Turbulence-free ghost imaging is a promising solution for the degraded image caused by atmospheric turbulence. However, turbulence-free ghost imaging requires two harsh conditions. To solve this problem, the temporal statistical property of the photon number fluctuations introduced by space-time fluctuating atmospheric turbulence is investigated. We find that the photons collected by the detectors is a superposition of the fluctuating photons introduced by space-time fluctuating atmospheric turbulence and the nonfluctuating photons with probabilities inversely proportional to the beam diameter. The fluctuating photons, which cause image degradation, lead to the absence of stable temporal photon number correlations, while the nonfluctuating photons have the opposite effect. Thus, fluctuating photons are eliminated by measuring the temporal correlations of the signal light and reference light separately. The results show that turbulence-free ghost images can be reconstructed even if the typical conditions are not met. This work does not negate the results of Meyers et al. and provides a method to address the harsh constraints of turbulence-free ghost imaging.
REFERENCES
1.
R. E.
Meyers
,
K. S.
Deacon
, and
Y.
Shih
, “
Turbulence-free ghost imaging
,” Appl. Phys. Lett.
98
(11
), 111115
(2011
).2.
R. E.
Meyers
,
K. S.
Deacon
, and
Y. H.
Shi
, “
Positive-negative turbulence-free ghost imaging
,” Appl. Phys. Lett.
100
, 131114
(2012
).3.
Y.
Shih
, An Introduction to Quantum Optics: Photon and Biphoton Physics (Series in Optics and Optoelectronics)
, 1st ed. (
Taylor & Francis
,
London
, 2011
).4.
T. A.
Smith
and
Y.
Shih
, “
Turbulence-free double-slit interferometer
,” Phys. Rev. Lett.
120
, 063606
(2018
).5.
Y.
Shih
, “
The physics of turbulence-free ghost imaging
,” Technologies
4
, 39
(2016
).6.
J. H.
Shapiro
, “
Comment on ‘Turbulence-free ghost imaging’ [Appl. Phys. Lett. 98, 111115 (2011)]
,” arXiv:1201.4513 (2012
).7.
M.-F.
Li
,
L.
Yan
,
R.
Yang
,
J.
Kou
, and
Y.-S.
Liu
, “
Turbulence-free intensity fluctuation self-correlation imaging with sunlight
,” Acta Phys. Sin.
68
, 094204
(2019
).8.
Y.-C.
He
,
G.
Wang
,
G.-X.
Dong
,
S.-T.
Zhu
,
H.
Chen
,
A.-X.
Zhang
, and
Z.
Xu
, “
Ghost imaging based on deep learning
,” Sci. Rep.
8
, 6469
(2018
).9.
H.
Zhang
and
D.-Y.
Duan
, “
Turbulence-immune computational ghost imaging based on a multi-scale generative adversarial network
,” Opt. Express
29
, 43929
–43937
(2021
).10.
H.
Zhang
and
D.-Y.
Duan
, “
Computational ghost imaging with compressed sensing based on a convolutional neural network
,” Chin. Opt. Lett.
19
, 101101
(2021
).11.
H.
Zhang
,
Y.-J.
Xia
, and
D.-Y.
Duan
, “
Computational ghost imaging with deep compressed sensing
,” Chin. Phys. B
30
, 124209
(2021
).12.
H.
Liu
,
Y.-N.
Chen
,
L.
Zhang
,
D.-H.
Li
, and
X.-W.
Li
, “
Color ghost imaging through the scattering media based on A-cGAN
,” Opt. Lett.
47
, 569
–572
(2022
).13.
Y.-F.
Chen
,
Z.
Sun
,
C.
Li
, and
X.-L.
Li
, “
Computational ghost imaging in turbulent water based on self-supervised information extraction network
,” Opt. Laser Technol.
167
, 109735
(2023
).14.
L.-H.
Zhang
,
Y.-J.
Zhai
,
R.-C.
