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Photonics Research
Vol. 5, Issue 5, 431 (2017)

Performance analysis of ghost imaging lidar in background light environment

Chenjin Deng^1、2, Long Pan^1、2, Chenglong Wang^1、2, Xin Gao¹, Wenlin Gong^1、*, and Shensheng Han¹

Author Affiliations

¹Key Laboratory for Quantum Optics and Center for Cold Atom Physics of CAS, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.1364/PRJ.5.000431 Cite this Article Set citation alerts

Chenjin Deng, Long Pan, Chenglong Wang, Xin Gao, Wenlin Gong, Shensheng Han. Performance analysis of ghost imaging lidar in background light environment[J]. Photonics Research, 2017, 5(5): 431 Copy Citation Text

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Abstract

The effect of background light on the imaging quality of three typical ghost imaging (GI) lidar systems (namely narrow pulsed GI lidar, heterodyne GI lidar, and pulse-compression GI lidar via coherent detection) is investigated. By computing the signal-to-noise ratio (SNR) of fluctuation-correlation GI, our analytical results, which are backed up by numerical simulations, demonstrate that pulse-compression GI lidar via coherent detection has the strongest capacity against background light, whereas the reconstruction quality of narrow pulsed GI lidar is the most vulnerable to background light. The relationship between the peak SNR of the reconstruction image and σ (namely, the signal power to background power ratio) for the three GI lidar systems is also presented, and the results accord with the curve of SNR-σ.

Keywords

(110.1758) Computational imaging.(110.2990) Image formation theory (110.0110) Imaging systems

⟨ G_{i} (x_{r}) ⟩ = ⟨ δ I_{i} δ I_{r} (x_{r}) ⟩,

(1)

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⟨ Δ G_{i}^{2} (x_{r}) ⟩ = ⟨ δ I_{i}^{2} δ I_{r}^{2} (x_{r}) ⟩ - {⟨ δ I_{i} δ I_{r} (x_{r}) ⟩}^{2} .

(2)

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{SNR}_{i} = \frac{{[Δ ⟨ G_{i} ⟩]}_{\min}^{2}}{⟨ Δ G_{i}^{2} ⟩} .

(3)

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E_{s, i} (x_{s}, t) = s_{i} (t) E_{s} (x_{s}),

(4)

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E_{total, i} (x_{o}, t) = E_{s, i} (x_{o}, t) + E_{b g} (x_{o}, t),

(5)

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⟨ E_{b g}^{*} (x_{o_{1}}, t_{1}) E_{b g} (x_{o_{2}}, t_{2}) ⟩ = ⟨ I_{b g} ⟩ K_{b g} (x_{o_{1}} - x_{o_{2}}) R_{b g} (t_{1} - t_{2}),

(6)

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I_{A} = \int_{0}^{T_{A}} d t \int_{A_{beam}} d x_{o} [{| E_{s} (x_{o}, t) |}^{2} + {| E_{b g} (x_{o}, t) |}^{2}] O (x_{o}) ≜ I_{A, s} + I_{A, b g},

(7)

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⟨ G_{A} (x_{r}) ⟩ = T_{A} A_{coh, s} ⟨ I_{r} ⟩ ⟨ I_{s} ⟩ O .

(8)

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⟨ Δ G_{A}^{2} ⟩ = [⟨ δ I_{A, s}^{2} δ I_{r}^{2} ⟩ - {⟨ δ I_{A, s} δ I_{r} ⟩}^{2}] + ⟨ δ I_{A, b g}^{2} ⟩ ⟨ δ I_{r}^{2} ⟩ = ⟨ δ I_{A, s}^{2} ⟩ ⟨ δ I_{r}^{2} ⟩ + ⟨ δ I_{A, b g}^{2} ⟩ ⟨ δ I_{r}^{2} ⟩ = T_{A}^{2} A_{beam} A_{coh, s} {⟨ I_{r} ⟩}^{2} {⟨ I_{s} ⟩}^{2} \bar{O^{2}} (1 + \frac{τ_{b g}}{T_{A}} \frac{A_{coh, b g}}{A_{coh, s}} \frac{1}{σ^{2}}),

(9)

