- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Geometrical effects of the source size in correlation imaging

Giuseppe Lerario

Milena D'Angelo* and Gianlorenzo Massaro

  • *Contact author: milena.dangelo@uniba.it
PDF

Phys. Rev. A 113, 053709 – Published 7 May, 2026

DOI: https://doi.org/10.1103/6g9j-5xx3

Abstract

Correlation imaging (CI) is an emerging approach to imaging aimed at overcoming the limitations of conventional, intensity-based imaging modalities. In this paper, we focus on a peculiarity of chaotic-light-based CI: the strict link between image properties, and source size and geometry. We will show that the light source acts as a limiting aperture, whose geometrical properties significantly affect image formation, hence, the defocused resolution and depth of field. In ghost imaging, the image quality is typically associated with the speckle size, namely, with wave-optics effects; here, we evaluate the second-order correlation function of an out-of-focus CI system and demonstrate that the out-of-focus point-spread function is governed by a geometrical circle of confusion determined by the illumination numerical aperture. Both analytical results and numerical simulations indicate that this geometrical effect dominates the optical response of CI systems both in out-of-focus conditions and when large sources are employed. Even more, in correlation plenoptic imaging, the axial resolution is found to be directly linked to the illumination geometry, as the source size is found to constrain both the quality of the refocused images and the axial sectioning capability. The presented analysis applies to all CI architectures, thus providing a comprehensive framework for understanding and optimizing source-dependent effects in CI.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. P. A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, Imaging with quantum states of light, Nat. Rev. Phys. 1, 367 (2019).
  2. M. Genovese, Real applications of quantum imaging, J. Opt. 18, 073002 (2016).
  3. Y. Shih, Quantum imaging, IEEE J Select. Topics Quantum Electron. 13, 1016 (2007).
  4. M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Perspectives for applications of quantum imaging, Laser Photon. Rev. 13, 1900097 (2019).
  5. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Correlated imaging, quantum and classical, Phys. Rev. A 70, 013802 (2004).
  6. B. E. A Saleh and M. Carl Teich, Noise in classical and quantum photon-correlation imaging, in Advances in Information Optics and Photonics, Vol. PM183, edited by A. T. Fr berg and R. Dändliker (SPIE Press, Bellingham, WA, 2008), Chap. 21, pp. 423–436.
  7. S. Vernekar and J. Xavier, Quantum correlation enhanced optical imaging, Quantum Beam Sci. 8, 19 (2024).
  8. G. Massaro, F. V. Pepe, and M. D'Angelo, Correlation hyperspectral imaging, Phys. Rev. Lett. 133, 183802 (2024).
  9. G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Quantum imaging with undetected photons, Nature (London) 512, 409 (2014).
  10. M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Theory of quantum imaging with undetected photons, Phys. Rev. A 92, 013832 (2015).
  11. J. H. Shapiro, D. Venkatraman, and F. N. Wong, Classical imaging with undetected photons, Sci. Rep. 5, 10329 (2015).
  12. M. Gilaberte Basset, R. Sondenheimer, J. Fuenzalida, A. Vega, S. Töpfer, E. A. Santos, S. Saravi, F. Setzpfandt, F. Steinlechner, and M. Gräfe, Experimental analysis of image resolution of quantum imaging with undetected light through position correlations, Phys. Rev. A 108, 052610 (2023).
  13. G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, Measurement of sub-shot-noise spatial correlations without background subtraction, Phys. Rev. Lett. 102, 213602 (2009).
  14. G. Brida, M. Genovese, and I. R. Berchera, Experimental realization of sub-shot-noise quantum imaging, Nature Photon. 4, 227 (2010).
  15. N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Genovese, Realization of the first sub-shot-noise wide field microscope, Light: Sci. Appl. 6, e17005 (2017).
  16. A. Meda, E. Losero, N. Samantaray, F. Scafirimuto, S. Pradyumna, A. Avella, I. Ruo-Berchera, and M. Genovese, Photon-number correlation for quantum enhanced imaging and sensing, J. Opt. 19, 094002 (2017).
