Quantum Information Processing

, Volume 11, Issue 4, pp 949–993 | Cite as

The physics of ghost imaging

  • Jeffrey H. ShapiroEmail author
  • Robert W. Boyd


Ghost images are obtained by correlating the output of a single-pixel (bucket) photodetector—which collects light that has been transmitted through or reflected from an object—with the output from a high spatial-resolution scanning photodetector or photodetector array whose illumination has not interacted with that object. The term “ghost image” is apt because neither detector’s output alone can yield an image: the bucket detector has no spatial resolution, while the high spatial-resolution detector has not viewed the object. The first ghost imaging experiment relied on the entangled signal and idler outputs from a spontaneous parametric downconverter, and hence the image was interpreted as a quantum phenomenon. Subsequent theory and experiments showed, however, that classical correlations can be used to form ghost images. For example, ghost images can be formed with pseudothermal light, for which quantum mechanics is not required to characterize its photodetection statistics. This paper presents an overview of the physics of ghost imaging. It clarifies and unites two disparate interpretations of pseudothermal ghost imaging—two-photon interference and classical intensity-fluctuation correlations—that had previously been thought to be conflicting. It also reviews recent work on ghost imaging in reflection, ghost imaging through atmospheric turbulence, computational ghost imaging, and two-color ghost imaging.


