Abstract

Tracking trajectories of objects is conventionally achieved by direct beam probing or by sequential imaging of the target during its evolution. However, these strategies fail quickly when the direct line of sight is inhibited. Here, we propose and experimentally demonstrate real-time tracking of objects, which are completely surrounded by scattering media that practically conceal the objects. We show that full 3D motion can be effectively encoded in the statistical properties of spatially diffused but temporally coherent radiation. The method relies on measurements of integrated scattered intensity performed anywhere outside the disturbance region, which renders flexibility for different sensing scenarios as well as low-light capabilities.

© 2017 Optical Society of America

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References

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  1. I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  13. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
    [Crossref]
  14. 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).
    [Crossref]
  15. O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
    [Crossref]
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  20. F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
    [Crossref]
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    [Crossref]
  23. E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. 95, 193904 (2005).
    [Crossref]
  24. D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
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  25. T. W. Kohlgraf-Owens and A. Dogariu, “Transmission matrices of random media: means for spectral polarimetric measurements,” Opt. Lett. 35, 2236–2238 (2010).
    [Crossref]
  26. M. I. Akhlaghi and A. Dogariu, “Stochastic optical sensing,” Optica 3, 58–63 (2016).
    [Crossref]
  27. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [Crossref]
  28. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
    [Crossref]
  29. R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
    [Crossref]
  30. E. Baleine and A. Dogariu, “Variable coherence tomography,” Opt. Lett. 29, 1233–1235 (2004).
    [Crossref]
  31. J. Fleischer, “Imaging: making sensing of incoherence,” Nat. Photonics 10, 211–213 (2016).
    [Crossref]
  32. P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,” Signal Process. 24, 11–20 (1991).
    [Crossref]
  33. C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
    [Crossref]

2016 (2)

J. Fleischer, “Imaging: making sensing of incoherence,” Nat. Photonics 10, 211–213 (2016).
[Crossref]

M. I. Akhlaghi and A. Dogariu, “Stochastic optical sensing,” Optica 3, 58–63 (2016).
[Crossref]

2015 (3)

M. Buttafava, J. Zeman, A. Tosi, K. Eliceiri, and A. Velten, “Non-line-of-sight imaging using a time-gated single photon avalanche diode,” Opt. Express 23, 20997–21011 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

2014 (2)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

2012 (4)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

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).
[Crossref]

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, “Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging,” Nat. Commun. 3, 745 (2012).
[Crossref]

2010 (1)

2008 (2)

I. Vellekoop and A. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

2006 (1)

S. T. Acton and N. Ray, “Biomedical image analysis: tracking,” Synth. Lect. Image Video Multimedia Process. 2, 1–152 (2006).
[Crossref]

2005 (2)

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
[Crossref]

E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. 95, 193904 (2005).
[Crossref]

2004 (1)

2001 (1)

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

1996 (1)

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[Crossref]

1991 (3)

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[Crossref]

P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,” Signal Process. 24, 11–20 (1991).
[Crossref]

C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
[Crossref]

1989 (1)

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

1988 (2)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

1983 (2)

F. Daum and R. Fitzgerald, “Decoupled Kalman filters for phased array radar tracking,” IEEE Trans. Autom. Control 28, 269–283 (1983).
[Crossref]

A. T. Friberg and R. J. Sudol, “The spatial coherence properties of Gaussian Schell-model beams,” J. Mod. Opt. 30, 1075–1097 (1983).

Acton, S. T.

S. T. Acton and N. Ray, “Biomedical image analysis: tracking,” Synth. Lect. Image Video Multimedia Process. 2, 1–152 (2006).
[Crossref]

Akhlaghi, M. I.

Baleine, E.

E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. 95, 193904 (2005).
[Crossref]

E. Baleine and A. Dogariu, “Variable coherence tomography,” Opt. Lett. 29, 1233–1235 (2004).
[Crossref]

Bawendi, M. G.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, “Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging,” Nat. Commun. 3, 745 (2012).
[Crossref]

Bayley, H.

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

Berkovits, R.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Bharali, D. J.

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
[Crossref]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Buller, G. S.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Buttafava, M.

Cloude, S. R.

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[Crossref]

Comon, P.

P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,” Signal Process. 24, 11–20 (1991).
[Crossref]

Cremer, P. S.

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

Daum, F.

F. Daum and R. Fitzgerald, “Decoupled Kalman filters for phased array radar tracking,” IEEE Trans. Autom. Control 28, 269–283 (1983).
[Crossref]

Dogariu, A.

Eliceiri, K.

Faccio, D.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

Feng, S.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

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).
[Crossref]

Fitzgerald, R.

F. Daum and R. Fitzgerald, “Decoupled Kalman filters for phased array radar tracking,” IEEE Trans. Autom. Control 28, 269–283 (1983).
[Crossref]

Fleischer, J.

J. Fleischer, “Imaging: making sensing of incoherence,” Nat. Photonics 10, 211–213 (2016).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Friberg, A. T.

A. T. Friberg and R. J. Sudol, “The spatial coherence properties of Gaussian Schell-model beams,” J. Mod. Opt. 30, 1075–1097 (1983).

Gao, L.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Gariepy, G.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena (Springer, 1975), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley, 2015).

Gori, F.

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[Crossref]

Gupta, O.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, “Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging,” Nat. Commun. 3, 745 (2012).
[Crossref]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Henderson, R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

Herault, J.

P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,” Signal Process. 24, 11–20 (1991).
[Crossref]

C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
[Crossref]

Heshmat, B.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jutten, C.

