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Object reconstruction from multiplexed quantum ghost images using reduction technique

  • D. A. BalakinEmail author
  • A. V. Belinsky
  • A. S. Chirkin
Article

Abstract

We apply the measurement reduction technique to optimally reconstruct an object image from multiplexed ghost images (GI) while taking into account both GI correlations and object image sparsity. The measurement reduction technique is employed because it provides a unified framework for optimal processing of multiplexed and non-multiplexed images with different information about the measurement model, the research object and the research objective. We show that one can reconstruct an image in that way even if the object is illuminated by a small photon number. We consider frequency GI multiplexing using coupled parametric processes. We revealed that the imaging condition depends on the type of parametric process, namely, whether down- or up-conversion is used. Influence of information about sparsity in discrete cosine transform and Haar transform bases on reconstruction quality is studied. In addition, we compared ordinary images and GI when the detectors are additionally illuminated by noise photons in a computer experiment, which showed increased noise immunity of GI, especially with processing via the proposed technique.

Keywords

Measurement reduction Ghost images Multiplexed ghost images Entangled photons Compressive sensing 

Notes

Acknowledgements

The authors are grateful for help to T. Yu. Lisovskaya.

References

  1. 1.
    Belinskii, A.V., Klyshko, D.N.: Two-photon optics: diffraction, holography, and transformation of two-dimensional signals. J. Exp. Theor. Phys. 78(3), 259–262 (1994)ADSGoogle Scholar
  2. 2.
    Gatti, A., Brambilla, E., Bache, M., Lugiato, L.A.: Correlated imaging, quantum and classical. Phys. Rev. A 70(1), 013802 (2004).  https://doi.org/10.1103/PhysRevA.70.013802 ADSCrossRefGoogle Scholar
  3. 3.
    Gatti, A., Brambilla, E., Bache, M., Lugiato, L.A.: Ghost imaging. In: Kolobov, M.I. (ed.) Quantum Imaging, pp. 79–111. Springer, New York (2007)CrossRefGoogle Scholar
  4. 4.
    Chan, K.W.C., O’Sullivan, M.N., Boyd, R.W.: High-order thermal ghost imaging. Opt. Lett. 34(21), 3343–3345 (2009).  https://doi.org/10.1364/ol.34.003343 ADSCrossRefGoogle Scholar
  5. 5.
    Erkman, B.I., Shapiro, J.H.: Ghost imaging: from quantum to classical to computational. Adv. Opt. Photonics 2(4), 405–450 (2010).  https://doi.org/10.1364/aop.2.000405 ADSCrossRefGoogle Scholar
  6. 6.
    Shapiro, J.H., Boyd, R.W.: The physics of ghost imaging. Quantum Inf. Process. 11(4), 949–993 (2012).  https://doi.org/10.1007/s11128-011-0356-5 zbMATHCrossRefGoogle Scholar
  7. 7.
    Chirkin, A.S.: Multiplication of a ghost image by means of multimode entangled quantum states. JETP Lett. 102(6), 404–407 (2015).  https://doi.org/10.1134/S0021364015180046 ADSCrossRefGoogle Scholar
  8. 8.
    Balakin, D.A., Belinsky, A.V., Chirkin, A.S., Yakovlev, V.S.: Multiplicated ghost images reconstruction. In: ICONO/LAT 2016 Technical Digest, ICONO-03 Quantum and Atom Optics (2016)Google Scholar
  9. 9.
    Balakin, D.A., Belinsky, A.V., Chirkin, A.S.: Correlations of multiplexed quantum ghost images and improvement of the quality of restored image. J. Russ. Laser Res. 38(2), 164–172 (2017).  https://doi.org/10.1007/s10946-017-9630-z CrossRefGoogle Scholar
  10. 10.
    Balakin, D.A., Belinsky, A.V., Chirkin, A.S.: Improvement of the optical image reconstruction based on multiplexed quantum ghost images. J. Exp. Theor. Phys. 125(2), 210–222 (2017).  https://doi.org/10.1134/S1063776117070147 ADSCrossRefGoogle Scholar
  11. 11.
    Rodionov, A.V., Chirkin, A.S.: Entangled photon states in consecutive nonlinear optical interactions. JETP Lett. 79(6), 253–256 (2004).  https://doi.org/10.1134/1.1759404 ADSCrossRefGoogle Scholar
  12. 12.
    Ferraro, A., Paris, M.G.A., Bondani, M., Allevi, A., Puddu, E., Andreoni, A.: Three-mode entanglement by interlinked nonlinear interactions in optical \(\chi ^{(2)}\) media. JOSA B 21(6), 1241–1249 (2004).  https://doi.org/10.1364/JOSAB.21.001241 ADSGoogle Scholar
