• Photonics Research
  • Vol. 11, Issue 12, 2072 (2023)
Zhiming Tian1, Ming Zhao1、*, Dong Yang2, Sen Wang1, and An Pan3、4、5
Author Affiliations
  • 1College of Information Science Technology, Dalian Maritime University, Dalian 116026, China
  • 2China Academy of Space Technology, Beijing 100086, China
  • 3State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
  • 4University of Chinese Academy of Sciences, Beijing 100049, China
  • 5e-mail: panan@opt.cn
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    DOI: 10.1364/PRJ.493938 Cite this Article Set citation alerts
    Zhiming Tian, Ming Zhao, Dong Yang, Sen Wang, An Pan. Optical remote imaging via Fourier ptychography[J]. Photonics Research, 2023, 11(12): 2072 Copy Citation Text show less

    Abstract

    Combining the synthetic aperture radar (SAR) with the optical phase recovery, Fourier ptychography (FP) can be a promising technique for high-resolution optical remote imaging. However, there are still two issues that need to be addressed. First, the multi-angle coherent model of FP would be destroyed by the diffuse object; whether it can improve the resolution or just suppress the speckle is unclear. Second, the imaging distance is in meter scale and the diameter of field of view (FOV) is around centimeter scale, which greatly limits the application. In this paper, the reasons for the limitation of distance and FOV are analyzed, which mainly lie in the illumination scheme. We report a spherical wave illumination scheme and its algorithm to obtain larger FOV and longer distance. A noise suppression algorithm is reported to improve the reconstruction quality. The theoretical interpretation of our system under random phase is given. It is confirmed that FP can improve the resolution to the theoretical limit of the virtual synthetic aperture rather than simply suppressing the speckle. A 10 m standoff distance experiment with a six-fold synthetic aperture up to 31 mm over an object of size 1 m×0.7 m is demonstrated.
    S(x)exp(ik2zs(xxs)2)=CsQs(x)Ls(x),

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    Es(x)=S(x)O(x)=S(x)A(x)exp(ikθo(x))=CsA(x)exp(ikθo(x))Qs(x)Ls(x),

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    I(ξ)=|F1{F{Es(x)Qo(x)}×P(u)}|2=|F1{F{A(x)eikθo(x)Qs(x)Qo(x)Ls(x)}×P(u)}|2,

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    P(u)={1|u|<D/20else.

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    ω(x)=A(x)exp(ikθo(x))Qs(x)Qo(x)=A(x)exp(ik(1zs+1zo)x·x+iθo(x)).

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    Is(ξ)=|F1{F{ω(x)Ls(x)}×P(u)}|2=|F1{Ω(uus)P(u)}|2,

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    ϕs(m+1)(ξ)=Is(ξ)ϕs(m)(ξ)|ϕs(m)(ξ)|.

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    Ω(m+1)(u)=Ω(m)(u)+conj(P(m)(u+us))max2(|P(m)(u+us)|)(Ψs(m+1)(u+us)Ψs(m)(u+us)),

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    P(m+1)(u)=P(m)(u)+conj(Ω(m)(uus))max2(|Ω(m)(uus)|)×  (Ψs(m+1)(u)Ψs(m)(u)).

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    Ilog=ln(I)=ln(μ)+ln(n)=μlog+nlog.

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    R=1.60λD,

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    C=WBW+B,

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    PSFC(θ)=2J1(kDθ/2)kDθ/2,(A1)

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    I(θ;Δθ)=|PSFC(θ)+ejφ0PSFC(θ+Δθ)|2=PSFC2(θ)+PSFC2(θ+Δθ)+2PSFC(θ)PSFC(θ+Δθ)cos(φ0),(A2)

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    I(θ;Δθ)=PSFC2(θ)+PSFC2(θ+Δθ)+2PSFC(θ)PSFC(θ+Δθ)=(PSFC(θ)+PSFC(θ+Δθ))2.(A3)

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    Δθ=1.60λD.(A4)

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    Ilog=ln(I)=ln(μ)+ln(n)=μlog+nlog,(B1)

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    P(Nlog<nlog)=P(N<exp(nlog))=0exp(nlog)exp(n)dn,(B2)

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    p(nlog)d(1exp(exp(nlog))d(nlog)exp(nlogexp(nlog)).(B3)

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    f(u)={u,u<0u,u0.(B4)

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    p(ntran)={2ntranexp(ntran2exp(ntran2)),ntran<0exp(ntranexp(ntran)),ntran0.(B5)

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    pfit(ntran)={0.518exp((ntran+0.9588)20.4951),ntran<00.3817exp(ntran21.23),ntran0.(B6)

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    n^log=IlogDe(Ilog)=nlog+ϕlog,(B7)

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    I^tran=De(Ilog)+n^tran.(B8)

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    I^tran=De(Ilog)+ϕlog+nlog=De(Ilog)+ϕlog+ntran.(B9)

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    n^tran=(nlog+ϕlog)=nlogϕlog12nlog+o(ϕlog2)ntran+ϕlog12ntran.(B10)

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    I^tran=De(Ilog)+ϕlog12ntran+ntran.(B11)

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    μ^log=De(I^tran).(B12)

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    μ^=φ(μ^log)=exp(0.0349μ^log2+1.2175μ^log+0.1292).(B13)

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    Zhiming Tian, Ming Zhao, Dong Yang, Sen Wang, An Pan. Optical remote imaging via Fourier ptychography[J]. Photonics Research, 2023, 11(12): 2072
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