Ghost imaging Photon statistics Entanglement Coherence theory Atmospheric turbulence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pittman T.B., Shih Y.H., Strekalov D.V., Sergienko A.V.: Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A 52, R3429–R3432 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    Abouraddy A.F., Saleh B.E.A., Sergienko A.V., Teich M.C.: Role of entanglement in two-photon imaging. Phys. Rev. Lett. 87, 123602 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    Bennink R.S., Bentley S.J., Boyd R.W.: “Two-photon” coincidence imaging with a classical source. Phys. Rev. Lett. 89, 113601 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Gatti A., Brambilla E., Lugiato L.A.: Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm. Phys. Rev. Lett. 90, 133603 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Bennink R.S., Bentley S.J., Boyd R.W., Howell J.C.: Quantum and classical coincidence imaging. Phys. Rev. Lett. 92, 033601 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    Howell J.C., Bennink R.S., Bentley S.J., Boyd R.W.: Realization of the Einstein–Podolsky–Rosen paradox using momentum and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92, 210403 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    Reid M.D.: Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification. Phys. Rev. A 40, 913–923 (1989)ADSCrossRefGoogle Scholar
  8. 8.
    Gatti A., Brambilla E., Bache M., Lugiato L.A.: Correlated imaging, quantum and classical. Phys. Rev. A 70, 013802 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    Gatti A., Brambilla E., Bache M., Lugiato L.A.: Ghost imaging with thermal light: comparing entanglement and classical correlation. Phys. Rev. Lett. 93, 093602 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    Cai Y., Zhu S.-Y.: Ghost imaging with incoherent and partially coherent light radiation. Phys. Rev. E 71, 056607 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Cai Y., Zhu S.-Y.: Ghost interference with partially coherent light radiation. Opt. Lett. 29, 2716–2718 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    Valencia A., Scarcelli G., D’Angelo M., Shih Y.: Two-photon imaging with thermal light. Phys. Rev. Lett. 94, 063601 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Ferri F., Magatti D., Gatti A., Bache M., Brambilla E., Lugiato L.A.: High-resolution ghost image and ghost diffraction experiments with thermal light. Phys. Rev. Lett. 94, 183602 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Scarcelli G., Berardi V., Shih Y.: Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?. Phys. Rev. Lett. 96, 063602 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    Erkmen B.I., Shapiro J.H.: Unified theory of ghost imaging with Gaussian-state light. Phys. Rev. A 77, 043809 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Shapiro J.H.: Computational ghost imaging. Phys. Rev. A 78, 061802(R) (2008)ADSGoogle Scholar
  17. 17.
    Shapiro, J.H.: The quantum theory of optical communications. IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569 (2009); Shapiro, J.H. Corrections to “The quantum theory of optical communications” IEEE J. Sel. Top. Quantum Electron. 16, 698 (2010)Google Scholar
  18. 18.
    Erkmen B.I., Shapiro J.H.: Ghost imaging: from quantum to classical to computational. Adv. Opt. Photon. 2, 405–450 (2010)CrossRefGoogle Scholar
  19. 19.
    Meyers R., Deacon K.S., Shih Y.: Ghost-imaging experiment by measuring reflected photons. Phys. Rev. A 77, 041801(R) (2008)ADSCrossRefGoogle Scholar
  20. 20.
    Meyers R.E., Deacon K.S., Shih Y.: Quantum imaging of an obscured object by measurement of reflected photons. Proc. SPIE 7092, 70920E (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Meyers R.E., Deacon K.S.: Quantum ghost imaging experiments at ARL. Proc. SPIE 7815, 78150I (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Cheng J.: Ghost imaging through turbulent atmosphere. Opt. Express 17, 7916–7921 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Hardy N.D., Shapiro J.H.: Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio. Proc. SPIE 7815, 78150P (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Hardy, N.D.: Analyzing and improving image quality in reflective ghost imaging. S.M. thesis, MIT (2011)Google Scholar
  25. 25.
    Bromberg Y., Katz O., Silberberg Y.: Ghost imaging with a single detector. Phys. Rev. A 79, 053840 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Katz O., Bromberg Y., Silberberg Y.: Compressive ghost imaging. Appl. Phys. Lett. 95, 131110 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    Rubin M.H., Shih Y.: Resolution of ghost imaging for nondegenerate spontaneous parametric downconversion. Phys. Rev. A 78, 033836 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Chan K.W.C., O’Sullivan M.N., Boyd R.W.: Two-color ghost imaging. Phys. Rev. A 79, 033808 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    Karmakar S., Shih Y.: Observation of two-color ghost imaging. Proc. SPIE 7815, 78150R (2010)Google Scholar
  30. 30.
