Optimization of time-multiplexed computer-generated holograms with surrogate gradients

Gradient descent is an efficient algorithm to optimize differentiable functions with continuous variables, yet it is not suitable for computer generated holography (CGH) with binary light modulators. To address this, we replaced binary pixel values with continuous variables that are binarized with a thresholding operation, and we introduced gradients of the sigmoid function as surrogate gradients to ensure the differentiability of the binarization step. We implemented this method both to directly optimize binary holograms, and to train deep learning-based CGH models. Simulations and experimental results show that our method achieves greater speed, and higher accuracy and contrast than existing algorithms.