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{SNR}_{A} = \frac{N}{N_{sp}} \frac{Δ O_{\min}^{2}}{[1 + \frac{τ_{b g}}{T_{A}} \frac{A_{coh, b g}}{A_{coh, s}} \frac{1}{σ^{2}}] \bar{O^{2}}},

(10)

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I_{B} (f) = FFT {[s_{LO} (t) i_{B} (t)] \otimes H_{B} (t)} = \frac{m}{2} T_{B} sinc [T_{B} (f - f_{z})] \exp [j ϕ_{B}] \int d x_{o} {| E_{B_{s}} (x_{o}, t) |}^{2} O (x_{o}) + FFT {s_{LO} (t) [(\int d x_{o} {| E_{b g} (x_{o}, t) |}^{2} O (x_{o})) \otimes H_{B} (t)]} ≜ I_{B, s} (f) + I_{B, b g} (f),

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⟨ G_{B} (x_{r}) ⟩ = \frac{m}{2} T_{B} A_{coh, s} ⟨ I_{r} ⟩ ⟨ I_{s} ⟩ O,

(12)

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⟨ Δ G_{B}^{2} ⟩ = \frac{m^{2}}{4} T_{B}^{2} A_{coh, s} A_{beam} {⟨ I_{r} ⟩}^{2} {⟨ I_{s} ⟩}^{2} \bar{O^{2}} \times (1 + \frac{2}{m^{2}} \frac{τ_{b g}}{T_{B}} \frac{A_{coh, b g}}{A_{coh, s}} \frac{1}{σ^{2}}) .

(13)

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{SNR}_{B} = \frac{N}{N_{sp}} \frac{Δ O_{\min}^{2}}{[1 + \frac{2}{m^{2}} \frac{τ_{b g}}{T_{B}} \frac{A_{coh, b g}}{A_{coh, s}} \frac{1}{σ^{2}}] \bar{O^{2}}} .

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I_{C} (f_{z}) = \sum_{x_{t}} \frac{m^{4}}{4} T_{C}^{2} I_{LO} I_{s} (x_{t}) + \sum_{x_{t}} {| i_{C, b g} (x_{t}, f_{z}) |}^{2} + 2 Re {\sum_{x_{t}} [m^{2} I_{LO} T_{C} \exp (j ϕ_{C}) E_{s} (x_{t})] {[i_{C, b g} (x_{t}, f_{z})]}^{*}} ≜ I_{C, s} (f_{z}) + I_{C, b g} (f_{z}) + I_{C, m u} (f_{z}),

(15)

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⟨ G_{C} (x_{r}) ⟩ = \frac{m^{4}}{4} I_{LO} T_{C}^{2} A_{coh, s} ⟨ I_{r} ⟩ ⟨ I_{s} ⟩ O

(16)

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⟨ Δ G_{C}^{2} ⟩ = \frac{m^{8}}{16} I_{LO}^{2} T_{C}^{4} A_{beam} A_{coh, s} {⟨ I_{r} ⟩}^{2} {⟨ I_{s} ⟩}^{2} \bar{O^{2}} \times [1 + \frac{64 {(2 + m^{2})}^{2}}{m^{8}} {(\frac{τ_{b g}}{T_{C}})}^{2} \frac{A_{coh, b g}}{A_{coh, s}} \frac{{⟨ I_{b g} ⟩}^{2}}{{⟨ I_{s} ⟩}^{2}}] .

(17)

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{SNR}_{C} = \frac{N}{N_{sp}} \frac{Δ O_{\min}^{2}}{[1 + \frac{64 {(2 + m^{2})}^{2}}{m^{8}} {(\frac{τ_{b g}}{T_{C}})}^{2} \frac{A_{coh, b g}}{A_{coh, s}} \frac{1}{σ^{2}}] \bar{O^{2}}} .

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{PSNR}_{i} = 10 \times \log_{10} [\frac{{(2^{p} - 1)}^{2}}{{MSE}_{i}}] .

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{MSE}_{i} = \frac{1}{N_{pixel}} \sum_{m, n} {[⟨ G_{i} (m, n) ⟩ - O (m, n)]}^{2},

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Chenjin Deng, Long Pan, Chenglong Wang, Xin Gao, Wenlin Gong, Shensheng Han. Performance analysis of ghost imaging lidar in background light environment[J]. Photonics Research, 2017, 5(5): 431

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