3D global optimization of calibration parameters of deflectometry system by using a spherical mirror

The calibration of a deflectometry system is an essential requirement for achieving accurate specular surface reconstruction. In this paper, we propose a 3D-based optimization method for the calibration of system parameters, which achieves the same level of accuracy as the 2D multi-pose optimization, but utilizes only a single pose. Our approach introduces a high-precision spherical mirror as the target mirror (TM), and the cost function is the residual of the reconstruction of the TM, as opposed to the 2D re-projection error in image space. Singlepose calibration optimization is achieved because the spherical surface can be regarded as a combination of multiple pose plane mirrors. The simulations and experiments demonstrate that TM with a smaller radius outperforms other methods, and the surface reconstruction error of a spherical mirror with a radius of 500 mm is 186.3 nm RMS, offering a fast and efficient system calibration scheme for in-situ measurement in practical application scenarios.