  17. I. R. Berchera and I. P. Degiovanni, Quantum imaging with sub-Poissonian light: Challenges and perspectives in optical metrology, Metrologia 56, 024001 (2019).
  18. P. Zhang, W. Gong, X. Shen, and S. Han, Correlated imaging through atmospheric turbulence, Phys. Rev. A 82, 033817 (2010).
  19. G. Scala, G. Massaro, G. Borreggine, C. Lupo, M. D'Angelo, and F. V. Pepe, Robustness of chaotic-light correlation imaging against turbulence, Eur. Phys. J. Plus 139, 1010 (2024).
  20. Wenlin Gong and W. Gong, Correlated imaging in scattering media, Opt. Lett. 36, 394 (2011).
  21. G. Lubin, D. Oron, U. Rossman, R. Tenne, and V. J. Yallapragada, Photon correlations in spectroscopy and microscopy, ACS Photon. 9, 2891 (2022).
  22. B. Ndagano, H. Defienne, D. Branford, Y. D. Shah, A. Lyons, N. Westerberg, E. M. Gauger, and D. Faccio, Quantum microscopy based on Hong–Ou–Mandel interference, Nature Photon. 16, 384 (2022).
  23. 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).
  24. R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon” coincidence imaging with a classical source, Phys. Rev. Lett. 89, 113601 (2002).
  25. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Quantum and classical coincidence imaging, Phys. Rev. Lett. 92, 033601 (2004).
  26. A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, Two-photon imaging with thermal light, Phys. Rev. Lett. 94, 063601 (2005).
  27. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, High-resolution ghost image and ghost diffraction experiments with thermal light, Phys. Rev. Lett. 94, 183602 (2005).
  28. G. Scarcelli, V. Berardi, and Y. Shih, Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations? Phys. Rev. Lett. 96, 063602 (2006).
  29. J. H. Shapiro and R. W. Boyd, The physics of ghost imaging, Quantum Info. Proc. 11, 949 (2012).
  30. J. H. Shapiro and B. I. Erkmen, Ghost imaging: From quantum to classical to computational, Adv. Opt. Photon. 2, 405 (2010).
  31. Y.-H. Zhai, D. Zhang, L.-A. Wu, and X.-H. Chen, Correlated two-photon imaging with true thermal light, Opt. Lett. 30, 2354 (2005).
  32. S. Han, H. Yu, X. Shen, H. Liu, W. Gong, and Z. Liu, A review of ghost imaging via sparsity constraints, Appl. Sci. 8, 1379 (2018).
  33. J. H. Shapiro, Computational ghost imaging, Phys. Rev. A 78, 061802(R) (2008).
  34. P. A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, Ghost imaging using optical correlations, Laser Photon. Rev. 12, 1700143 (2018).
  35. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Differential ghost imaging, Phys. Rev. Lett. 104, 253603 (2010).
  36. O. Katz, Y. Bromberg, and Y. Silberberg, Compressive ghost imaging, Appl. Phys. Lett. 95, 131110 (2009).
  37. P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, Ghost imaging in the time domain, Nature Photon. 10, 167 (2016).
  38. M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, Deep-learning-based ghost imaging, Sci. Rep. 7, 17865 (2017).
  39. B. I. Erkmen, Computational ghost imaging for remote sensing, J. Opt. Soc. Am. A, 29, 782 (2012).
  40. N. D. Hardy and J. H. Shapiro, Computational ghost imaging versus imaging laser radar for three-dimensional imaging, Phys. Rev. A 87, 023820 (2013).
  41. M. D'Angelo, F. V. Pepe, A. Garuccio, and G. Scarcelli, Correlation plenoptic imaging, Phys. Rev. Lett. 116, 223602 (2016).
  42. F. V. Pepe, F. Di Lena, A. Garuccio, G. Scarcelli, and M. D'Angelo, Correlation plenoptic imaging with entangled photons, Technologies 4, 17 (2016).
  43. G. Massaro, D. Giannella, A. Scagliola, F. D. Lena, G. Scarcelli, A. Garuccio, F. V. Pepe, and M. D'Angelo, Light-field microscopy with correlated beams for high-resolution volumetric imaging, Sci. Rep. 12, 16823 (2022).
  44. G. Massaro, Analytical form of the refocused images from correlation plenoptic imaging, Opt. Express 32, 35755 (2024).
  45. D. Giannella, G. Massaro, B. Stoklasa, M. D'Angelo, and F. V. Pepe, Light-field imaging from position-momentum correlations, Phys. Lett. A 494, 129298 (2024).
  46. G. Massaro, P. Mos, S. Vasiukov, F. Di Lena, F. Scattarella, F. V. Pepe, A. Ulku, D. Giannella, E. Charbon, C. Bruschini, and M. D'Angelo, Correlated-photon imaging at 10 volumetric images per second, Sci. Rep. 13, 12813 (2023).
