Abstract

We experimentally demonstrate the use of the transmission matrix (TM) to quantitatively control the amplitude and phase of the light transmitted through highly scattering media. This is achieved by measuring the absolute value of the TM elements. We also use the fact that the cross-correlations between the contributions of different input channels at the observation plane is important in describing the transmitted optical field. In addition, we demonstrate both quantitative control of the intensity at multiple output spatial modes, each with a different intensity, as well as a “dark” area of low intensity. Our experiments are carried out using a low cost (less than US$600) spatial binary amplitude modulator that we modify for phase-only operation, as well as a novel optical setup that enables independent control of a reference and control signal while maintaining interferometric stability. The optical implementation used in this paper will make such experiments widely accessible to many researchers. Furthermore, the results presented could serve as the foundation for many useful potential applications ranging from the biomedical sciences to optical communications.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32, 2309–2311 (2007).
    [CrossRef] [PubMed]
  2. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered meta-materials,” Opt. Express16, 67–80 (2008).
    [CrossRef] [PubMed]
  3. 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).
    [CrossRef] [PubMed]
  4. D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express20, 1733–1740 (2012).
    [CrossRef] [PubMed]
  5. S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express20, 16067–16076 (2012).
    [CrossRef] [PubMed]
  6. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, 2007).
  7. A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
    [CrossRef]
  8. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
    [CrossRef]
  9. S. Tripathi and K. C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express20, 10788–10795 (2012).
    [CrossRef] [PubMed]
  10. Q. Zhan, “Cylindrical vector beams: From mathematical concepts to applications,” Adv. Opt. Photon.1, 1–57 (2009).
    [CrossRef]
  11. S. Tripathi, B. J. Davis, K. C. Toussaint, and P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B: At. Mol. Opt. Phys.44, 015401 (2011).
    [CrossRef]
  12. S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
    [CrossRef]
  13. S. Tripathi and K. C. Toussaint, “Rapid Mueller matrix polarimetry based on parallelized polarization state generation and detection,” Opt. Express17, 21396–21407 (2009).
    [CrossRef] [PubMed]
  14. Texas Instruments, DLP®LightCrafterTMEvaluation Module (EVM): User’s Guide(2013).
  15. W. H. Lee, “Binary synthetic holograms,” Appl. Optics13, 1677–1682 (1974).
    [CrossRef]
  16. S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
    [CrossRef]
  17. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2007).
  18. R. H. Byrd, J. Nocedal, and R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in “Large Scale Nonlinear Optimization,”, G. D. Pillo and F. Giannessi, eds. (Springer Verlag, 2006), pp. 35–59.
    [CrossRef]
  19. L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
    [CrossRef]
  20. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
    [CrossRef] [PubMed]
  21. D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express20, 27312–27318 (2012).
    [CrossRef] [PubMed]

2013 (1)

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

2012 (4)

2011 (3)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

S. Tripathi, B. J. Davis, K. C. Toussaint, and P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B: At. Mol. Opt. Phys.44, 015401 (2011).
[CrossRef]

2010 (2)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (1)

1990 (1)

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
[CrossRef]

1974 (1)

W. H. Lee, “Binary synthetic holograms,” Appl. Optics13, 1677–1682 (1974).
[CrossRef]

Bezdetnaya, L.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Bifano, T.

Bina, M.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Boccara, A. C.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Bressenot, A.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Byrd, R. H.

R. H. Byrd, J. Nocedal, and R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in “Large Scale Nonlinear Optimization,”, G. D. Pillo and F. Giannessi, eds. (Springer Verlag, 2006), pp. 35–59.
[CrossRef]

Caravaca-Aguirre, A. M.

Carminati, R.

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).
[CrossRef] [PubMed]

Carney, P. S.

S. Tripathi, B. J. Davis, K. C. Toussaint, and P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B: At. Mol. Opt. Phys.44, 015401 (2011).
[CrossRef]

Cerchiari, G.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Conkey, D. B.

D’Hallewin, M. A.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Davis, B. J.

S. Tripathi, B. J. Davis, K. C. Toussaint, and P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B: At. Mol. Opt. Phys.44, 015401 (2011).
[CrossRef]

Escobedo-Sanchez, M. A.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Ferri, F.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Fink, M.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Ford, D. H.

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
[CrossRef]

Francois, A.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Gigan, S.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

Guillemin, F.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

Kimura, W. D.

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
[CrossRef]

Lagendijk, A.

Lee, W. H.