  13. 13.
    Olsen, M.K., Drummond, P.D.: Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical down-converters. Phys. Rev. A 71(5), 053803 (2005).  https://doi.org/10.1103/PhysRevA.71.053803 ADSCrossRefGoogle Scholar
  14. 14.
    Solntsev, A.S., Sukhorukov, A.A., Neshev, D.N., Kivshar, Y.S.: Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides. Phys. Rev. Lett. 108(2), 023601 (2012).  https://doi.org/10.1103/physrevlett.108.023601 ADSCrossRefGoogle Scholar
  15. 15.
    Kruse, R., Katzschmann, F., Christ, A., Schreiber, A., Wilhelm, S., Laiho, K., Gábris, A., Hamilton, C.S., Jex, I., Silberhorn, C.: Spatio-spectral characteristics of parametric down-conversion in waveguide arrays. New J. Phys. 15(8), 083046 (2013).  https://doi.org/10.1088/1367-2630/15/8/083046 ADSCrossRefGoogle Scholar
  16. 16.
    Daems, D., Bernard, F., Cerf, N.J., Kolobov, M.I.: Tripartite entanglement in parametric down-conversion with spatially structured pump. JOSA B 27(3), 447–451 (2010).  https://doi.org/10.1364/josab.27.000447 ADSCrossRefGoogle Scholar
  17. 17.
    Chirkin, A.S., Shutov, I.V.: On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping. JETP Lett. 86(11), 693–697 (2008).  https://doi.org/10.1134/S0021364007230014 ADSCrossRefGoogle Scholar
  18. 18.
    Chirkin, A.S., Shutov, I.V.: Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals. J. Exp. Theor. Phys. 109(4), 547–556 (2009).  https://doi.org/10.1134/S1063776109100021 ADSCrossRefGoogle Scholar
  19. 19.
    Saygin, M.Y., Chirkin, A.S.: Simultaneous parametric generation and up-conversion of entangled optical images. J. Exp. Theor. Phys. 111(1), 11–21 (2010).  https://doi.org/10.1134/S1063776110070022 ADSCrossRefGoogle Scholar
  20. 20.
    Saygin, M.Y., Chirkin, A.S.: Quantum properties of optical images in coupled nondegenerate parametric processes. Opt. Spectrosc. 110(1), 97–104 (2011).  https://doi.org/10.1134/S0030400X11010152 ADSCrossRefGoogle Scholar
  21. 21.
    Saygin, M.Y., Chirkin, A.S., Kolobov, M.I.: Quantum holographic teleportation of entangled two-color optical images. JOSA B 29(8), 2090–2098 (2012).  https://doi.org/10.1364/josab.29.002090 ADSCrossRefGoogle Scholar
  22. 22.
    Tlyachev, T.V., Chebotarev, A.M., Chirkin, A.S.: A new approach to quantum theory of multimode coupled parametric processes. Phys. Scr. T153, 014060 (2013).  https://doi.org/10.1088/0031-8949/2013/T153/014060 ADSCrossRefGoogle Scholar
  23. 23.
    Duan, D., Du, S., Xia, Y.: Multiwavelength ghost imaging. Phys. Rev. A 88(5), 053842 (2013).  https://doi.org/10.1103/physreva.88.053842 ADSCrossRefGoogle Scholar
  24. 24.
    Zhang, D.J., Li, H.G., Zhao, Q.L., Wang, S., Wang, H.B., Xiong, J., Wang, K.: Wavelength-multiplexing ghost imaging. Phys. Rev. A 92(1), 013823 (2015).  https://doi.org/10.1103/physreva.92.013823 ADSCrossRefGoogle Scholar
  25. 25.
    Shi, D., Zhang, J., Huang, J., Wang, K., Yuan, K., Cao, K., Xie, C., Liu, D., Zhu, W.: Polarization-multiplexing ghost imaging. Opt. Lasers Eng. 102, 100–105 (2018).  https://doi.org/10.1016/j.optlaseng.2017.10.022 CrossRefGoogle Scholar
  26. 26.
    Chirkin, A.S., Gostev, P.P., Agapov, D.P., Magnitskiy, S.A.: Ghost polarimetry: ghost imaging of polarization-sensitive objects. Laser Phys. Lett. 15(11), 115404 (2018).  https://doi.org/10.1088/1612-202x/aae4a6 ADSCrossRefGoogle Scholar
  27. 27.
    Morris, P.A., Aspden, R.S., Bell, J.E.C., Boyd, R.W., Padgett, M.J.: Imaging with a small number of photons. Nat. Commun. 6, 5913 (2015).  https://doi.org/10.1038/ncomms6913 ADSCrossRefGoogle Scholar
  28. 28.
    Zerom, P., Chan, K.W.C., Howell, J.C., Boyd, R.W.: Entangled-photon compressive ghost imaging. Phys. Rev. A 84(6), 061804 (2011).  https://doi.org/10.1103/physreva.84.061804 ADSCrossRefGoogle Scholar
  29. 29.
    Gong, W., Han, S.: Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints. Phys. Lett. A 376(17), 1519–1522 (2012).  https://doi.org/10.1016/j.physleta.2012.03.027 ADSCrossRefGoogle Scholar
