• Chinese Optics Letters
  • Vol. 20, Issue 2, 021101 (2022)
Yaping Zhang1、*, Houxin Fan1, and Ting-Chung Poon2
Author Affiliations
  • 1Yunnan Provincial Key Laboratory of Modern Information Optics, Kunming University of Science and Technology, Kunming 650500, China
  • 2The Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
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    DOI: 10.3788/COL202220.021101 Cite this Article Set citation alerts
    Yaping Zhang, Houxin Fan, Ting-Chung Poon. Optical image processing using acousto-optic modulators as programmable volume holograms: a review [Invited][J]. Chinese Optics Letters, 2022, 20(2): 021101 Copy Citation Text show less

    Abstract

    Bragg processing using a volume hologram offers an alternative in optical image processing in contrast to Fourier-plane processing. By placing a volume hologram near the object in an optical imaging setup, we achieve Bragg processing. In this review, we discuss various image processing methods achievable with acousto-optic modulators as dynamic and programmable volume holograms. In particular, we concentrate on the discussion of various differentiation operations leading to edge extraction capabilities.
    h˜k+1=h˜k0+h˜K,

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    k+1=k0+K.

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    ω+1=ω0+Ω,

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    k1=k0K,

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    ω1=ω0Ω,

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    sinϕB=|K|2|k0|=K2k0=λ02Λ,

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    Q=2πLλ0Λ2.

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    dψm(ξ)dξ=jα2ej12Qξ[ϕincϕB+(2m1)]ψm1(ξ)jα2ej12Qξ[ϕincϕB+(2m+1)]ψm+1(ξ),

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    α=Ck0AL/2,

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    dψ0(ξ)dξ=jα2ejδQξ/2ψ1(ξ),(10a)

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    dψ1(ξ)dξ=jα2ejδQξ/2ψ0(ξ),

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    ψ0(ξ)=ψincejδQξ/4{cos[(δQ/4)2+(α/2)2]1/2ξ+jδQ4sin[(δQ/4)2+(α/2)2]1/2ξ[(δQ/4)2+(α/2)2]1/2},(11a)

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    ψ1(ξ)=ψincejδQξ/4{jα2sin[(δQ/4)2+(α/2)2]1/2ξ[(δQ/4)2+(α/2)2]1/2}.(11b)

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    ψ0(ξ)=ψinccos(αξ2),(12a)

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    ψ1(ξ)=jψincsin(αξ2).

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    H0(δ)=ψ0(ξ)|ξ=1ψinc=ejδQ/4{cos[(δQ/4)2+(α/2)2]1/2+jδQ4sin[(δQ/4)2+(α/2)2]1/2[(δQ/4)2+(α/2)2]1/2},(13a)

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    H1(δ)=ψ1(ξ)|ξ=1ψinc=ejδQ/4{jα2sin[(δQ/4)2+(α/2)2]1/2[(δQ/4)2+(α/2)2]1/2}.(13b)

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    F{ψinc(x)}=Ψinc(kx),

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    kx=k0sinϕk0ϕ=k0×δ×ϕB=πδ/Λ,

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    H0(kxΛ/π)=ejkxΛQ/4π{cos[(kxΛQ/4π)2+(α/2)2]1/2+jkxΛ4πsin[(kxΛQ/4π)2+(α/2)2]1/2[(kxΛQ/4π)2+(α/2)2]1/2},(16a)

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    H1(kxΛ/π)=ejkxΛQ/4π{jα2sin[(kxΛQ/4π)2+(α/2)2]1/2[(kxΛQ/4π)2+(α/2)2]1/2},

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    ψ0(x)=F1{Ψ0(kx)}=F1{Ψinc(kx)H0(kxΛ/π)}.(17a)

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    ψ1(x)=F1{Ψ1(kx)}=F1{Ψinc(kx)H1(kxΛ/π)},

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    H0(kxΛ/π)=ejkxΛQ4π(A+jBkx),

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    H0(kxΛ/π)A+jBkx.

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    ψ0(x,y)=F1{Ψinc(kx,ky)H0(kxΛ/π)}=F1{Ψinc(kx,ky)(A+jBkx)}=(ABx)ψinc(x,y).

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    ψ0(x,y)=Bψinc(x,y)x,

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    ψ0(1)(x,y)=(A1B1x)ψinc(x,y).

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    ψ0(2)(x,y)=(A2B2x)ψ0(1)(x,y),

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    ψ0(2)(x,y)=[B1B22x2(A1B2+A2B1)x+A1A2]ψinc(x,y).

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    ψ0(2)(x,y)=(A2B2y)ψ0(1)(x,y),

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    ψ0(2)(x,y)=(A2B2y)(A1B1x)ψinc(x,y).

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    ψ0(2)(x,y)=B1B22ψinc(x,y)yx,

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    U(x,y)(x+y)ψinc(x,y),

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    H0(kxΛπΔδ),

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    kc=ΔδπΛ.

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    Yaping Zhang, Houxin Fan, Ting-Chung Poon. Optical image processing using acousto-optic modulators as programmable volume holograms: a review [Invited][J]. Chinese Optics Letters, 2022, 20(2): 021101
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