A plethora of research advances have emerged in the fields of optics and photonics that benefit from harnessing the power of machine learning. Specifically, there has been a revival of interest in optical computing hardware due to its potential advantages for machine learning tasks in terms of parallelization, power efficiency and computation speed. Diffractive deep neural networks (D2NNs) form such an optical computing framework that benefits from deep learning-based design of successive diffractive layers to all-optically process information as the input light diffracts through these passive layers. D2NNs have demonstrated success in various tasks, including object classification, the spectral encoding of information, optical pulse shaping and imaging. Here, we substantially improve the inference performance of diffractive optical networks using feature engineering and ensemble learning. After independently training 1252 D2NNs that were diversely engineered with a variety of passive input filters, we applied a pruning algorithm to select an optimized ensemble of D2NNs that collectively improved the image classification accuracy. Through this pruning, we numerically demonstrated that ensembles of N = 14 and N = 30 D2NNs achieve blind testing accuracies of 61.14 ± 0.23% and 62.13 ± 0.05%, respectively, on the classification of CIFAR-10 test images, providing an inference improvement of >16% compared to the average performance of the individual D2NNs within each ensemble. These results constitute the highest inference accuracies achieved to date by any diffractive optical neural network design on the same dataset and might provide a significant leap to extend the application space of diffractive optical image classification and machine vision systems.

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Reconstruction of inline holograms of unknown objects in general suffers from twin-image artifacts due to the appearance of an out-of-focus image overlapping with the desired image to be reconstructed. Computer-based iterative phase retrieval algorithms and learningbased methods have been used for the suppression of such image artifacts in digital holography.Here we present a conceptual framework and the corresponding numerical simulation results for an all-optical hologram reconstruction method that can instantly retrieve the image of an unknown object from its inline hologram and eliminate twin-image artifacts without using a digital processor or a computer. Multiple transmissive diffractive layers are trained using deep learning so that the diffracted light from an arbitrary input hologram is processed all-optically, through light−matter interaction, to reconstruct the image of an unknown object at the speed of light propagation and without the need for any external power. This passive all-optical processor composed of spatially engineered transmissive layers forms a diffractive network that successfully generalizes to reconstruct inline holograms of unknown, new objects and exhibits improved diffraction efficiency as well as extended depth-of-field at the hologram recording distance. This all-optical hologram processor and the underlying design framework can find numerous applications in coherent imaging and holographic display-related applications owing to its major advantages in terms of image reconstruction speed and computer-free operation.

A Correction to this paper has been published: https://doi.org/10.1038/s41377-021-00473-1

We report ensemble learning of diffractive optical neural networks that result in substantial improvements in the all-optical image classification accuracy of the resulting models.