C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
[Crossref]

P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,” Signal Process. 24, 11–20 (1991).
[Crossref]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

Kaur, N.

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
[Crossref]

Kaveh, M.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

Kohlgraf-Owens, T. W.

Krstajic, N.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

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).
[Crossref]

Leach, J.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Lerosey, G.

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).
[Crossref]

Li, C.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Liang, J.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Mistretta, R. A.

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
[Crossref]

Mosk, A.

I. Vellekoop and A. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

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).
[Crossref]

Ohulchanskyy, T. Y.

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
[Crossref]

Pottier, E.

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. Remote Sens. 34, 498–518 (1996).
[Crossref]

Prasad, P. N.

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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U. Wandinger, “Introduction to lidar,” in Lidar (Springer, 2005), pp. 1–18.

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A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, “Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging,” Nat. Commun. 3, 745 (2012).
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A. T. Friberg and R. J. Sudol, “The spatial coherence properties of Gaussian Schell-model beams,” J. Mod. Opt. 30, 1075–1097 (1983).

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A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, “Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging,” Nat. Commun. 3, 745 (2012).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
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G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10, 23–26 (2015).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
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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).
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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
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Opt. Lett. (2)

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I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
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I. Vellekoop and A. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
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Proc. Natl. Acad. Sci. USA (1)

I. Roy, T. Y. Ohulchanskyy, D. J. Bharali, H. E. Pudavar, R. A. Mistretta, N. Kaur, and P. N. Prasad, “Optical tracking of organically modified silica nanoparticles as DNA carriers: a nonviral, nanomedicine approach for gene delivery,” Proc. Natl. Acad. Sci. USA 102, 279–284 (2005).
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Supplementary Material (7)

NameDescription
» Supplement 1: PDF (1584 KB)      supplementary materials
» Visualization 1: MP4 (1325 KB)      video 1
» Visualization 2: MP4 (3235 KB)      video2
» Visualization 3: MP4 (6457 KB)      video 3
» Visualization 4: MP4 (18041 KB)      video 4
» Visualization 5: MP4 (3190 KB)      video 5
» Visualization 6: MP4 (10280 KB)      video 6

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Figures (8)

Fig. 1.
Fig. 1.

Tracking a hidden target enclosed in a “scattering box” that impedes direct imaging. A coherent source of radiation generates a spatially and temporally varying field that illuminates the target. Fluctuations of the integrated intensity are detected outside the enclosure and are used to track the target position.

Fig. 2.
Fig. 2.

Schematic illustration of using (a) the memory effect associated with the light propagating through the scattering wall and (b) the increase of the illumination speckle size used to encode the transversal and axial motions of the target, respectively.

Fig. 3.
Fig. 3.

(a) Image of a laser beam with beam waist of d520  μm scattered at the front and back walls of the box. The scale bar is 2.5 cm. (b) Amplitude of the autocorrelation function |Ci(τ)| of the recorded intensity corresponding to different target transversal displacements Δx. The decorrelation time (black band) depends linearly on the target transversal motion, as expected from Eq. (5). The lower left inset illustrates the linear relation between the decorrelation time and the target transversal motion. The upper right inset shows the approximately 5  mm×5  mm size object under uniform illumination.

Fig. 4.
Fig. 4.

(a) Integrated intensity variance spectrum for varying secondary source size d. The dotted red curve indicates the shift in the variance spectrum as a function of the axial motion of a target for ±2  mm. The green dot shows the optimum secondary source size d0520  μm. (b) Linear dependency of the integrated intensity variance as a function of the target axial displacement for d=d0. For clarity, all measured variances are normalized by the value of the maximum variance.

Fig. 5.
Fig. 5.

(a) Experimental demonstration of 3D tracking: the blue line represents the imposed target displacement, while the red dashed line indicates the reconstructed trajectory. (b) One-dimensional representations of the imposed and recovered trajectories shown in (a), where tm denotes one measurement duration. The solid blue line denotes the exact trajectory, while the dashed red line indicates the reconstructed trajectory. Also, see Visualization 1.

Fig. 6.
Fig. 6.

Experimental demonstration of 3D tracking using a priori calibrations to extract the constants in Eq. (7). The blue line represents the imposed target displacement, while the red dashed line indicates the reconstructed trajectory.

Fig. 7.
Fig. 7.

Evolution of the relative error ε/Δr during the tracking procedure. The error in reconstructing the target location is evaluated as ε2(t)=εx2(t)+εy2(t)+εz2(t), and Δr denotes the average step size in moving the target. The solid line and the shaded area indicate the average and the standard deviation of the error over one hundred trajectories.

Fig. 8.
Fig. 8.

Error evolution in recovering an absolute trajectory. The time variable is normalized by the measurement time tm. The error in reconstructing the target location is evaluated as ε2(t)=εx2(t)+εy2(t)+εz2(t). The solid line and the shaded area show the average and the standard deviation of errors over one hundred trajectories, respectively.

Equations (8)

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

Is(r,t)=P*(r,t)P(r,t)E*(r,t)E(r,t)G*(r,r)G(r,r)drdrα,
i(t)=Mr2VT(r,t)I(r,t)dr,
Ci(τ)=tM10tMCI(Δr(t)τΔv)CT(Δr(t))dt,
Ci(τ)(ξ/(sinh(ξ)))20tMCI(Δr(t))CT(Δr(t))dt.
τi|vIvT|1vI1(1+vT,vI),
σi2=Ci(0)0tMCI(Δr(t))CT(Δr(t))dt,
ρ=aρξ+bρ,
Δρm/Δρ0=Δξm/Δξ0,

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