Abstract

The efficiency of using intensity modulated light for the estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric is defined to quantify the efficiency of ballistic photon filtering which may be sought when imaging through turbid media. The analytical derivation of this metric shows that the minimum modulation frequency required to attain significant ballistic discrimination depends only on the reduced scattering coefficient of the medium in a linear fashion for a highly scattering medium.

© 2016 Optical Society of America

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2016 (2)

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

M. Ghijsen, B. Choi, A. Durkin, S. Gioux, and B. Tromberg, “Real-time simultaneous single snapshot of optical properties and blood flow using coherent spatial frequency domain imaging (cSFDI),” Biomed. Opt. Express 7, 870–882 (2016).
[Crossref] [PubMed]

2011 (2)

D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express 19, 1866–1883 (2011).
[Crossref] [PubMed]

F. Mufti and R. Mahony, “Statistical analysis of signal measurement in time-of-flight cameras,” ISPRS J. Photogramm. 66, 720–731 (2011).
[Crossref]

2008 (2)

2007 (2)

2004 (1)

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

2003 (1)

2002 (1)

G. Strangman, D. A. Boas, and J. P. Sutton, “Non-invasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679–693 (2002).
[Crossref] [PubMed]

2001 (2)

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Elect. 37, 390–397 (2001).
[Crossref]

2000 (1)

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

1999 (2)

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[Crossref]

1998 (1)

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[Crossref]

1997 (2)

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587 (1997).
[Crossref] [PubMed]

1996 (3)

1995 (2)

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[Crossref] [PubMed]

M. Brewster and Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Tran. 38, 2569–2581 (1995).
[Crossref]

1994 (1)

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref] [PubMed]

1993 (4)

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A. 10, 127–140 (1993).
[Crossref] [PubMed]

D. A. Benaron and D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[Crossref] [PubMed]

R. Berg, O. Jarlman, and S. Svanberg, “Medical transillumination imaging using short-pulse diode lasers,” Appl. Opt. 32, 574 (1993).
[Crossref] [PubMed]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607 (1993).
[Crossref] [PubMed]

1991 (1)

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] [PubMed]

1989 (2)

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[Crossref] [PubMed]

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] [PubMed]

Alouini, M.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[Crossref]

Aubert, D.

N. Hautiere, J. P. Tarel, and D. Aubert, “Towards Fog-Free In-Vehicle Vision Systems through Contrast Restoration,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Barbieri, B.

Benaron, D. A.

D. A. Benaron and D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[Crossref] [PubMed]

Berg, R.

Berrocal, E.

Beuthan, J.

Boas, D.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Boas, D. A.

G. Strangman, D. A. Boas, and J. P. Sutton, “Non-invasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679–693 (2002).
[Crossref] [PubMed]

Bretenaker, F.

Brewster, M.

M. Brewster and Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Tran. 38, 2569–2581 (1995).
[Crossref]

Brooks, D.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Butler, J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Cerussi, A.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Chance, B.

Choi, B.

Christofferson, J.

Colak, S. B.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

Concannon, B.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Contini, D.

Cubeddu, R.

CuQlock-Knopp, V. G.

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

D’Amico, E.

DiMarzio, C.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Durkin, A.

Emile, O.

Eriksson, B.

Espinoza, J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Fabiani, M.

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

Fade, J.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Fantini, S.

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

J. B. Fishkin, S. Fantini, M. J. vande Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: Theory and experiments,” Phys. Rev. E 53, 2307–2319 (1996).
[Crossref]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steadystate diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4) (1992).
[Crossref] [PubMed]

Farsiu, S.

Fishkin, J. B.

J. B. Fishkin, S. Fantini, M. J. vande Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: Theory and experiments,” Phys. Rev. E 53, 2307–2319 (1996).
[Crossref]

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A. 10, 127–140 (1993).
[Crossref] [PubMed]

Floch, A. L.

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

Franceschini, M. a.

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

Friedlander, B.

Garthwaite, P. H.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Oxford University, 2002).

Gaudette, R.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Ghijsen, M.

Gioux, S.

Gratton, E.

