Vision ray model based stereo deflectometry for the measurement of the specular surface

As a slope measuring specular surface measurement technique, deflectometry relies on the characterization of camera vision ray, which is commonly achieved with the distortion compensated pinhole model. However, this model is an approximate and inadequate description of lens layout and distortion, leading to low reproducibility of calibration and uncertainty in vision ray, and hence surface uncertainty. We implement the vision ray model (VRM) to stereo deflectometry, providing a pixelwise characterization of the vision ray that is free of intrinsic lens layout and distortion representation. Based on the VRM, the calibration method and surface reconstruction algorithm are proposed. We demonstrate with experimental study that the VRM can improve both the calibration performance and the surface measurement accuracy. The experimental results of a flat optical element and a concave spherical mirror indicate that the VRM based stereo deflectometry can achieve ten nanometers level RMS error.