Complex-to-binary amplitude hologram conversion using complex loss functions

In this paper, we propose a binary-stochastic gradient descent optimization scheme that uses complex loss functions to generate binary amplitude holograms (BAHs) capable of reproducing a variety of target complex fields with improved accuracy. We introduce two complex loss functions, based on the mean squared error and correlation coefficient metrics, for use during BAH optimization. To the best of our knowledge, this is the first time that such complex loss functions have been applied to convert arbitrary complex, phase, or amplitude holograms into binary amplitude holograms. The proposed approach allows reproducing 3D distributions by evaluating the field at a single plane, enhancing versatility and increasing computation speed compared to conventional optimization schemes that require evaluating the intensity of the field at multiple planes. We perform numerical and experimental tests to reproduce complex target fields, including color 3D, multiplane, extended-depth-of-focus, and experimentally recorded scenes. The results demonstrate that the proposed approach yields improved reconstruction quality over direct binarization of amplitude holograms. Projection of different types of scenes using an experimental digital micromirror device-based holographic augmented reality setup is demonstrated, further confirming the effectiveness of our proposal.