  47. F. Scattarella, D. Diacono, A. Monaco, N. Amoroso, L. Bellantuono, G. Massaro, F. V. Pepe, S. Tangaro, R. Bellotti, and M. D'Angelo, Deep learning approach for denoising low-SNR correlation plenoptic images, Sci. Rep. 13, 19645 (2023).
  48. I. Petrelli, F. Santoro, G. Massaro, F. Scattarella, F. V. Pepe, F. Mazzia, M. Ieronymaki, G. Filios, D. Mylonas, N. Pappas, C. Abbattista, and M. D'Angelo, Compressive sensing-based correlation plenoptic imaging, Front. Phys. 11, 1287740 (2023).
  49. F. D. Lena, G. Massaro, A. Lupo, A. Garuccio, F. V. Pepe, and M. D'Angelo, Correlation plenoptic imaging between arbitrary planes, Opt. Express 28, 35857 (2020).
  50. F. Di Lena, F. V. Pepe, A. Garuccio, and M. D'Angelo, Correlation plenoptic imaging: An overview, Appl. Sci. 8, 1958 (2018).
  51. C. Abbattista, L. Amoruso, S. Burri, E. Charbon, F. Di Lena, A. Garuccio, D. Giannella, Z. Hradil, M. Iacobellis, G. Massaro, P. Mos, L. Motka, M. Paúr, F. V. Pepe, M. Peterek, I. Petrelli, J. Řeháček, F. Santoro, F. Scattarella, A. Ulku, et al., Towards quantum 3D imaging devices, Appl. Sci. 11, 6414 (2021).
  52. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  53. G. Massaro, F. Di Lena, M. D'angelo, and F. V. Pepe, Effect of finite-sized optical components and pixels on light-field imaging through correlated light, Sensors 22, 2778 (2022).
  54. N.  Bleistein and R.  A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986).
  55. The infinitely sized bucket detector approximation does not entail any loss of generality, as it simply implies neglecting photon loss. Likewise, the pointlike reference pixels approximation has the only effect of neglecting pixel-limited resolution, which is of no interest for this paper.
  56. X.-H. Zhu, Y.-F. Bai, W. Tan, L.-Y. Zhou, X.-W. Huang, T.-J. Jiang, T. Jiang, S.-Q. Nan, and X.-Q. Fu, High-resolution microscopic ghost imaging for bioimaging, Phys. Rev. Appl. 20, 014028 (2023).
  57. W. Tan, Y. Bai, Y. Bai, X. Huang, T. Jiang, S. Nan, Q. Fu, X. Zou, X. Fu, and X. Fu, Enhancing critical resolution of a ghost imaging system by using a vortex beam, Opt. Express, 30, 14061 (2022).
  58. P. Zerom, Z. Shi, M. N. O'Sullivan, K. Wai Clifford Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, Thermal ghost imaging with averaged speckle patterns, Phys. Rev. A 86, 063817 (2012).
  59. F. Ferri, D. Magatti, V. G. Sala, and A. Gatti, Longitudinal coherence in thermal ghost imaging, Appl. Phys. Lett. 92, 261109 (2008).
  60. B. I. Erkmen and J. H. Shapiro, Signal-to-noise ratio of Gaussian-state ghost imaging, Phys. Rev. A 79, 023833 (2009).
  61. E. Lantz, P. A. Moreau, and F. Devaux, Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays, Phys. Rev. A 90, 063811 (2014).
  62. M. N. O'Sullivan, K. W. C. Chan, and R. W. Boyd, Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging, Phys. Rev. A 82, 053803 (2010).
  63. See Ref. [71] for the analysis of out-of-focus lensless ghost imaging in the case of far-field illumination.
  64. G. Massaro, B. Barile, G. Scarcelli, F. V. Pepe, G. P. Nicchia, and M. D'Angelo, Direct 3D imaging through spatial coherence of light, Laser Photon. Rev. 18, 2301155 (2024).
  65. G. Massaro and M. D'Angelo, Characterization of defocused coherent imaging systems with periodic objects, Sensors 24, 6885 (2024).
  66. S. de Gioia, G. Massaro, and M. D'Angelo, A pseudo-thermal simulation strategy for correlation imaging, Eur. Phys. J. Plus 140, 1097 (2025).
  67. G. Massaro, S. de Gioia, A. Brunetti, F. V. Pepe, and M. D'angelo, Two-point resolution of a defocused imaging system based on spatially coherent illumination, Photon. 11, 1203 (2024).
  68. G. Massaro, F. V. Pepe, and M. D'Angelo, Refocusing algorithm for correlation plenoptic imaging, Sensors 22, 6665 (2022).
  69. G. Massaro, Assessing the 3D resolution of refocused correlation plenoptic images using a general-purpose image quality estimator, Eur. Phys. J. Plus 139, 727 (2024).
  70. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  71. G. Lerario, G. Massaro, and M. D'Angelo, Effect of the finite size of the source in correlation imaging, in Proceeding SPIE, Quantum Communications and Quantum Imaging XXIII, 136180A, Vol. 13618 (San Diego, California, United States 2025).

Outline

Information

Phys. Rev. A 113, 053709– Published 7 May, 2026
  • Received 23 December 2025
  • Accepted 13 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation