Thermal light subwavelength diffraction using positive and negative correlations

Mingjie Sun; Xingdan He; Mingfei Li; Ling'an Wu

doi:10.3788/COL201614.040301

Journals >Chinese Optics Letters >Volume 14 >Issue 4 >Page 040301 > Article

Chinese Optics Letters
Vol. 14, Issue 4, 040301 (2016)

Thermal light subwavelength diffraction using positive and negative correlations

Mingjie Sun^1、*, Xingdan He¹, Mingfei Li^2、3, and Ling'an Wu²

Author Affiliations

¹Department of Opto-Electronic Engineering, Beihang University, Beijing 100191, China

²Laboratory of Optical Physics, Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China

³Quantum Engineering Research Center, Beijing Institute of Aerospace Control Devices, China Aerospace, Beijing 100094, China

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DOI: 10.3788/COL201614.040301 Cite this Article Set citation alerts

Mingjie Sun, Xingdan He, Mingfei Li, Ling'an Wu. Thermal light subwavelength diffraction using positive and negative correlations[J]. Chinese Optics Letters, 2016, 14(4): 040301 Copy Citation Text

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Abstract

Ghost imaging and diffraction, inspired by the Hanbury Brown and Twiss effect, have potential in both classical and quantum optics regimes on account of their nonlocal characteristics and subwavelength resolution capability, and therefore have aroused particular interest. By extending the correspondence imaging scheme, we utilize the positive and negative intensity correlations in diffraction and perform subwavelength diffraction with pseudo-thermal light. In the experiment, a subwavelength (

λ / 2

) resolution and a better signal-to-noise ratio (10.3% improvement) are simultaneously achieved. The scheme can be utilized as a complement to the existing ghost imaging scheme to improve image quality.

g_{C I}^{(2)} = \frac{〈 I_{1} (x_{0}) I_{2} (x_{2}) 〉}{〈 I_{1} (x_{0}) I_{2} (x_{2}) 〉} = 1 + \frac{cov (I_{1} (x_{0}) I_{2} (x_{2}))}{〈 I_{1} (x_{0}) 〉 〈 I_{2} (x_{2}) 〉},

(1)

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g_{S I}^{(2)} = \frac{〈 I_{1} (x) I_{2} (- x) 〉}{〈 I_{1} (x) 〉 〈 I_{2} (- x) 〉} = 1 + \frac{cov (I_{1} (x) I_{2} (- x))}{〈 I_{1} (x) 〉 〈 I_{2} (- x) 〉},

(2)

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g_{SIF}^{(2)} = \frac{〈 I_{1} (x) I_{2} (- x) 〉}{(\bar{I_{1}} (x) \bar{I_{2}} (- x))} - 1 = \frac{〈 cov (I_{1} (x) I_{2} (- x)) 〉}{〈 I_{1} (x) 〉 〈 I_{2} (- x) 〉},

(3)

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I_{1} = {\begin{matrix} I_{1 +} (x), & I_{1} (x) \geq \bar{I_{1}} (x) \\ I_{1 -} (x), & I_{1} (x) < \bar{I_{1}} (x) \end{matrix}, I_{2} (- x) = {\begin{matrix} I_{2 +} (- x), & I_{2} (- x) \geq \bar{I_{2}} (- x) \\ I_{2 -} (- x), & I_{2} (- x) < \bar{I_{2}} (- x) \end{matrix} .

(4)

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〈 I_{1 +} I_{2 +} 〉 = \frac{1}{4} 〈 ({\bar{I}}_{1} + Δ I_{1 +}) ({\bar{I}}_{2} + Δ I_{2 +}) 〉 = \frac{1}{4} ({\bar{I}}_{1} {\bar{I}}_{2} + {\bar{I}}_{1} 〈 Δ I_{2 +} 〉 + 〈 Δ I_{1 +} 〉 {\bar{I}}_{2} + 〈 Δ I_{1 +} Δ I_{2 +} 〉),

(5)

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〈 I_{1 +} I_{2 -} 〉 = \frac{1}{4} 〈 ({\bar{I}}_{1} + Δ I_{1 +}) ({\bar{I}}_{2} + Δ I_{2 -}) 〉 = \frac{1}{4} ({\bar{I}}_{1} {\bar{I}}_{2} + {\bar{I}}_{1} 〈 Δ I_{2 -} 〉 + 〈 Δ I_{1 +} 〉 {\bar{I}}_{2} + 〈 Δ I_{1 +} Δ I_{2 -} 〉),

(6)

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〈 I_{1 -} I_{2 +} 〉 = \frac{1}{4} 〈 ({\bar{I}}_{1} + Δ I_{1 -}) ({\bar{I}}_{2} + Δ I_{2 +}) 〉 = \frac{1}{4} ({\bar{I}}_{1} {\bar{I}}_{2} + {\bar{I}}_{1} 〈 Δ I_{2 +} 〉 + 〈 Δ I_{1 -} 〉 {\bar{I}}_{2} + 〈 Δ I_{1 -} Δ I_{2 +} 〉),

(7)

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〈 I_{1 -} I_{2 -} 〉 = \frac{1}{4} 〈 ({\bar{I}}_{1} + Δ I_{1 -}) ({\bar{I}}_{2} + Δ I_{2 -}) 〉 = \frac{1}{4} ({\bar{I}}_{1} {\bar{I}}_{2} + {\bar{I}}_{1} 〈 Δ I_{2 -} 〉 + 〈 Δ I_{1 -} 〉 {\bar{I}}_{2} + 〈 Δ I_{1 -} Δ I_{2 -} 〉) .

(8)

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g_{SIP}^{(2)} = 0.5 + \frac{〈 Δ I_{1 +} I_{2 +} 〉}{2 \bar{I_{1}} \bar{I_{2}}},

(9)

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g_{SIN}^{(2)} = 0.5 + \frac{〈 Δ I_{1 -} I_{2 +} 〉}{2 \bar{I_{1}} \bar{I_{2}}} .

(10)

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g_{SI (P - N)}^{(2)} = \frac{(〈 Δ I_{1 +} Δ I_{2 +} 〉 - 〈 Δ I_{1 -} Δ I_{2 +} 〉)}{2 \bar{I_{1}} \bar{I_{2}}} .

(11)

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SNR = 1 / δ g^{(2)},

(12)

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MSE = \frac{1}{m n} \sum_{i = 1}^{m} \sum_{j = 1}^{n} {(g^{(2)} (i, j) - \bar{g^{(2)}})}^{2},

(13)

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Mingjie Sun, Xingdan He, Mingfei Li, Ling'an Wu. Thermal light subwavelength diffraction using positive and negative correlations[J]. Chinese Optics Letters, 2016, 14(4): 040301

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