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.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
  3. D. Zhang, Y. Zhai, L. Wu, and X. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
    [Crossref]
  4. J. Cheng and S. Han, “Theoretical analysis of quantum noise in ghost imaging,” Chin. Phys. Lett. 22, 1676–1679 (2005).
    [Crossref]
  5. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
    [Crossref]
  6. W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (4)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

C. Deng, W. Gong, and S. Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24, 25983–25994 (2016).
[Crossref]

2015 (2)

2013 (2)

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

2012 (3)

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

2009 (1)

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

2006 (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

2005 (4)

M. D. Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[Crossref]

D. Z. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[Crossref]

D. Zhang, Y. Zhai, L. Wu, and X. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[Crossref]

J. Cheng and S. Han, “Theoretical analysis of quantum noise in ghost imaging,” Chin. Phys. Lett. 22, 1676–1679 (2005).
[Crossref]

1970 (1)

N. S. Kopeika and J. Bordogna, “Background noise in optical communication systems,” Proc. IEEE 58, 1571–1577 (1970).
[Crossref]

Angelo, M. D.

M. D. Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[Crossref]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Bo, Z.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

Bordogna, J.

N. S. Kopeika and J. Bordogna, “Background noise in optical communication systems,” Proc. IEEE 58, 1571–1577 (1970).
[Crossref]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Cao, D. Z.

D. Z. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[Crossref]

Cao, F.

Chen, M.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Chen, X.

Cheng, J.

J. Cheng and S. Han, “Theoretical analysis of quantum noise in ghost imaging,” Chin. Phys. Lett. 22, 1676–1679 (2005).
[Crossref]

Deng, C.

Edgar, M. P.

Erkmen, B. I.

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Gong, W.

C. Deng, W. Gong, and S. Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24, 25983–25994 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photon. Res. 3, 234–237 (2015).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Han, S.

C. Deng, W. Gong, and S. Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24, 25983–25994 (2016).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

J. Cheng and S. Han, “Theoretical analysis of quantum noise in ghost imaging,” Chin. Phys. Lett. 22, 1676–1679 (2005).
[Crossref]

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

Kopeika, N. S.

N. S. Kopeika and J. Bordogna, “Background noise in optical communication systems,” Proc. IEEE 58, 1571–1577 (1970).
[Crossref]

Li, E.

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

Padgett, M. J.

Peng, J.

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

Shen, X.

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

Shi, J.

Shih, Y.

M. D. Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[Crossref]

Sun, B.

Wang, H.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Wang, K.

D. Z. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[Crossref]

Wang, Q.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Welsh, S. S.

Wu, L.

Xiong, J.

D. Z. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[Crossref]

Xu, L.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Xu, W.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Xu, X.

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

Yang, C.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Yang, X.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Yang, Y.

Yu, H.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

Zeng, G.

Zhai, Y.

Zhang, D.

Zhang, P.

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

Zhang, Y.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Zhao, C.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Zhao, Y.

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Chin. Phys. Lett. (1)

J. Cheng and S. Han, “Theoretical analysis of quantum noise in ghost imaging,” Chin. Phys. Lett. 22, 1676–1679 (2005).
[Crossref]

J. Mod. Opt. (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

Laser Phys. Lett. (1)

M. D. Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[Crossref]

Opt. Commun. (1)

X. Yang, Y. Zhang, C. Yang, L. Xu, Q. Wang, and Y. Zhao, “Heterodyne 3D ghost imaging,” Opt. Commun. 368, 1–6 (2016).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Photon. J. (1)

M. Chen, E. Li, W. Gong, Z. Bo, X. Xu, C. Zhao, X. Shen, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints in real atmosphere,” Opt. Photon. J. 3, 83–85 (2013).
[Crossref]

Photon. Res. (1)

Phys. Rev. A (2)

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

D. Z. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[Crossref]

Phys. Rev. Lett. (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref]

Proc. IEEE (1)

N. S. Kopeika and J. Bordogna, “Background noise in optical communication systems,” Proc. IEEE 58, 1571–1577 (1970).
[Crossref]

Remote Sens. (1)

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8, 991 (2016).
[Crossref]

Sci. Rep. (1)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6, 26133 (2016).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of GI lidar via different detection mechanisms: (A) narrow pulsed GI lidar, (B) heterodyne GI lidar, and (C) pulse-compression GI lidar via coherent detection.

Fig. 2.
Fig. 2.

Image reconstruction results. The signal power to background power ratio σ for columns (1)–(6) is 40, 30, 20, 10, 0, and 10 dB, respectively, and rows (A)–(C) correspond to lidar systems (A)–(C), respectively.

Fig. 3.
Fig. 3.

Comparison among the normalized SNR SNRi/N[(ΔO)min]2 for lidar systems (A)–(C). The numerical results (dashed lines) for lidar systems (A)–(C) come from the simulation results, while theoretical behaviors [Eqs. (10), (14), and (18)] are indicated by three solid lines.

Fig. 4.
Fig. 4.

Comparison among PSNR for lidar systems (A)–(C).

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

Gi(xr)=δIiδIr(xr),
ΔGi2(xr)=δIi2δIr2(xr)δIiδIr(xr)2.
SNRi=[ΔGi]min2ΔGi2.
Es,i(xs,t)=si(t)Es(xs),
Etotal,i(xo,t)=Es,i(xo,t)+Ebg(xo,t),
Ebg*(xo1,t1)Ebg(xo2,t2)=IbgKbg(xo1xo2)Rbg(t1t2),
IA=0TAdtAbeamdxo[|Es(xo,t)|2+|Ebg(xo,t)|2]O(xo)IA,s+IA,bg,
GA(xr)=TAAcoh,sIrIsO.
ΔGA2=[δIA,s2δIr2δIA,sδIr2]+δIA,bg2δIr2=δIA,s2δIr2+δIA,bg2δIr2=TA2AbeamAcoh,sIr2Is2O2¯(1+τbgTAAcoh,bgAcoh,s1σ2),
SNRA=NNspΔOmin2[1+τbgTAAcoh,bgAcoh,s1σ2]O2¯,
IB(f)=FFT{[sLO(t)iB(t)]HB(t)}=m2TBsinc[TB(ffz)]exp[jϕB]dxo|EBs(xo,t)|2O(xo)+FFT{sLO(t)[(dxo|Ebg(xo,t)|2O(xo))HB(t)]}IB,s(f)+IB,bg(f),
GB(xr)=m2TBAcoh,sIrIsO,
ΔGB2=m24TB2Acoh,sAbeamIr2Is2O2¯×(1+2m2τbgTBAcoh,bgAcoh,s1σ2).
SNRB=NNspΔOmin2[1+2m2τbgTBAcoh,bgAcoh,s1σ2]O2¯.
IC(fz)=xtm44TC2ILOIs(xt)+xt|iC,bg(xt,fz)|2+2Re{xt[m2ILOTCexp(jϕC)Es(xt)][iC,bg(xt,fz)]*}IC,s(fz)+IC,bg(fz)+IC,mu(fz),
GC(xr)=m44ILOTC2Acoh,sIrIsO
ΔGC2=m816ILO2TC4AbeamAcoh,sIr2Is2O2¯×[1+64(2+m2)2m8(τbgTC)2Acoh,bgAcoh,sIbg2Is2].
SNRC=NNspΔOmin2[1+64(2+m2)2m8(τbgTC)2Acoh,bgAcoh,s1σ2]O2¯.
PSNRi=10×log10[(2p1)2MSEi].
MSEi=1Npixelm,n[Gi(m,n)O(m,n)]2,

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