Abstract

Imaging through complex media is a well-known challenge, as scattering distorts a signal and invalidates imaging equations. For coherent imaging, the input field can be reconstructed using phase conjugation or knowledge of the complex transmission matrix. However, for incoherent light, wave interference methods are limited to small viewing angles. On the other hand, time-resolved methods do not rely on signal or object phase correlations, making them suitable for reconstructing wide-angle, larger-scale objects. Previously, a time-resolved technique was demonstrated for uniformly reflecting objects. Here, we generalize the technique to reconstruct the spatially varying reflectance of shapes hidden by angle-dependent diffuse layers. The technique is a noninvasive method of imaging three-dimensional objects without relying on coherence. For a given diffuser, ultrafast measurements are used in a convex optimization program to reconstruct a wide-angle, three-dimensional reflectance function. The method has potential use for biological imaging and material characterization.

© 2014 Optical Society of America

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2013 (3)

S. S. Gorthi, D. Schaak, and E. Schonbrun, “Fluorescence imaging of flowing cells using a temporally coded excitation,” Opt. Express 21, 5164–5170 (2013).
[CrossRef]

K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
[CrossRef]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[CrossRef]

2012 (8)

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (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]

O. Gupta, T. Willwacher, A. Velten, A. Veeraraghavan, and R. Raskar, “Reconstruction of hidden 3D shapes using diffuse reflections,” Opt. Express 20, 19096–19108 (2012).
[CrossRef]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

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[CrossRef]

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (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]

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]

2011 (4)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[CrossRef]

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (2011).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

N. Naik, S. Zhao, A. Velten, R. Raskar, and K. Bala, “Single view reflectance capture using multiplexed scattering and time-of-flight imaging,” ACM Trans. Graph. 30, 171 (2011).
[CrossRef]

2010 (6)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35, 1245–1247 (2010).
[CrossRef]

C. L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
[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]

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

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

2008 (2)

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[CrossRef]

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27, 1152–1163 (2008).
[CrossRef]

2007 (1)

2006 (2)

E. Betzig, G. H. Patterson, R. Sougrat, O. Wolf Lindwasser, S. Olenych, J. S. Bonifacine, M. W. Davidson, J. Libbincot-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy,” Nat. Methods 3, 793–796 (2006).
[CrossRef]

2005 (1)

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745–755 (2005).
[CrossRef]

1999 (1)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

1997 (1)

1991 (3)

I. Freund, “Image reconstruction through multiple scattering media,” Opt. Commun. 86, 216–227 (1991).
[CrossRef]

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

1990 (1)

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[CrossRef]

1988 (2)

S. Fend, C. Kane, A. Lee, and D. A. 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]

’t Hooft, G. W.

Adam, J.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
[CrossRef]

Aegerter, C. M.

Alfano, R. R.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef]

Andalman, A. S.

K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
[CrossRef]

Ayazi, A.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
[CrossRef]

Bacskai, B. J.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27, 1152–1163 (2008).
[CrossRef]

Bala, K.

N. Naik, S. Zhao, A. Velten, R. Raskar, and K. Bala, “Single view reflectance capture using multiplexed scattering and time-of-flight imaging,” ACM Trans. Graph. 30, 171 (2011).
[CrossRef]

Barsi, C.

D. Wu, G. Wetzstein, C. Barsi, T. Willwacher, Q. Dai, and R. Raskar, “Ultra-fast lensless computational imaging through 5D frequency analysis of time-resolved light transport,” Int. J. Comput. Vis., doi: 10.1007/s11263-013-0686-0 (in press).
[CrossRef]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy,” Nat. Methods 3, 793–796 (2006).
[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]

Bernstein, H.

K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
[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]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. Wolf Lindwasser, S. Olenych, J. S. Bonifacine, M. W. Davidson, J. Libbincot-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[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]

Boas, D. A.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27, 1152–1163 (2008).
[CrossRef]

Boccara, A. C.

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]

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

Bonifacine, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. Wolf Lindwasser, S. Olenych, J. S. Bonifacine, M. W. Davidson, J. Libbincot-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef]

Brackbill, N.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
[CrossRef]

Bromberg, Y.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

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]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Chen, B.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745–755 (2005).
[CrossRef]

Chung, K.

