Generic phase correction method based on phase recoding for deflectometry

The uniform spatial phase assumption is the core basis of the phase measuring deflectometry (PMD). However, deflectometry, as an inherently defocused system, coupled with fringe distortion factors such as gamma distortion and image saturation, destroys the ideal linear mapping relationship between the phase and the display pixel coordinates. To address this issue, a generic phase correction method based on phase recoding is proposed, for what we believe to be, the first time in this paper. We established a photometric model to analyze the inherent nonlinear mapping between the computed phase and the display coordinates in PMD. A high-precision calibration procedure was then developed to implement phase recoding of the display coordinates, enabling phase correction via a simple lookup table during measurement. Experimental results on four types of distorted fringes show that, based on the three-step phase-shifting algorithm, the phase reconstruction accuracy is improved by up to 255 times, the 3D reconstruction accuracy is improved by up to 18 times, and the RMS error of the reconstructed 3D surface reaches the 10^-5 mm level.