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  • Received: Mar. 8, 2019

    Accepted: May. 20, 2019

    Posted: Jun. 19, 2019

    Published Online: Jun. 19, 2019

    The Author Email: Tian Lei (leitian@bu.edu)

    DOI: 10.1117/1.AP.1.3.036003

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    Waleed Tahir, Ulugbek S. Kamilov, Lei Tian. Holographic particle localization under multiple scattering[J]. Advanced Photonics, 2019, 1(3): 036003

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Im(x0)=|uin(x0,0)+E(x0,0)|2=|uin|2+2uinRe{E}+|E|2,(1)

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Re{E(x0,0)}=[E(x0,0)+E*(x0,0)]2=Im(x0)|uin|22uin.(2)

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E(x0,0)=Ωf(x,z)uK(x,z)h(x0x,z)d2xdz,(3)

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uk(x,z)=uin(x,z)+Ωf(x,z)uk1(x,z)h(xx,zz)d2xdz,(4)

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E=Hdiag(uK)f,(5)

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uk=uin+Gdiag(uk1)f,(6)

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f^=argminfF{C(f)}=argminfF{D(f)+τfTV},(7)

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fTV=Δn=1N[Df]nl2=n=1N|[Dxf]n|2+|[Dyf]n|2+|[Dzf]n|2,(8)

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ftproxτTV[ft1αD(f)f],(9)

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D(f)f=Re{diag(u¯K)HHr+[uKf]Hdiag(f)HHr},(10)

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[ukf]Ha=diag(u¯k1)GHa+[uk1f]Hdiag(f)GHa,(11)

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Rg=total cross-sections of all scatterersarea of the hologramNpπr2NxNyδxδy,(12)

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e=AuKu0,(13)

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SNR=20log10(ftrueftruef^),(14)

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D=2i=1Npigii=1Npi2+i=1Ngi2,(15)

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