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Transmission Matrix Noise Elimination for an Optical Disordered Medium

  • Wang, Lin (School of Electronic and Optical Engineering, Nanjing University of Science and Technology) ;
  • Li, Yangyan (School of Electronic and Optical Engineering, Nanjing University of Science and Technology) ;
  • Xin, Yu (School of Electronic and Optical Engineering, Nanjing University of Science and Technology) ;
  • Wang, Jue (College of Electrical, Energy and Power Engineering, Yangzhou University) ;
  • Chen, Yanru (School of Electronic and Optical Engineering, Nanjing University of Science and Technology)
  • Received : 2019.08.20
  • Accepted : 2019.10.18
  • Published : 2019.12.25

Abstract

We propose a method to eliminate the noise of a disordered medium optical transmission matrix. Gaussian noise exists whenever light passes through the medium, during the measurement of the transmission matrix and thus cannot be ignored. Experiments and comparison of noise eliminating before and after are performed to illustrate the effectiveness and advance presented by our method. After noise elimination, the results of focusing and imaging are better than the effect before noise elimination, and the measurement of the transmission matrix is more consistent with the theoretical analysis as well.

Keywords

References

  1. A. Ishimaru, Wave propagation and scattering in random media (Academic Press, New York, USA, 1978), Vol. 2.
  2. M. Kerker, The scattering of light and other electromagnetic radiation: physical chemistry: a series of monographs (Academic Press, New York, USA, 2013), Vol. 16, pp. 189-254.
  3. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492 (1958). https://doi.org/10.1103/PhysRev.109.1492
  4. M. Cui and C. Yang, "Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation," Opt. Express 18, 3444-3455 (2010). https://doi.org/10.1364/OE.18.003444
  5. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, "Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media," Phys. Rev. Lett. 104, 100601 (2010). https://doi.org/10.1103/PhysRevLett.104.100601
  6. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, "Maximal energy transport through disordered media with the implementation of transmission eigenchannels," Nat. Photonics 6, 581-585 (2012). https://doi.org/10.1038/nphoton.2012.159
  7. I. M. Vellekoop and A. P. Mosk, "Focusing coherent light through opaque strongly scattering media," Opt. Lett. 32, 2309-2311 (2007). https://doi.org/10.1364/OL.32.002309
  8. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, "Controlling waves in space and time for imaging and focusing in complex media," Nat. Photonics 6, 283-292 (2012). https://doi.org/10.1038/nphoton.2012.88
  9. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, "Spatial confinement of laser light in active random media," Phys. Rev. Lett. 84, 5584 (2000). https://doi.org/10.1103/PhysRevLett.84.5584
  10. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, "Overcoming the diffraction limit using multiple light scattering in a highly disordered medium," Phys. Rev. Lett. 107, 023902 (2011). https://doi.org/10.1103/PhysRevLett.107.023902
  11. Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, "Polarization control of multiply scattered light through random media by wavefront shaping," Opt. Lett. 37, 4663-4665 (2012). https://doi.org/10.1364/OL.37.004663
  12. A. Dremeau, A. Liutkus, D. Martina, O. Katz, C. Schulke, F. Krzakala, S. Gigan, and L. Daudet, "Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques," Opt. Express 23, 11898-11911 (2015). https://doi.org/10.1364/OE.23.011898
  13. X. Tao, D. Bodington, M. Reinig, and J. Kubby, "High-speed scanning interferometric focusing by fast measurement of binary transmission matrix for channel demixing," Opt. Express 23, 14168-14187 (2015). https://doi.org/10.1364/OE.23.014168
  14. A. A. Farid and S. Hranilovic, "Capacity bounds for wireless optical intensity channels with gaussian noise," IEEE Trans. Inf. Theory 56, 6066-6077 (2010). https://doi.org/10.1109/TIT.2010.2080470
  15. J. Brenner and L. Cummings, "The hadamard maximum determinant problem," Am. Math. Mon. 79, 626-630 (1972). https://doi.org/10.2307/2317092
  16. W. K. Pratt, J. Kane, and H. C. Andrews, "Hadamard transform image coding," Proc. IEEE 57, 58-68 (1969). https://doi.org/10.1109/PROC.1969.6869
  17. J. A. Tropp, "Improved analysis of the subsampled randomized hadamard transform," Adv. Adapt. Data Anal. 3, 115-126 (2011). https://doi.org/10.1142/S1793536911000787
  18. N. J. A. Sloane and M. Harwit, "Masks for hadamard transform optics, and weighing designs," Appl. Opt. 15, 107-114 (1976). https://doi.org/10.1364/AO.15.000107
  19. J. Schwider, O. R. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1886 (1993). https://doi.org/10.1117/12.143340
  20. P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987). https://doi.org/10.1364/AO.26.002504
  21. P. Hariharan, "Phase-shifting interferometry: minimization of systematic errors," Opt. Eng. 39, 967-969 (2000). https://doi.org/10.1117/1.602443
  22. M. Jang, H. Ruan, I. M. Vellekoop, B. Judkewitz, E. Chung, and C. Yang, "Relation between speckle decorrelation and optical phase conjugation (OPC)-based turbidity suppression through dynamic scattering media: a study on in vivo mouse skin," Biomed. Opt. Express 6, 72-85 (2015). https://doi.org/10.1364/BOE.6.000072
  23. D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, "Focusing through dynamic tissue with millisecond digital optical phase conjugation," Optica 2, 728-735 (2015). https://doi.org/10.1364/OPTICA.2.000728
  24. J. Park, C. Park, K. Lee, Y.-H. Cho, and Y. Park, "Timereversing a monochromatic subwavelength optical focus by optical phase conjugation of multiply-scattered light," Sci. Rep. 7, 41384 (2017). https://doi.org/10.1038/srep41384
  25. Y. Shen, Y. Liu, C. Ma, and L. V. Wang, "Focusing light through scattering media by full-polarization digital optical phase conjugation," Opt. Lett. 41, 1130-1133 (2016). https://doi.org/10.1364/OL.41.001130
  26. V. Bacot, M. Labousse, A. Eddi, M. Fink, and E. Fort, "Time reversal and holography with spacetime transformations," Nat. Phys. 12, 972-977 (2016). https://doi.org/10.1038/nphys3810
  27. A. E. Fouda and F. L. Teixeira, "Statistical stability of ultrawideband time-reversal imaging in random media," IEEE Trans. Geosci. Remote Sens. 52, 870-879 (2014). https://doi.org/10.1109/TGRS.2013.2245137
  28. A. Edelman and N. R. Rao, "Random matrix theory," Acta Numerica. 14, 233-297 (2005). https://doi.org/10.1017/S0962492904000236
  29. V. A. Marcenko and L. A. Pastur, "Distribution of eigenvalues for some sets of random matrices," Math. USSR-Sbornik 1, 457 (1967). https://doi.org/10.1070/SM1967v001n04ABEH001994
  30. C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, "Correlation-enhanced control of wave focusing in disordered media," Nat. Phys. 13, 497-502 (2017). https://doi.org/10.1038/nphys4036