  30. 30.
    Gong, W., Han, S.: High-resolution far-field ghost imaging via sparsity constraint. Sci. Rep. 5(1), 9280 (2015).  https://doi.org/10.1038/srep09280 ADSCrossRefGoogle Scholar
  31. 31.
    Katz, O., Bromberg, Y., Silberberg, Y.: Compressive ghost imaging. Appl. Phys. Lett. 95(13), 131110 (2009).  https://doi.org/10.1063/1.3238296 ADSCrossRefGoogle Scholar
  32. 32.
    Suchowski, H., Bruner, B.D., Israel, Y., Ganany-Padowicz, A., Arie, A., Silverberg, Y.: Broadband photon pair generation at \(3 \omega /2\). Appl. Phys. B 122(2), 25 (2016).  https://doi.org/10.1007/s00340-015-6304-9 ADSGoogle Scholar
  33. 33.
    Vyunishev, A.M., Arkhipkin, V.G., Chirkin, A.S.: Theory of second-harmonic generation in a chirped 2d nonlinear optical superlattice under nonlinear raman-nath diffraction. JOSA B 32(12), 2411–2416 (2015).  https://doi.org/10.1364/josab.32.002411 ADSCrossRefGoogle Scholar
  34. 34.
    Akhmanov, S.A., D’yakov, Y.E., Chirkin, A.S.: Introduction to Statistical Radiophysics and Optics. Nauka, Moscow (1981). [in Russian]Google Scholar
  35. 35.
    Goodman, J.W.: Introduction to Fourier Optics, 3rd edn. Roberts & Company Publishers, Englewood (2004)Google Scholar
  36. 36.
    Shi, X., Huang, X., Nan, S., Li, H., Bai, Y., Fu, X.: Image quality enhancement in low-light-level ghost imaging using modified compressive sensing method. Laser Phys. Lett. 15(4), 045204 (2018).  https://doi.org/10.1088/1612-202x/aaa5f6 ADSCrossRefGoogle Scholar
  37. 37.
    Pyt’ev, Y.P.: Methods of Mathematical Modeling of Measuring-Computing Systems, 3rd edn. Fizmatlit, Moscow (2012). [in Russian]Google Scholar
  38. 38.
    Pyt’ev, Y.P., Chulichkov, A.I.: Foundations for a theory of computer assisted superhigh resolution measurement systems. Meas. Tech. 41(2), 111–121 (1998).  https://doi.org/10.1007/BF02524537 CrossRefGoogle Scholar
  39. 39.
    Pyt’ev, Y.P.: On the problem of superresolution of blurred images. Pattern Recognit. Image Anal. 14(1), 50–59 (2004)Google Scholar
  40. 40.
    Pyt’ev, Y.P.: Measurement-computation converter as a measurement facility. Autom. Remote Control 71(2), 303–319 (2010).  https://doi.org/10.1134/s0005117910020116 MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Balakin, D.A., Pyt’ev, Y.P.: A comparative analysis of reduction quality for probabilistic and possibilistic measurement models. Moscow Univ. Phys. Bull. 72(2), 101–112 (2017).  https://doi.org/10.3103/S0027134917020047 ADSCrossRefGoogle Scholar
  42. 42.
    Solomon, O., Mutzafi, M., Segev, M., Eldar, Y.C.: Sparsity-based super-resolution microscopy from correlation information. Opt. Express 26(14), 18238–18269 (2018).  https://doi.org/10.1364/oe.26.018238 ADSCrossRefGoogle Scholar
  43. 43.
    Balakin, D.A., Pyt’ev, Y.P.: Improvement of measurement reduction in the case when the feature of interest to the researcher belongs to an a priori known convex closed set [in russian]. In: Lomonosov readings—2018. Proceedings of Physics section., pp. 155–158. M. V. Lomonosov Moscow State University. Faculty of Physics, Moscow (2018)Google Scholar
  44. 44.
    Peřina, J., Svozilík, J.: Randomly poled nonlinear crystals as a source of photon pairs. Phys. Rev. A 83(3), 033808 (2011).  https://doi.org/10.1103/physreva.83.033808 ADSCrossRefGoogle Scholar
  45. 45.
    Pelton, M., Marsden, P., Ljunggren, D., Tengner, M., Karlsson, A., Fragemann, A., Canalias, C., Laurell, F.: Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP. Opt. Express 12(15), 3573–3580 (2004).  https://doi.org/10.1364/opex.12.003573 ADSCrossRefGoogle Scholar
  46. 46.
    Du, J., Gong, W., Han, S.: The influence of sparsity property of images on ghost imaging with thermal light. Opt. Lett. 37(6), 1067–1069 (2012).  https://doi.org/10.1364/ol.37.001067 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of PhysicsM. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.The International Laser CenterM. V. Lomonosov Moscow State UniversityMoscowRussia

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