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Learned residual Gerchberg-Saxton network for computer generated holography

Computer generated holography (CGH) aims to generate phase plates that create an intensity pattern at a certain distance behind the holography plate when illuminated. Since only the intensity and not the phase of the wave is of interest, this is an ill-defined inverse problem. Usually these problems are tackled by iterative optimization algorithms which are part of the convex optimization framework. These algorithms essentially minimize a loss using a forward model. Even though many of the tackled inverse problems are non-convex, these algorithms reach acceptable solutions by finding a local minimum. The ability of Deep Neural Networks to estimate a large range of functions has made a different approach to these problems possible. Instead of an iterative optimization algorithm that converges to a (sub-)optimal solution, the inverse problem can be solved by training a neural network to directly estimate the inverse operator. However simple convolutional neural networks tend to overfit when learning the inverse operator and do not generalize well outside the training distribution. Therefore this paper introduces a hybrid approach that can be interpreted as an unrolled Gerchberg-Saxton algorithm, which we term Learned Residual Gerchberg-Saxton (LRGS) network. We train this network for the generation of multi-focus computer generated holograms, and beat state-of-the-art existing methods.

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