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  • Received: Feb. 4, 2020

    Accepted: Mar. 27, 2020

    Posted: Mar. 30, 2020

    Published Online: May. 20, 2020

    The Author Email: Xing Lin (, Qionghai Dai (

    DOI: 10.1364/PRJ.389553

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    Tiankuang Zhou, Lu Fang, Tao Yan, Jiamin Wu, Yipeng Li, Jingtao Fan, Huaqiang Wu, Xing Lin, Qionghai Dai. In situ optical backpropagation training of diffractive optical neural networks[J]. Photonics Research, 2020, 8(6): 06000940

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Photonics Research, Vol. 8, Issue 6, 06000940 (2020)

In situ optical backpropagation training of diffractive optical neural networks 

Tiankuang Zhou1,2,3,†, Lu Fang2,3,†, Tao Yan1,2, Jiamin Wu1,2, Yipeng Li1,2, Jingtao Fan1,2, Huaqiang Wu4,5, Xing Lin1,2,4,7,*, and Qionghai Dai1,2,6,8,*

Author Affiliations

  • 1Department of Automation, Tsinghua University, Beijing 100084, China
  • 2Institute for Brain and Cognitive Science, Tsinghua University, Beijing 100084, China
  • 3Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
  • 4Beijing Innovation Center for Future Chip, Tsinghua University, Beijing 100084, China
  • 5Institute of Microelectronics, Tsinghua University, Beijing 100084, China
  • 6Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China
  • 7e-mail:
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Training an artificial neural network with backpropagation algorithms to perform advanced machine learning tasks requires an extensive computational process. This paper proposes to implement the backpropagation algorithm optically for in situ training of both linear and nonlinear diffractive optical neural networks, which enables the acceleration of training speed and improvement in energy efficiency on core computing modules. We demonstrate that the gradient of a loss function with respect to the weights of diffractive layers can be accurately calculated by measuring the forward and backward propagated optical fields based on light reciprocity and phase conjunction principles. The diffractive modulation weights are updated by programming a high-speed spatial light modulator to minimize the error between prediction and target output and perform inference tasks at the speed of light. We numerically validate the effectiveness of our approach on simulated networks for various applications. The proposed in situ optical learning architecture achieves accuracy comparable to in silico training with an electronic computer on the tasks of object classification and matrix-vector multiplication, which further allows the diffractive optical neural network to adapt to system imperfections. Also, the self-adaptive property of our approach facilitates the novel application of the network for all-optical imaging through scattering media. The proposed approach paves the way for robust implementation of large-scale diffractive neural networks to perform distinctive tasks all-optically.

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