V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2717–2729 (2003).
[Crossref] [PubMed]

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

J. B. Fishkin, S. Fantini, M. J. vande Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: Theory and experiments,” Phys. Rev. E 53, 2307–2319 (1996).
[Crossref]

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A. 10, 127–140 (1993).
[Crossref] [PubMed]

Gratton, G.

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

Gu, X.

Haskell, R. C.

Hautiere, N.

N. Hautiere, J. P. Tarel, and D. Aubert, “Towards Fog-Free In-Vehicle Vision Systems through Contrast Restoration,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Hielscher, A. H.

Ho, P. P.

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] [PubMed]

Hooft, G. W.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

Hoogenraad, J. H.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

Hueber, D.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley, 1999).
[Crossref]

Jacques, S. L.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

Jarlman, O.

Jiang, H.

Jolliffe, I. T.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Oxford University, 2002).

Jones, B.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Oxford University, 2002).

Jordan, J. B.

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

Karpel, N.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (CVPR IEEE2004) pp. I-536–I-543 Vol. 1.

Katsev, I. L.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Kilmer, M.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Kim, H. K.

Kuijpers, F. A.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

Lange, R.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Elect. 37, 390–397 (2001).
[Crossref]

Lanning, R.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Laux, A.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Linne, M.

Liu, C.

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] [PubMed]

Mahony, R.

F. Mufti and R. Mahony, “Statistical analysis of signal measurement in time-of-flight cameras,” ISPRS J. Photogramm. 66, 720–731 (2011).
[Crossref]

Martelli, F.

Mathew, J.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Merritt, J. O.

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

Milanfar, P.

Miller, E.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Mufti, F.

F. Mufti and R. Mahony, “Statistical analysis of signal measurement in time-of-flight cameras,” ISPRS J. Photogramm. 66, 720–731 (2011).
[Crossref]

Mullen, L.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Narayanan, A.

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[Crossref]

Netz, U. J.

Nowak, R.

Osterberg, U. L.

Panigrahi, S.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Patterson, M. S.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[Crossref] [PubMed]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steadystate diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4) (1992).
[Crossref] [PubMed]

Paulsen, K. D.

Pham, T.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Pifferi, A.

Pogue, B. W.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref] [PubMed]

Prikhach, A. S.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Ramachandran, H.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[Crossref]

Ren, K.

Schechner, Y. Y.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (CVPR IEEE2004) pp. I-536–I-543 Vol. 1.

Sedarsky, D.

Seitz, P.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Elect. 37, 390–397 (2001).
[Crossref]

Shah, N.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Shakouri, A.

Stevenson, D. K.

D. A. Benaron and D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[Crossref] [PubMed]

Strangman, G.

G. Strangman, D. A. Boas, and J. P. Sutton, “Non-invasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679–693 (2002).
[Crossref] [PubMed]

Sudarsanam, S.

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Sutton, J. P.

G. Strangman, D. A. Boas, and J. P. Sutton, “Non-invasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679–693 (2002).
[Crossref] [PubMed]

Svaasand, L.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Svaasand, L. O.

Svanberg, S.

Tarel, J. P.

N. Hautiere, J. P. Tarel, and D. Aubert, “Towards Fog-Free In-Vehicle Vision Systems through Contrast Restoration,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Taroni, P.

Tofsted, D. H.

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

Toronov, V.

Torricelli, A.

Tromberg, B.

Tromberg, B. J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607 (1993).
[Crossref] [PubMed]

Tsay, T.-T.

Valentini, G.

Van Der Linden, E. S.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

Van DerMark, M. B.

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

vande Ven, M. J.

J. B. Fishkin, S. Fantini, M. J. vande Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: Theory and experiments,” Phys. Rev. E 53, 2307–2319 (1996).
[Crossref]

Wang, L.

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] [PubMed]

Wang, L. V.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Watkins, W. R.

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

Webb, A.

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steadystate diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4) (1992).
[Crossref] [PubMed]

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[Crossref] [PubMed]

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

Yamada, Y.

M. Brewster and Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Tran. 38, 2569–2581 (1995).
[Crossref]

Zaccanti, G.

Zege, E. P.

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[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] [PubMed]

Zhang, Q.

