Holography optimization based on combining iterative Green's function algorithm and deep learning method

In this Letter, we present a novel, to the best of our knowledge, approach that combines a new numerical iterative algorithm with a physics-informed neural network (PINN) architecture to solve the Helmholtz equation, thereby achieving highly generalized refractive index modulation holography. Firstly, we design a non-uniform refractive index convolutional neural network (NRI-CNN) to modify the refractive index and extract a feature vector. Then we propose an iterative Green's function algorithm (IGFA) to approximately solve the Helmholtz equation. In order to enhance the generalization ability of the solution, the abstracted vector is utilized as a multiplier term in IGFA, obtaining an approximately spatial distribution of the light field. Ultimately, we design a U-net to handle residuals of the Helmholtz equation and phases of optical fields (ERPU-net). We apply this method for holographic reconstructions on random Gaussian beams, beams with image data, and those altered by simulated turbulent phases.