Ray tracing modeling and errors analysis for phase measuring deflectometry based on preset surface types

In the current field of phase measuring deflectometry (PMD) techniques, the primary factor affecting the low-order shape errors of the measured specular surface originates from the uncertainty in geometric calibration. To address this issue, this paper presents a full simulation pipeline of PMD using the ray tracing technology within the Python framework. It integrates phase analysis and gradient-surface reconstruction algorithms based on preset surface types to analyze the error impact on the final retrieved profile, with the help of Zernike coefficients characterization. To further analyze the potential error influences of the PMD system in actual physical scenarios, a comprehensive ray tracing modeling simulation was conducted, considering system noises, nonlinear effects of the imaging subsystem, geometric calibration errors and the impact of displayer surface deformation. This simulation starts from forward ray tracing to construct the model of fringe signal propagation and combined it with reverse ray tracing to solve for the surface shape of the measured specular surface. It further clarifies that under the hybrid influence of comprehensive error sources, the primary contributing factors to the surface shape residuals of the measured mirror are low-order shape errors and certain high-order shape errors such as astigmatism and coma aberrations.