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

Appl. Opt. (7)

Appl. Optics (1)

L. Mullen, A. Laux, B. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Optics 43, 3874–3892 (2004).
[Crossref]

Biol. Psychiat. (1)

G. Strangman, D. A. Boas, and J. P. Sutton, “Non-invasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679–693 (2002).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

IEEE J. Quantum Elect. (1)

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Elect. 37, 390–397 (2001).
[Crossref]

IEEE J. Sel. Top. Quant. (1)

S. B. Colak, M. B. Van DerMark, G. W. Hooft, J. H. Hoogenraad, E. S. Van Der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quant. 5, 1143–1158 (1999).
[Crossref]

IEEE Signal Proc. Mag. (1)

D. Boas, D. Brooks, E. Miller, C. DiMarzio, M. Kilmer, R. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Proc. Mag. 18, 57–75 (2001).
[Crossref]

IEEE T. Biomed Eng. (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE T. Biomed Eng. 36, 1162–1168 (1989).
[Crossref]

Int. J. Heat Mass Tran. (1)

M. Brewster and Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Tran. 38, 2569–2581 (1995).
[Crossref]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[Crossref]

ISPRS J. Photogramm. (1)

F. Mufti and R. Mahony, “Statistical analysis of signal measurement in time-of-flight cameras,” ISPRS J. Photogramm. 66, 720–731 (2011).
[Crossref]

J. Biomed. Opt. (1)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

J. Opt. Soc. Am. A. (1)

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A. 10, 127–140 (1993).
[Crossref] [PubMed]

Neoplasia (1)

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive In Vivo Characterization of Breast Tumors Using Photon Migration Spectroscopy,” Neoplasia 2, 26–40 (2000).
[Crossref] [PubMed]

Opt. Commun. (1)

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Philos. Trans. R. Soc. B Biol. Sci. (1)

E. Gratton, S. Fantini, M. a. Franceschini, G. Gratton, and M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. B Biol. Sci. 352, 727–735 (1997).
[Crossref]

Phys. Med. Biol. (1)

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref] [PubMed]

Phys. Rev. E (1)

J. B. Fishkin, S. Fantini, M. J. vande Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: Theory and experiments,” Phys. Rev. E 53, 2307–2319 (1996).
[Crossref]

Sci. Rep. (1)

S. Sudarsanam, J. Mathew, S. Panigrahi, J. Fade, M. Alouini, and H. Ramachandran, “Real-time imaging through strongly scattering media: seeing through turbid media, instantly,” Sci. Rep. 6, 25033 (2016).
[Crossref] [PubMed]

Science (2)

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] [PubMed]

D. A. Benaron and D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[Crossref] [PubMed]

Other (8)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steadystate diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4) (1992).
[Crossref] [PubMed]

W. R. Watkins, D. H. Tofsted, V. G. CuQlock-Knopp, J. B. Jordan, and J. O. Merritt, “Navigation through fog using stereoscopic active imaging,” Proc. SPIE4023, Enhanced and Synthetic Vision 2000, 20 (2000).
[Crossref]

N. Hautiere, J. P. Tarel, and D. Aubert, “Towards Fog-Free In-Vehicle Vision Systems through Contrast Restoration,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (CVPR IEEE2004) pp. I-536–I-543 Vol. 1.

WMO-No. 8, “Guide to Meteorological Instruments and Methods of Observation,” 7th edition, World Meteo., (2008).

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Oxford University, 2002).

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley, 1999).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Imaging scheme: A directional source of light with power, P0, forward cone solid angle, Ω, having a limited spectral width (λ ± Δλ) is detected at a distance r by a detector that subtends an angle dΩ from the source.

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Fig. 2
Fig. 2 Illustration of the optical signal received at the detector. As an example, four samples are shown here to form the quadrature components which, consequently, can be used for estimation of amplitude and phase of the signal.

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Fig. 3
Fig. 3 (a) Ratio of the optimal frequency ωopt to standard operating frequency ωa = µc as a function of the normalized optical attenuation Rδ. (b) Loss in precision in the estimation of Rδ using modulation angular frequency ωa as opposed to ωopt as a function of Rδ. (c) Contours of optimal frequency of modulation as a function of absorption coefficient µ and reduced scattering coefficient σ and the detection distance r for an intervening medium having refractive index 1. The frequencies can be scaled down by a factor of n for a medium with refractive index n.

