measuring efficiency. Experiments demonstrate that the re-projection error can be significantly decreased, and also that the measuring accuracy of specular surfaces is comparable to high-precision interferometry.