W. H. Lee, “Binary synthetic holograms,” Appl. Optics13, 1677–1682 (1974).
[CrossRef]

Lerosey, G.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Mosk, A. P.

Nocedal, J.

R. H. Byrd, J. Nocedal, and R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in “Large Scale Nonlinear Optimization,”, G. D. Pillo and F. Giannessi, eds. (Springer Verlag, 2006), pp. 35–59.
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

Paxman, R.

Piestun, R.

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

Popoff, S. M.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

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).
[CrossRef] [PubMed]

Rojas, L. F.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, 2007).

Salvadori, A.

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Scheffold, F.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, 2007).

Tidwell, S. C.

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
[CrossRef]

Toussaint, K. C.

Tripathi, S.

van Putten, E. G.

Vellekoop, I. M.

Waltz, R. A.

R. H. Byrd, J. Nocedal, and R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in “Large Scale Nonlinear Optimization,”, G. D. Pillo and F. Giannessi, eds. (Springer Verlag, 2006), pp. 35–59.
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

Zhan, Q.

Adv. Opt. Photon. (1)

Appl. Optics (2)

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Optics29, 2234–2239 (1990).
[CrossRef]

W. H. Lee, “Binary synthetic holograms,” Appl. Optics13, 1677–1682 (1974).
[CrossRef]

Eur. Phys. J: Spec. Top. (1)

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo-Sanchez, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J: Spec. Top.199, 167–180 (2011).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

S. Tripathi, B. J. Davis, K. C. Toussaint, and P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B: At. Mol. Opt. Phys.44, 015401 (2011).
[CrossRef]

J. Urology (1)

A. Francois, A. Salvadori, A. Bressenot, L. Bezdetnaya, F. Guillemin, and M. A. D’Hallewin, “How to avoid local side effects of bladder photodynamic therapy: Impact of the fluence rate,” J. Urology190, 731–736 (2013).
[CrossRef]

Nat. Commun. (1)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun.1, 81 (2010).
[CrossRef] [PubMed]

New J. Phys. (1)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: Transmission matrix approach,” New J. Phys.13, 123021 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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).
[CrossRef] [PubMed]

Other (5)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, 2007).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

Texas Instruments, DLP®LightCrafterTMEvaluation Module (EVM): User’s Guide(2013).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

R. H. Byrd, J. Nocedal, and R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in “Large Scale Nonlinear Optimization,”, G. D. Pillo and F. Giannessi, eds. (Springer Verlag, 2006), pp. 35–59.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Hologram in (a) generates both the reference and control signals whereas those in (b) and (c) generate a control signal and the reference signal, respectively.

Fig. 3
Fig. 3

The experimentally measured magnitude of the cross-correlation between the control signal corresponding to each Hadamard basis input and the reference signal at an observation region.

Fig. 4
Fig. 4

Experimentally observed intensities versus the targeted intensities. The red line represents the ideal results when observed and targeted intensities are equal. The inset shows example intensity distributions in each area (shown by a black square) where the intensity is controlled. The intensity distributions are shown for the targeted intensities of 10 to 250 in steps of 30 in images i to ix, respectively.

Fig. 5
Fig. 5

Quantitative control of intensity at multiple points: in (a) we optimize for the right region to be brighter whereas in (b) the left area is tuned to be brighter.

Fig. 6
Fig. 6

Experimental demonstration of the ability to generate extended low intensity areas. The area under control is demarcated by a white rectangle.

Fig. 7
Fig. 7

Experimentally observed phase values versus the targeted phase values for a constant targeted intensity of 190 DN. The red line shows ideal results when the observed and targeted phase values are equal.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

f ( x , y ) = { 1 if cos { g ( x , y ) + 2 π x T } > cos ( π q ) 0 Otherwise ,
t n , m S = | g n m | I n , m C I n , m R e i φ n , m ,
t n , m = | g n m | I n , m C e i φ n , m ,
| g n m | = | t n , m | / I n , m C .
I n , m = I n , m C + I n , m R + 2 I n , m C I n , m R | g n m | cos ( φ n , m + α ) ;
Minimize ϕ m k = k 1 , k 2 , , k N ( | I k P | 2 I k D ) 2 ,
I k P = m | T k , m | 2 + m m , m m | g m , m k | | T k , m | 2 | T k , m | 2 cos ( δ m , m k ) ,
u k P = m T k , m e i ϕ m .
Minimize ϕ m ( I k P I k D ) 2 subject to u k P = ϕ n D .

Metrics