Fig. 1. Dataset examples. (a) MNIST dataset; (b) Fashion-MNIST dataset
Fig. 2. Structural diagrams of nonlinear all-optical diffraction deep neural network. (a) Physical model of system; (b) optical path model; (c) neural network model
Fig. 3. Mathematical models of different activation functions. (a) Leaky-ReLU and PReLU; (b) RReLU
Fig. 4. Image label design
Fig. 5. Output image of each layer of grating after training
Fig. 6. Classification accuracy corresponding to each number of grating layers in MNIST dataset
Fig. 7. Classification accuracy of Fashion-MNIST dataset corresponding to each number of grating layers in Fashion-MNIST dataset
Fig. 8. Classification results of MNIST dataset by standard all-optical diffraction deep neural network. (a) Classification accuracy; (b) confusion matrix
Fig. 9. Classification results of Fashion-MNIST dataset by standard all-optical diffraction deep neural network. (a) Classification accuracy; (b) confusion matrix
Fig. 10. Classification accuracies and confusion matrixes of MNIST dataset by all-optical diffraction deep neural networks with different activation functions. (a)(b) Leaky-ReLU; (c)(d) PReLU; (e)(f) RReLU
Fig. 11. Recognition accuracy of each number in MNIST dataset by each all-optical diffraction deep neural network model
Fig. 12. Classification accuracies and confusion matrixes of Fashion-MNIST dataset by all-optical diffraction deep neural networks with different activation functions. (a)(b) Leaky-ReLU; (c)(d) PReLU; (e)(f) RReLU
Fig. 13. Recognition accuracy of each number in Fashion-MNIST dataset by each all-optical diffraction deep neural network model
Label number | Category |
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0 | T-shirt | 1 | Trousers | 2 | Pullover | 3 | Dress | 4 | Coat | 5 | Sandal | 6 | Shirt | 7 | Sneaker | 8 | Bag | 9 | Ankle boot |
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Table 1. Label numbers and categories in Fashion-MNIST dataset
Grating parameter | Value |
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Wavelength | 10.6 μm | Cell size | 5 μm | Grating spacing | 70λ |
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Table 2. Physical parameters of neural network grating in MNIST dataset
Training parameter | Value |
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Number of grating layers | 6 | Number of neurons per layer | 60×60 | Batch size | 100 | Epoch | 50 | Learning rate | 10-2 |
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Table 3. Neural network training parameters in MNIST dataset
Spacing | Pixel size of 30×30 | Pixel size of 40×40 | Pixel size of 50×50 | Pixel size of 60×60 | Pixel size of 70×70 |
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30λ | 0.8427 | 0.8642 | 0.8736 | 0.8694 | 0.8664 | 40λ | 0.8218 | 0.8623 | 0.8707 | 0.8744 | 0.8667 | 50λ | 0.7545 | 0.8614 | 0.8594 | 0.8759 | 0.8712 | 60λ | 0.6499 | 0.8327 | 0.8710 | 0.8714 | 0.8741 | 70λ | 0.6190 | 0.8304 | 0.8683 | 0.8765 | 0.8696 |
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Table 4. Classification accuracy of MNIST dataset corresponding to each pixel size and diffraction grating spacing
Grating parameter | Value |
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Wavelength | 10.6 μm | Cell size | 5 μm | Grating spacing | 30λ |
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Table 5. Physical parameters of neural network grating in Fashion-MNIST dataset
Training parameter | Value |
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Number of grating layers | 6 | Number of neurons per layer | 70×70 | Batch size | 100 | Epoch | 50 | Learning rate | 10-2 |
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Table 6. Neural network training parameters in Fashion-MNIST dataset
Spacing | Pixel size of 30×30 | Pixel size of 40×40 | Pixel size of 50×50 | Pixel size of 60×60 | Pixel size of 70×70 |
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30λ | 0.7012 | 0.7797 | 0.7943 | 0.7969 | 0.7994 | 40λ | 0.6569 | 0.7539 | 0.7882 | 0.7903 | 0.7947 | 50λ | 0.6137 | 0.7419 | 0.7664 | 0.7849 | 0.7937 | 60λ | 0.6098 | 0.7411 | 0.7574 | 0.7831 | 0.7935 | 70λ | 0.6069 | 0.7246 | 0.7539 | 0.7735 | 0.7809 |
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Table 7. Classification accuracy of Fashion-MNIST dataset corresponding to each pixel size and diffraction grating spacing
Activation function | Accuracy |
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Leaky-ReLU | 0.9609 | PReLU | 0.9628 | RReLU | 0.9630 |
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Table 8. Classification accuracies of MNIST dataset by nonlinear all-optical diffraction deep neural networks with different activation functions
Activation function | Accuracy |
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Leaky-ReLU | 0.8717 | PReLU | 0.8736 | RReLU | 0.8743 |
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Table 9. Classification accuracies of Fashion-MNIST dataset by nonlinear all-optical diffraction deep neural networks with different activation functions