    Erkmen B.I., Shapiro J.H.: Signal-to-noise ratio of Gaussian-state ghost imaging. Phys. Rev. A 79, 023833 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    O’Sullivan M.N., Chan K.W.C., Boyd R.W.: Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging. Phys. Rev. A 82, 053803 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Chan K.W.C., O’Sullivan M.N., Boyd R.W.: High-order thermal ghost imaging. Opt. Lett. 34, 3343–3345 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    Chan K.W.C., O’Sullivan M.N., Boyd R.W.: Optimization of thermal ghost imaging: high-order correlations vs. background subtraction. Opt. Express 18, 5562–5573 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Wong F.N.C., Kim T., Shapiro J.H.: Efficient generation of polarization-entangled photons in a nonlinear crystal. Laser Phys. 16, 1517–1524 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    Le Gouët J., Venkatraman D., Wong F.N.C., Shapiro J.H.: Classical low-coherence interferometry based on broadband parametric fluorescence and amplification. Opt. Express 17, 17874 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    Yuen H.P., Shapiro J.H.: Optical communication with two-photon coherent states—Part III: Quantum measurements realizable with photoemissive detectors. IEEE Trans. Inf. Theory 26, 78–92 (1980)MathSciNetADSzbMATHCrossRefGoogle Scholar
  37. 37.
    Wozencraft J.M., Jacobs I.M.: Principles of Communication Engineering, pp. 205–206. Wiley, New York (1965)Google Scholar
  38. 38.
    Shapiro J.H., Sun K.-X.: Semiclassical versus quantum behavior in fourth-order interference. J. Opt. Soc. Am. B 11, 1130–1141 (1994)ADSCrossRefGoogle Scholar
  39. 39.
    Mandel L., Wolf E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)Google Scholar
  40. 40.
    Shapiro J.H., Shakeel A.: Optimizing homodyne detection of quadratures-noise squeezing via local-oscillator selection. J. Opt. Soc. Am. B 14, 232–249 (1997)ADSCrossRefGoogle Scholar
  41. 41.
    Saleh B.E.A., Abouraddy A.R., Sergienko A.V., Teich M.C.: Duality between partial coherence and partial entanglement. Phys. Rev. A 62, 043816 (2000)ADSCrossRefGoogle Scholar
  42. 42.
    Erkmen B.I., Shapiro J.H.: Optical coherence theory for phase-sensitive light. Proc. SPIE 6305, 63050G (2006)ADSCrossRefGoogle Scholar
  43. 43.
    Yuen H.P., Shapiro J.H.: Optical communication with two-photon coherent states—Part I: quantum state propagation and quantum noise reduction. IEEE Trans. Inf. Theory 24, 657–668 (1978)MathSciNetADSzbMATHCrossRefGoogle Scholar
  44. 44.
    Shih Y.: Quantum imaging. IEEE J. Sel. Top. Quantum Electron. 13, 1016–1030 (2007)CrossRefGoogle Scholar
  45. 45.
    Goodman J.W.: Speckle Phenomena in Optics: Theory and Applications. Roberts & Co., Englewood, CO (2007)Google Scholar
  46. 46.
    Glauber R.J.: Optical coherence and photon statistics. In: DeWitt, C., Blandin, A., Cohen-Tannoudji, C. (eds) Quantum Optics and Electronics, Gordon and Breach, New York (1965)Google Scholar
  47. 47.
    Tatarski V.I.: Wave Propagation in a Turbulent Medium. Dover Publications, New York (1961)zbMATHGoogle Scholar
  48. 48.
    Strohbehn, J.W. (eds): Laser Beam Propagation in the Atmosphere. Springer, Berlin (1978)Google Scholar
  49. 49.
    Ishimaru A.: Wave Propagation and Scattering in Random Media. Academic Press, New York (1978)Google Scholar
  50. 50.
    Shapiro J.H., Capron B.A., Harney R.C.: Imaging and target detection with a heterodyne-reception optical radar. Appl. Opt. 20, 3292–3313 (1981)ADSCrossRefGoogle Scholar
  51. 51.
    Dixon P.B., Howland G., Chan K.W.C., O’Sullivan-Hale C., Rodenburg B., Hardy N.D., Shapiro J.H., Simon D.S., Sergienko A.V., Boyd R.W., Howell J.C.: Quantum ghost imaging through turbulence. Phys. Rev. A 83, 051803(R) (2011)ADSCrossRefGoogle Scholar
  52. 52.
    Candès E., Wakin M.B.: Compressive sampling. IEEE Signal Proc. Mag. 25, 21–30 (March 2008)Google Scholar
  53. 53.
    Duarte M.F., Davenport M.A., Takhar D., Laska J.N., Sun T., Kelly K.F., Baraniuk R.G.: Single-pixel imaging via compressive sampling. IEEE Signal Proc. Mag. 25, 83–91 (March 2008)Google Scholar
  54. 54.
    Jack B., Leach J., Romero J., Franke-Arnold S., Ritsch-Marte M., Barnett S.M., Padgett M.J.: Holographic ghost imaging and the violation of a Bell inequality. Phys. Rev. Lett. 103, 083602 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    Malik M., Shin H., O’Sullivan M., Zerom P., Boyd R.W.: Quantum ghost image discrimination with correlated photon pairs. Phys. Rev. Lett. 104, 163602 (2010)ADSCrossRefGoogle Scholar
  56. 56.
    Liu Q., Chen X.-H., Luo K.-H., Wu W., Wu L.-A.: Role of multiphoton bunching in high-order ghost imaging with thermal light sources. Phys. Rev. A 79, 053844 (2009)ADSCrossRefGoogle Scholar
  57. 57.
    Ou L.-H., Kuang L.-M.: Ghost imaging with third-order correlated thermal light. J. Phys B 40, 1833–1844 (2007)ADSCrossRefGoogle Scholar
  58. 58.
    Bache M., Brambilla E., Gatti A., Lugiato L.A.: Ghost imaging using homodyne detection. Phys. Rev. A 70, 023823 (2004)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institute of Optics and Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  3. 3.Department of PhysicsUniversity of OttawaOttawaCanada

Personalised recommendations