Positive influence of the scattering medium on reflective ghost imaging

Qin Fu; Yanfeng Bai; Xianwei Huang; Suqin Nan; Peiyi Xie; Xiquan Fu

doi:10.1364/PRJ.7.001468

Journals >Photonics Research >Volume 7 >Issue 12 >Page 1468 > Article

Photonics Research
Vol. 7, Issue 12, 1468 (2019)

Positive influence of the scattering medium on reflective ghost imaging

Qin Fu, Yanfeng Bai^*, Xianwei Huang, Suqin Nan..., Peiyi Xie and Xiquan Fu|Show fewer author(s)

Author Affiliations

College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China

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DOI: 10.1364/PRJ.7.001468 Cite this Article Set citation alerts

Qin Fu, Yanfeng Bai, Xianwei Huang, Suqin Nan, Peiyi Xie, Xiquan Fu, "Positive influence of the scattering medium on reflective ghost imaging," Photonics Res. 7, 1468 (2019) Copy Citation Text

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Abstract

The scattering medium is usually thought to have a negative effect on the imaging process. In this paper, it is shown that the imaging quality of reflective ghost imaging (GI) in the scattering medium can be improved effectively when the binary method is used. By the experimental and the numerical results, it is proved that the existence of the scattering medium is just the cause of this phenomenon, i.e., the scattering medium has a positive effect on the imaging quality of reflective GI. During this process, the effect from the scattering medium behaves as the random noise which makes the imaging quality of binary ghost imaging have an obvious improvement.

G (x_{r}, x_{t}) \propto {| \int ⟨ E^{*} (u_{1}) E (u_{2}) ⟩ h_{r} (u_{1}, x_{r}) h_{t}^{*} (u_{2}, x_{t}) d u_{1} d u_{2} |}^{2},

(1)

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⟨ E^{*} (u_{1}) E (u_{2}) ⟩ = \exp (- \frac{u_{1}^{2} + u_{2}^{2}}{2 a^{2}}) δ (u_{1} - u_{2}),

(2)

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h_{t} (u_{2}, x_{t}) \propto \int d ξ d x_{1} d x_{2} \exp [- \frac{j π}{λ z_{1}} (x_{1} - u_{2})^{2}] \times \exp [j ϕ (x_{1})] \exp [- \frac{j π}{λ Δ z} (ξ \cos θ_{i} - x_{1})^{2}] t (ξ) \exp [- \frac{j π}{λ Δ z} (x_{2} - ξ \cos θ_{o})^{2}] \times \exp [j ϕ (x_{2})] \exp [- \frac{j π}{λ z_{2}} (x_{t} - x_{2})^{2}],

(3)

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γ (x, x^{'}) = ⟨ \exp {j [ϕ (x) - ϕ (x^{'})]} ⟩ = \exp {- σ^{2} [1 - e^{- \frac{(x - x^{'})^{2}}{s^{2}}}]},

(4)

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h_{r} (u_{1}, x_{r}) \propto \exp [- \frac{j π}{λ z_{0}} (x_{r} - u_{1})^{2}] .

(5)

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G (x_{r}) \propto \int G (x_{r}, x_{t}) d x_{t} = \int d ξ d x_{1} d x_{1}^{'} {[t (ξ)]}^{2} \exp {- σ^{2} [1 - e^{- \frac{(x_{1} - x_{1}^{'})^{2}}{s^{2}}}]} \times {sinc}^{2} [\frac{a (ξ \cos θ_{i} - x_{r})}{λ z_{1}}],

(6)

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SNR = \frac{G (x_{r})}{Δ G (x_{r})} = \frac{G (x_{r})}{\sqrt{{[⟨ I_{r} (x_{r}) ⟩ ⟨ I_{t} (x_{t}) ⟩ + 2 G (x_{r})]}^{2} - G^{2} (x_{r})}} = \frac{\sqrt{N}}{\sqrt{{[\frac{π M a^{2}}{G (x_{r})} + 2]}^{2} - 1}},

(7)

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Qin Fu, Yanfeng Bai, Xianwei Huang, Suqin Nan, Peiyi Xie, Xiquan Fu, "Positive influence of the scattering medium on reflective ghost imaging," Photonics Res. 7, 1468 (2019)

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