Second-order cumulants ghost imaging

Huan Zhao; Xiaoqian Wang; Chao Gao; Zhuo Yu; Shuang Wang; Lidan Gou; Zhihai Yao

doi:10.3788/COL202220.112602

Journals >Chinese Optics Letters >Volume 20 >Issue 11 >Page 112602 > Article

Chinese Optics Letters
Vol. 20, Issue 11, 112602 (2022)

Second-order cumulants ghost imaging

Huan Zhao¹, Xiaoqian Wang^1、**, Chao Gao¹, Zhuo Yu^1、2, Shuang Wang¹, Lidan Gou¹, and Zhihai Yao^1、*

Author Affiliations

¹Department of Physics, Changchun University of Science and Technology, Changchun 130022, China

²School of Physics and Electronics, Baicheng Normal University, Baicheng 137000, China

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DOI: 10.3788/COL202220.112602 Cite this Article Set citation alerts

Huan Zhao, Xiaoqian Wang, Chao Gao, Zhuo Yu, Shuang Wang, Lidan Gou, Zhihai Yao. Second-order cumulants ghost imaging[J]. Chinese Optics Letters, 2022, 20(11): 112602 Copy Citation Text

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Abstract

Ghost imaging (GI) is a technique to retrieve images by correlating intensity fluctuations. In this Letter, we present a novel scheme for GI referred to as second-order cumulants GI (SCGI). The image is retrieved from fluctuation information, and resolution may be enhanced compared to traditional GI. We experimentally performed SCGI image reconstruction, and the results are in agreement with theoretical predictions.

Keywords

cumulants ghost imaging resolution

h (x, α) = \frac{e^{- i k z}}{i λ z} \exp [\frac{- i π}{λ z} {(x - α)}^{2}],

(1)

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E (α) = \int E (x) h (x, α) d x,

(2)

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I (α) = E^{*} (α) E (α) .

(3)

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B_{t} = \int I (α) {| T (α) |}^{2} d α .

(4)

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Δ G^{(2)} (α) = 〈 Δ I (α) Δ B_{t} 〉 = 〈 [I (α) - 〈 I (α) 〉] [B_{t} - 〈 B_{t} 〉] 〉 = 〈 [I (α) - 〈 I (α) 〉] [\int I (α^{'}) {| T (α^{'}) |}^{2} d α^{'} - 〈 \int I (α^{'}) {| T (α^{'}) |}^{2} d α^{'} 〉] 〉 = \int {| \int G^{(1)} (x, x^{'}) T (α^{'}) h^{*} (x, α) h (x^{'}, α^{'}) d x d x^{'} |}^{2} d α^{'},

(5)

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Δ G^{(2)} (α) = I_{0}^{2} \int {| T (α^{'}) |}^{2} {sinc}^{2} [\frac{2 π R}{λ z} (α - α^{'})] d α^{'},

(6)

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K (s, α) = \ln {〈 \exp [s Δ G^{(2)} (I_{0}, α)] 〉} = \sum_{n = 1}^{\infty} κ_{n} (α) \frac{s^{n}}{n!} = μ (α) \times s + σ^{2} (α) \times \frac{s^{2}}{2} + \dots,

(7)

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κ_{n} (α) = {\frac{d^{(n)} K (s, α)}{d s^{(n)}} |}_{s = 0} .

(8)

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κ_{2} (α) = 〈 {[Δ G^{(2)} (I_{0}, α) - 〈 Δ G^{(2)} (I_{0}, α) 〉]}^{2} 〉 = \int κ_{2} (α, α^{'}) d α^{'} + L (α),

(9)

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κ_{2} (α, α^{'}) = 〈 {[Δ G^{(2)} (I_{0}, α, α^{'}) - 〈 Δ G^{(2)} (I_{0}, α, α^{'}) 〉]}^{2} 〉 = 〈 {(I_{0}^{2} - 〈 I_{0}^{2} 〉)}^{2} 〉 \times {| T (α^{'}) |}^{4} \times {sinc}^{4} [\frac{2 π R}{λ z} (α - α^{'})],

(10)

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L (α) = \int_{α^{'}} \int_{α^{''} \neq α^{'}} 〈 [Δ G^{(2)} (I_{0}, α, α^{'}) - 〈 Δ G^{(2)} (I_{0}, α, α^{'}) 〉] [Δ G^{(2)} (I_{0}, α, α^{''}) - 〈 Δ G^{(2)} (I_{0}, α, α^{''}) 〉] 〉 d α^{'} d α^{''} = 〈 {(I_{0}^{2} - 〈 I_{0}^{2} 〉)}^{2} 〉 \times \int_{α^{'}} \int_{α^{''} \neq α^{'}} {| T (α^{'}) |}^{2} {| T (α^{''}) |}^{2} \times {sinc}^{2} [\frac{2 π R}{λ z} (α - α^{'})] {sinc}^{2} [\frac{2 π R}{λ z} (α - α^{''})] d α^{'} d α^{''},

(11)

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Huan Zhao, Xiaoqian Wang, Chao Gao, Zhuo Yu, Shuang Wang, Lidan Gou, Zhihai Yao. Second-order cumulants ghost imaging[J]. Chinese Optics Letters, 2022, 20(11): 112602

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