Xu
,
K.-M.
Wang
, and
D.-W.
Zhang
, “
End-to-end computational ghost imaging method that suppresses atmospheric turbulence
,” Appl. Opt.
62
(3
), 697
–705
(2023
).15.
J.
Cheng
, “
Ghost imaging through turbulent atmosphere
,” Opt. Express
17
, 7916
–7921
(2009
).16.
P.
Zhang
,
W.
Gong
,
X.
Shen
, and
S.
Han
, “
Correlated imaging through atmospheric turbulence
,” Phys. Rev. A
82
, 033817
(2010
).17.
N. D.
Hardy
and
J. H.
Shapiro
, “
Reflective ghost imaging through turbulence
,” Phys. Rev. A
84
, 063824
(2011
).18.
D.
Shi
,
C.
Fan
,
P.
Zhang
,
H.
Shen
,
J.
Zhang
,
C.
Qiao
, and
Y.
Wang
, “
Two-wavelength ghost imaging through atmospheric turbulence
,” Opt. Express
21
, 2050
–2064
(2013
).19.
J.
Cheng
and
J.
Lin
, “
Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere
,” Phys. Rev. A
87
, 043810
(2013
).20.
C.
Luo
,
J.
Cheng
,
A.
Chen
, and
Z.
Liu
, “
Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence
,” Opt. Commun.
352
, 155
–160
(2015
).21.
C.
Luo
,
P.
Lei
,
Z.
Li
,
J.
Qi
,
X.
Jia
,
F.
Dong
, and
Z.
Liu
, “
Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence
,” Laser Phys. Lett.
15
, 085201
(2018
).22.
W.
Tan
,
X.
Huang
,
S.
Nan
,
Y.
Bai
, and
X.
Fu
, “
Effect of the collection range of a bucket detector on ghost imaging through turbulent atmosphere
,” J. Opt. Soc. Am. A
36
, 1261
–1266
(2019
).23.
L. C.
Andrews
and
R. L.
Phillips
, Laser Beam Propagation through Random Media
(
SPIE Optical Engineering Press
,
Bellingham
, 2005
).24.
D. L.
Fried
, “
Probability of getting a lucky short-exposure image through turbulence
,” J. Opt. Soc. Am.
68
, 1651
–1657
(1978
).25.
E.
Collett
and
E.
Wolf
, “
Beam generated by Gaussian quasi-homogeneous sources
,” Opt. Commun.
32
, 27
–31
(1980
).26.
J.
Cheng
and
S.-S.
Han
, “
Incoherent coincidence imaging and its applicability in x-ray diffraction
,” Phys. Rev. Lett.
92
, 093903
(2004
).27.
A.
Valencia
,
G.
Scarcelli
,
M.
D'Angelo
, and
Y.
Shih
, “
Two-photon imaging with thermal light
,” Phys. Rev. Lett.
94
, 063601
(2005
).28.
X.-H.
Chen
,
Q.
Liu
,
K.-H.
Luo
, and
L.-A.
Wu
, “
Lensless ghost imaging with true thermal light
,” Opt. Lett.
34
, 695
–697
(2009
).29.
X.-F.
Liu
,
X.-H.
Chen
,
X.-R.
Yao
,
W.-K.
Yu
,
G.-J.
Zhai
, and
L.-A.
Wu
, “
Lensless ghost imaging with sunlight
,” Opt. Lett.
39
, 2314
–2317
(2014
).30.
F.
Li
, “
Phase diversity wavefront sensing and its application in image restoration
,” Ph.D. thesis (
National University of Defense Technology
, 2012
).31.
G.-Q.
Liu
,
L.
Yang
,
L.-H.
Deng
,
Y.-Z.
Li
, and
Z.
Liu
, “
Influence of atmospheric turbulence on the accuracy of astronomical telescope auto-guiding system
,” Acta Opt. Sin.
33
, 0101002
(2012
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
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