K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
[CrossRef]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

Colak, S. B.

Cui, M.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

Dai, Q.

D. Wu, G. Wetzstein, C. Barsi, T. Willwacher, Q. Dai, and R. Raskar, “Ultra-fast lensless computational imaging through 5D frequency analysis of time-resolved light transport,” Int. J. Comput. Vis., doi: 10.1007/s11263-013-0686-0 (in press).
[CrossRef]

Dana, H.

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D. Wu, G. Wetzstein, C. Barsi, T. Willwacher, Q. Dai, and R. Raskar, “Ultra-fast lensless computational imaging through 5D frequency analysis of time-resolved light transport,” Int. J. Comput. Vis., doi: 10.1007/s11263-013-0686-0 (in press).
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A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27, 1152–1163 (2008).
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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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Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy,” Nat. Methods 3, 793–796 (2006).
[CrossRef]

Sadasivam, J.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
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Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

Schomberg, H.

Schonbrun, E.

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D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Segev, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
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P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745–755 (2005).
[CrossRef]

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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
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K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
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D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
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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. 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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K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
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X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[CrossRef]

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Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
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J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
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X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
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Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
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[CrossRef]

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Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[CrossRef]

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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
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K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
[CrossRef]

Zhang, G.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef]

Zhao, S.

N. Naik, S. Zhao, A. Velten, R. Raskar, and K. Bala, “Single view reflectance capture using multiplexed scattering and time-of-flight imaging,” ACM Trans. Graph. 30, 171 (2011).
[CrossRef]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy,” Nat. Methods 3, 793–796 (2006).
[CrossRef]

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

ACM Trans. Graph. (2)

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745–755 (2005).
[CrossRef]

N. Naik, S. Zhao, A. Velten, R. Raskar, and K. Bala, “Single view reflectance capture using multiplexed scattering and time-of-flight imaging,” ACM Trans. Graph. 30, 171 (2011).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Med. Imaging (1)

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27, 1152–1163 (2008).
[CrossRef]

J. Biomed. Opt. (1)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

Nat. Commun. (3)

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]

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[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]

Nat. Mater. (1)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[CrossRef]

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy,” Nat. Methods 3, 793–796 (2006).
[CrossRef]

Nat. Photonics (8)

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[CrossRef]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[CrossRef]

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[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]

Nature (2)

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]

K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, “Structural and molecular interrogation of intact biological systems,” Nature 497, 332–337 (2013).
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Opt. Commun. (1)

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Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

S. Fend, C. Kane, A. Lee, and D. A. 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).
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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).
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Physica A (1)

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Proc. Natl. Acad. Sci. USA (1)

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. USA 109, 11630–11635 (2012).
[CrossRef]

Science (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. Wolf Lindwasser, S. Olenych, J. S. Bonifacine, M. W. Davidson, J. Libbincot-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef]

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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G. W. Kamerman, The Infrared and Electro-Optical System Handbook (SPIE, 1993).

D. Wu, G. Wetzstein, C. Barsi, T. Willwacher, Q. Dai, and R. Raskar, “Ultra-fast lensless computational imaging through 5D frequency analysis of time-resolved light transport,” Int. J. Comput. Vis., doi: 10.1007/s11263-013-0686-0 (in press).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Experimental setup. Pulses from a Ti:sapphire laser are focused onto a ground glass diffuser. The scattered light strikes a three-dimensional scene (here, a collection of point objects Pj) and is scattered back through the diffuser, which is imaged onto a streak camera. A streak image is recorded for 16 different laser positions incident on the diffuser (top left inset). The streak camera has a one-dimensional aperture and records the time profile of a horizontal line (dotted green line) of the diffuser. Bottom right inset: a simulated streak image for the point cluster. Sample pixels A, B, and C record the time profile of every Pj at those positions. Scale: 20 mm (horizontal), 100 ps (vertical).

Fig. 2.
Fig. 2.

Ray optics model for simulating image formation. The model uses the angles and distances of the relevant scene for each object point x.

Fig. 3.
Fig. 3.

