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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.

We propose an iterative algorithm by introducing the strategy of gradient decent and magnitude modification into the Gerchburg-Saxton (GS) algorithm. Simulations and experimental results demonstrate its better performance for holographic display comparing with the GS.

It is well known that holographic display can provide 3D scenes with continuous viewpoints and is free of accommodation-convergence conflict. So far most of the research in this area focuses on the display end, leaving the acquisition end merely explored. For holographic content acquisition, one needs to capture the scene in 3D. Ways to do this include the traditional optical holography and integral imaging. However, optical holography suffers from serious speckle while integral imaging has a long march to increase the resolution. In this paper, we propose a technique based on a variation of the transport of intensity equation to calculate the “phase” information of a scene from its defocusd intensity captured by a color camera under white light illumination. With the defocused phase and intensity data at hand, we can calculate the infocused wavefront of the scene, and further encode it into a computer generated hologram for subsequent holographic display. We demonstrate the proposed technique by simulation and experimental results. Compared with existing 3D acquisition techniques for holographic display, our method may provide better viewing experience due to the free of speckle in the acquisition stage, as well as the fact that the resolution does not limited by the microlenslet.

One method of realizing color holographic imaging using one thin diffractive optical element (DOE) is proposed. This method can reconstruct a two-dimensional color image with one phase plate at user defined distance from DOE. For improving the resolution ratio of reproduced color images, the DOE is optimized by combining Gerchberg-Saxton algorithm and compensation algorithm. To accelerate the computational process, the Graphic Processing Unit (GPU) is used. In the end, the simulation result was analyzed to verify the validity of this method.