• Photonics Research
  • Vol. 4, Issue 6, 240 (2016)
Le Wang* and Shengmei Zhao
Author Affiliations
  • Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications (NUPT), Nanjing 210003, China
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    DOI: 10.1364/PRJ.4.000240 Cite this Article Set citation alerts
    Le Wang, Shengmei Zhao. Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform[J]. Photonics Research, 2016, 4(6): 240 Copy Citation Text show less

    Abstract

    In this paper, we propose a ghost imaging scheme with fast Walsh–Hadamard transform, named GIFWHT. In the scheme, Walsh–Hadamard pattern pairs are used to illuminate an object to generate pairs of detection results, and the corresponding differential detection result is used as the result as that from the conventional bucket detector. By performing the fast Walsh–Hadamard transform on 2k (k is a positive integer) differential detection results, the image of the object can be recovered. The experimental and numerical simulation results show that the reconstruction time of GIFWHT is greatly reduced, and the quality of the recovered image is noticeably improved. In addition, GIFWHT is robust against interference from environmental illumination and could savememory.Network Technology, Ministry of Education (NYKL2015011).
    Bi=ηIi(x,y)T(x,y)dxdy+n,(1)

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    B˜i=ηI˜i(x,y)T(x,y)dxdy+n.(2)

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    Di=BiB˜i=η(Ii(x,y)I˜i(x,y))T(x,y)dxdy=ηΔIi(x,y)T(x,y)dxdy,(3)

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    [D1D2DN]=η[ΔI1(1,1)ΔI1(1,2)ΔI1(Nx,Ny)ΔI2(1,1)ΔI2(1,2)ΔI2(Nx,Ny)ΔIN(1,1)ΔIN(1,2)ΔIN(Nx,Ny)][T(1,1)T(1,2)T(Nx,Ny)],(4)

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    Hk=[ΔI1(1,1)ΔI1(1,2)ΔI1(Nx,Ny)ΔI2(1,1)ΔI2(1,2)ΔI2(Nx,Ny)ΔIN(1,1)ΔIN(1,2)ΔIN(Nx,Ny)],(5)

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    D=ηHkT.(6)

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    Hk1=λHk,(7)

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    T=1ηHk1D=ληHkD.(8)

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    H1=[1111].(9)

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    Hk=[Hk1Hk1Hk1Hk1].(10)

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    h(i,j)={1if  i=0;0jN1(1)jif  i=1;0jN1h(i2,j2)h(i2i2,j)if  2iN1;0jN1,(11)

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    T(x,y)=1Ni=1N(DiD)Ii(x,y),(12)

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    MSE=1Nx,y(T(x,y)T(x,y))2,(13)

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    Le Wang, Shengmei Zhao. Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform[J]. Photonics Research, 2016, 4(6): 240
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