(a) Top, experimentally measured streak image for a single incident laser position and single object point for a ground glass diffuser. Bottom, same as above with the ground glass diffuser replaced by a multiple scattering paper sheet. Scale bars: 100 ps, 20 mm. Color scale same as in Fig. 1 inset. (b) Error map showing the calculated optimal diffuser parameters. We use convex optimization to minimize the mean normalized l2 error between simulation and captured data, and obtain the central direction (μ) and scattering width (σ) of the Gaussian. This error plot shows different errors for Gaussian parameters with the minimum marked by a white cross, for μ=0.48° and σ=8.33°, both comparable with the expected specifications.

Fig. 4.
Fig. 4.

Reconstruction errors in algorithm due to incorrect characterization of diffuser. Top row, reconstructed streak of a single white patch. Bottom row, error map for (a) σ=1.8°, (b) σ=8.8°, and (c) σ=15.8°. Color scale same as in Fig. 1 inset.

Fig. 5.
Fig. 5.

Validation of model and reconstruction algorithm. (a) Streak data for single patch rotated at an increasing angle relative to the diffuser normal. Color scale same as in Fig. 1 inset. (b) Mean percent error between the captured data and forward simulation is low across a 60° range. Scale bars: 50 mm (horizontal), 200 ps (vertical).

Fig. 6.
Fig. 6.

Validation of model and reconstruction algorithm. (a) Streak data for two patches with increasing separation Δx (in mm). Color scale same as in Fig. 1 inset. (b) Reflectance is reconstructed successfully for separation up to 125 mm. The error in reflectance estimation is random and arises due to background noise and calibration errors. Scale bars: 50 mm (horizontal), 200 ps (vertical). Color map same as in Fig. 1 inset.

Fig. 7.
Fig. 7.

Our geometric-optics-based model accurately simulates the streak image formation. The first column shows streak images captured for different θ using the configuration described in Fig. 4(a). The second column shows the pixel-wise percent error between the measured and computed intensity. Pixels with intensity below an absolute threshold (1% of maximum intensity) are set to zero, to avoid background noise. Scale bars: 25 mm (horizontal), 24 ps (vertical).

Fig. 8.
Fig. 8.

Reconstruction of a complex scene. (a) Experimental setup of scene. (b) Streak data for four different incident laser positions (spatial configuration as seen in Fig. 1). Inset: frontal view of occluded scene with white light illumination. Occluded objects are not visible to the naked eye. Scale bars: 50 mm (horizontal), 200 ps (vertical). Color scale for (b) same as in Fig. 1 inset.

Fig. 9.
Fig. 9.

Reconstruction of a complex scene. (a) Depth map of scene in Fig. 8, which is 110 mm wide with total depth variation 13 mm. (b) Comparison of reconstructed (blue circles) and ground truth (red squares) reflectances. (c) Ground truth and (d) reconstructed reflectance maps. Scale bars: 15 mm.

Fig. 10.
Fig. 10.

Reflectance reconstruction for the scene in Fig. 8, simulating different time resolutions.

Fig. 11.
Fig. 11.

Our approach is robust to small geometry errors. We can solve jointly for both reflectance and geometry to obtain accurate reconstruction given incorrect geometry.

Fig. 12.
Fig. 12.

Our reconstruction algorithm is robust to the presence of additional erroneous patches. We correctly reconstruct the reflectance of six original patches, while solving for ten patches in total. (a) Depth map, with artificial patches highlighted with a dotted square. (c) and (d) are the ground truth and recovered reflectance values. Scale bar: 15 mm. (b) Corresponding reconstructed reflectance values. Note that artificial patches reconstruct a reflectance value of zero.

Tables (1)

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Table 1. Reflectance Reconstruction Using Time Resolutions in Fig. 10 Becomes Worse with Poorer Time Resolution

Equations (4)

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Il(x,t)=I0g(xl,x,x)R(x)δ(ct(rl(x)+rc(x)))dx,
g(xl,x,x)=cos(ζ(xl))N(θin)cos(γ(x))cos(β(x))cos(α(x))π2rl2(x)rc2(x)N(θout),
arg minR(x),N(·)1Ll=1LI^lmeasκlI^lnum2,for0R(x)1.
Il(x,t)I0g(xl,x,x0)δ((ct(rl(x0))rc(x0))).

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