Fast and accurate single-shot nonlinear gamma correction based on weighted fitting of multi-region responses

In digital fringe projection systems, nonlinear gamma effects can cause fringe distortions and reduce phase measurement accuracy. To balance correction efficiency and accuracy, this paper proposes a fast and accurate single-frame nonlinear gamma correction method based on multi-region response weighted fitting. By projecting a single multi-level grayscale image, multiple local response curves are established. These curves are weighted and fitted using radial Gaussian weights based on the distance from each region center to the projection center, enabling the determination of the optimal pre-compensation gamma value. This approach effectively suppresses phase errors caused by uneven projection brightness and nonlinear response. Experimental results show that, compared with the traditional three-step phase-shifting algorithm, the proposed method reduces phase MAE and RMS errors by 94.98% and 94.12%, respectively, with a computation time of only 11.619 seconds. This significantly improves both measurement speed and accuracy, demonstrating the proposed method's effectiveness, flexibility, and robustness.