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The Gerchberg–Saxton (GS) algorithm is widely used in various disciplines of modern sciences and technologies where phase retrieval is required. However, this legendary algorithm most likely stagnates after a few iterations. Many efforts have been taken to improve this situation. Here we propose to introduce the strategy of gradient descent and weighting technique to the GS algorithm, and demonstrate it using two examples: design of a diffractive optical element (DOE) to achieve off-axis illumination in lithographic tools, and design of a computer generated hologram (CGH) for holographic display. Both numerical simulation and optical experiments are carried out for demonstration.

In this paper, we propose a simple method for realizing color holographic imaging using one thin diffractive optical element (DOE), which can reconstruct a two-dimensional color image with one phase plate at a user defined distance from phase plate. The phase plate is optimized by combining Gerchberg–Saxton algorithm and compensation algorithm for improving the resolution ratio of reproduced color images. For accelerating the computational time, the Graphic Processing Unit (GPU) is used for saving time costs. In the end, the simulation experiments verified our method.