• Photonics Research
  • Vol. 10, Issue 11, 2667 (2022)
Minjia Zheng1, Lei Shi1、2、3、*, and Jian Zi1、2、3、4
Author Affiliations
  • 1State Key Laboratory of Surface Physics, Key Laboratory of Micro- and Nano-Photonic Structures (Ministry of Education) and Department of Physics, Fudan University, Shanghai 200433, China
  • 2Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
  • 3Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 4e-mail:
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    DOI: 10.1364/PRJ.474535 Cite this Article Set citation alerts
    Minjia Zheng, Lei Shi, Jian Zi. Optimize performance of a diffractive neural network by controlling the Fresnel number[J]. Photonics Research, 2022, 10(11): 2667 Copy Citation Text show less

    Abstract

    To achieve better performance of a diffractive deep neural network, increasing its spatial complexity (neurons and layers) is commonly used. Subject to physical laws of optical diffraction, a deeper diffractive neural network (DNN) would be more difficult to implement, and the development of DNN is limited. In this work, we found controlling the Fresnel number can increase DNN’s capability of expression and its spatial complexity is even less. DNN with only one phase modulation layer was proposed and experimentally realized at 515 nm. With the optimal Fresnel number, the single-layer DNN reached a maximum accuracy of 97.08% in the handwritten digits recognition task.
    o=|uL+1|2=|Mu0|2,

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    ui+1input=Duioutput,

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    ui+1output=ui+1inputpi.

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    ui+1output=diag(pi)Duioutput.

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    M=Di=L1[diag(pi)D].

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    F=a2λd,

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    F(ui+1)=F(ui)H,

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    eSCE=j=1Tyjlogsj,

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    eMSE=oogt22,

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    u˜i=(00ui00).(A1)

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    r=d2+(N·a)2,(A2)

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    ϕrϕd2n1π.(A3)

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    rdn1λ.(A4)

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    d2+(N·a)2dn1λ,d2+(N·a)2(n1λ)2+d2+2n1λd,a2λdn12λN2d+2n1N2.(A5)

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    Fn12λN2d+2n1N2.(A6)

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    F2n1N2.(A7)

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    I(x,y)=I0sinc2(α)sinc2(β),(A8)

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    πxaλd=n2π,n2N.(A9)

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    Fn2N,(A10)

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    modReLU(u1)=ReLU(|u1|+b)eiϕu1.(A11)

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    Minjia Zheng, Lei Shi, Jian Zi. Optimize performance of a diffractive neural network by controlling the Fresnel number[J]. Photonics Research, 2022, 10(11): 2667
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