Polynomial color compensation model with neural network solver for color-coded fringe patterns in phase-measuring deflectometry

Abstract

The total image display/projection and image acquisition time in a projector-based phase-measuring deflectometry (PMD) measurement is reduced when color-coded fringe patterns are used since only a single image of the fringe pattern is sufficient to extract phase information using the phase-stepping method. This benefit is, however, offset by the difficulty in resolving various sources of color intensity errors of the fringe patterns in the camera view, such as uneven illumination, color imbalance, color crosstalk, and deviation of color intensity response of the camera and the projector from the calibrated color targets. Thus, a polynomial color compensation model is proposed in this study to compensate for color intensity errors. The model coefficients were estimated using the relationship between the captured and targeted color intensities, which are sequences of monochromatic 8-bit red, green, and blue (RGB) images for projection. The model was applied to modify the color intensities of the generated fringe patterns before projection. The modified color fringe patterns were then used for PMD measurement on spherical concave and convex mirrors. Based on the experimental results, the root-mean-squared (RMS) color intensity errors in R, G, and B channels were reduced by 33.3%, 58.3%, and 36.4%, respectively, after conducting the polynomial color compensation. The RMS phase errors in the fringe patterns were reduced by 71.9%. The RMS height errors and the radius percentage errors of the reconstructed concave and convex heightmaps were 1.87 μm (0.12%) and 1.55 μm (0.17%), respectively. The performance of the proposed polynomial color compensation model in reducing color intensity errors of the captured fringe patterns for accurate PMD measurement was demonstrated successfully.