N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).

[CrossRef]

B. I. Erkmen, “Computational ghost imaging for remote sensing applications,” Interplanet. Netw. Prog. Rep. 42–185, 1–23 (2011).

S. Komiyama, “Single-photon detectors in the terahertz range,” IEEE J. Sel. Top. Quantum Electron. 17, 54–66 (2011).

[CrossRef]

R. Meyers and K. S. Deacon, “Quantum ghost imaging experiments at ARL,” Proc. SPIE 7815, 78150I (2010).

[CrossRef]

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Proc. SPIE 7815, 78150L (2010).

[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).

[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).

[CrossRef]

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17, 7916–7921 (2009).

[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).

[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

M. J. Fitch and R. Osiander, “Terahertz waves for communications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

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

[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

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

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).

[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).

[CrossRef]

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

R. Meyers and K. S. Deacon, “Quantum ghost imaging experiments at ARL,” Proc. SPIE 7815, 78150I (2010).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

M. J. Fitch and R. Osiander, “Terahertz waves for communications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics (Ben Roberts, 2007).

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).

[CrossRef]

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Proc. SPIE 7815, 78150L (2010).

[CrossRef]

N. D. Hardy, “Analyzing and improving image quality in reflective ghost imaging,” S.M. thesis (Massachusetts Institute of Technology, 2011).

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).

[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

S. Komiyama, “Single-photon detectors in the terahertz range,” IEEE J. Sel. Top. Quantum Electron. 17, 54–66 (2011).

[CrossRef]

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

[CrossRef]

D. Kryskowski and G. H. Suits, Sources of Radiation (SPIE, 1993), Vol. 1, Chap. 3.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

R. Meyers and K. S. Deacon, “Quantum ghost imaging experiments at ARL,” Proc. SPIE 7815, 78150I (2010).

[CrossRef]

M. J. Fitch and R. Osiander, “Terahertz waves for communications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).

[CrossRef]

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Proc. SPIE 7815, 78150L (2010).

[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).

[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).

[CrossRef]

J. H. Shapiro, Imaging and Optical Communication Through Atmospheric Turbulence (Springer-Verlag, 1978), Chap. 6.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).

[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).

[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

D. Kryskowski and G. H. Suits, Sources of Radiation (SPIE, 1993), Vol. 1, Chap. 3.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).

[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).

[CrossRef]

S. Komiyama, “Single-photon detectors in the terahertz range,” IEEE J. Sel. Top. Quantum Electron. 17, 54–66 (2011).

[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).

[CrossRef]

B. I. Erkmen, “Computational ghost imaging for remote sensing applications,” Interplanet. Netw. Prog. Rep. 42–185, 1–23 (2011).

M. J. Fitch and R. Osiander, “Terahertz waves for communications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).

[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).

[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).

[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).

[CrossRef]

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).

[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).

[CrossRef]

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

[CrossRef]

R. Meyers and K. S. Deacon, “Quantum ghost imaging experiments at ARL,” Proc. SPIE 7815, 78150I (2010).

[CrossRef]

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Proc. SPIE 7815, 78150L (2010).

[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

N. D. Hardy, “Analyzing and improving image quality in reflective ghost imaging,” S.M. thesis (Massachusetts Institute of Technology, 2011).

We define a classical source as one whose photodetection statistics can be accurately described using the semiclassical (shot-noise) theory. This is equivalent to having a source state with a proper P-representation. [17] A quantum source is one whose photodetection statistics cannot be described by the semiclassical theory; i.e., the source state does not have a proper P-representation.

A more general and better filter is gn(t)≡ ∑kfk*(t)fk+n(t)-〈|fk(t)|2〉δ0,n, but because it complicates the forthcoming analysis, here we use the suboptimal filter in Eq. (14).

D. Kryskowski and G. H. Suits, Sources of Radiation (SPIE, 1993), Vol. 1, Chap. 3.

J. H. Shapiro, Imaging and Optical Communication Through Atmospheric Turbulence (Springer-Verlag, 1978), Chap. 6.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Although the Eq. (7) structure function was initially derived using the weak-fluctuation (Rytov) approximation, it remains valid well beyond the regime in which the Rytov approximation can be used [20].

A raster-scanning laser radar would share the same limitations with computational ghost imaging regarding forward-path turbulence, as the focused-spot size on the target surface would become turbulence-limited when the transmitter-aperture diameter exceeds the transmitter-plane coherence length.

Given that the atmospheric coherence time is typically longer than a millisecond, and SLMs have modulation bandwidths that are several MHz, correlations can be taken nominally over thousands of modulation symbols before the state of turbulence has significantly changed.

J. W. Goodman, Speckle Phenomena in Optics (Ben Roberts, 2007).