Multi-layer optical Fourier neural network based on the convolution theorem

To take full advantage of the application of neural networks to optical systems, we design an optical neural network based on the principle of free-space optical convolution. In this article, considering the need for a high-power light source to excite the nonlinearity of an optical material, we describe how to reduce the power consumption of the system by quantifying the output of each layer after the softmax operation as an 8-bit value and loading these values into amplitude-only spatial light modulators (SLMs). In addition, we describe how to load the matrix with positive and negative values in the amplitude-only SLM by utilizing Fourier properties of the odd-order square matrix. We apply our six-layer optical network to the classification of Mixed National Institute of Standards and Technology database (MNIST) and Fashion-MNIST and find that the accuracy reaches 92.51% and 80.67%, respectively. Finally, we consider the error analysis, power consumption, and response time of our framework.