Ms. Xin Yu Profile

Xin Yu

at Sichuan Univ

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Proceedings Article | 6 November 2023 Paper

Gamma rectification solutions based on probability density function

Xin Yu, Yuankun Liu, Wenjing Chen

Proceedings Volume 12921, 129210U (2023) https://doi.org/10.1117/12.2688052

KEYWORDS: Fringe analysis, Phase shifts, Phase measurement, Computer simulations, Projection systems, Phase unwrapping, Phase distribution, Light sources and illumination, Gamma correction, Cameras

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In phase measuring profilometry, the accuracy of the recovered 3D result relies heavily on the quality of the phase. However, the presence of gamma effect often introduces severe nonlinear phase errors, leading to ripple-like artifacts in the reconstructed surface profile. It has been proved that the Probability Density Function (PDF) of the wrapped phase values, i.e., regarded as phase histogram can well visualize the noticeable periodic errors introduced by the nonlinear gamma. Therefore, a variety of PDF-based solutions have been proposed, including calculating an optimal preset gamma value, searching better compensation coefficients and building an in-situ Look-Up-Table (LUT) and so on. Nonetheless, the influence of nonuniform intensity resulting from factors such as variations in illumination distance and imaging distance has not been adequately considered. In pursuit of further advancements, this paper introduces a real-time sub-regional compensation method based on PDF to mitigate the influence of uneven intensity distribution. In this solution, a series of simulated PDF curves, as well as gamma-value-based look-up tables that map phase-to-phase errors are created w.r.t different gamma values in advance. These simulated PDF curves are used to find the optimal gamma values of each sub-region that is divided based on a projected grayscale image. The adaptive LUTs are applied to each sub-region based on the respective gamma values, which results in improved calibration accuracy. By utilizing three-step phase-shifting fringe patterns and a grayscale image, the proposed method effectively addresses the influence of nonuniform intensity and avoids complexities of pre-calibration procedures. Experimental results validate the efficacy and practicality of this approach, highlighting its potential for high-precision and real-time measurements.

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