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Fig. 4
Fig. 4 (a) Contour plot of ln [ G b f ] for range σ/μ ∈ [1,100] and ω/μc ∈ [0.01,90], with anisotropy factor g = 0. (Inset) Shows a zoomed in section of the plot where the effect of the cosine term is clearly visible. The cosine term makes it difficult to analytically obtain the contour of unity gain but the condition of Eq. (11) for expecting a gain is displayed as red dashed line. The diffusion approximation remains valid in the region below the yellow sdashed line. (b) Same contour plot as (a) for anisotropy factor g = 0:15.

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Tables (2)

Tables Icon

Table 1 Left column: definitions, symbols and units of experimental parameters and diffusing medium parameters. Right column: definition of dimensionless reduced parameters.

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Tables Icon

Table 2 Expressions of intensity, modulation index and relative phase for the ballistic and diffuse components of the detected light.

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Equations (25)

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

α = I B I D = Ω ′ D r e − r ( μ + μ s − 1 / δ ) = Ω ′ e R δ − R b 3 R * ,
m D = M exp [ − r 3 μ ( μ + σ ) ( 1 + 1 + ( ω / μ c ) 2 2 − 1 ) ] = M e − R δ ( q − 1 ) ,
Δ ϕ = r 3 μ ( μ + σ ) − 1 + 1 + ( ω / μ c ) 2 2 = R δ q 2 − 1 .
R δ = Δ ϕ 2 − 2 ( ln [ β ] ) 2 4 ln [ β ] ,
q = Δ ϕ 2 + 2 ( ln [ β ] ) 2 Δ ϕ 2 − 2 ( ln [ β ] ) 2 .
P Z , Ψ ( z , ψ | A , ϕ , Λ 2 ) = z 2 π Λ 2 exp [ − 1 2 Λ 2 ( z 2 + A 2 − 2 z A cos [ ψ − ϕ ] ) ] .
ℱ ( θ ′ ) = ( A ) ( ϕ ) ( Λ 2 ) ( 1 Λ 2 0 0 0 A 2 Λ 2 0 0 0 1 Λ 4 ) ( A ) ( ϕ ) ( Λ 2 ) ,
C R B D ( θ ) = ( M ) ( R δ ) ( R * ) ( M 2 + 4 e ( − 1 + 2 q ) R δ q 3 ( 1 + q ) R * S 0 2 e ( − 1 + 2 q ) R δ 3 M ( 1 + q ) R * S 0 − M R * + 2 e ( − 1 + 2 q ) R δ 3 M ( 1 + q ) S 0 2 e ( − 1 + 2 q ) R δ 3 M ( 1 + q ) R * S 0 2 e ( − 1 + 2 q ) R δ 3 M 2 ( − 1 + q 2 ) R * S 0 2 e ( − 1 + 2 q ) R δ 3 M 2 ( − 1 + q 2 ) S 0 − M R * + 2 e ( − 1 + 2 q ) R δ 3 M ( 1 + q ) S 0 2 e ( − 1 + 2 q ) R δ 3 M 2 ( − 1 + q 2 ) S 0 R * 2 + 2 e ( − 1 + 2 q ) R δ R * 3 M 2 ( − 1 + q 2 ) S 0 ) ( M ) ( R δ ) ( R * ) ,
ω o p t μ c = 2 [ 1 + [ 1 + 4 R δ 2 ] 1 2 + R δ 2 ( 3 + [ 1 + 4 R δ 2 ] 1 2 ) ] 1 2 R δ 2 ,
G b f = [ ℱ ℬ ⊕ D ( θ ) ] 11 [ ℱ D ( θ ) ] 11 ,
G b f = 1 Λ ℬ ⊕ D 2 ( ∂ A ℬ ⊕ D ∂ M ) 2 1 Λ D 2 ( ∂ A D ∂ M ) 2 ,
G b f = 1 1 + α ( 1 + α 2 β 2 + 2 α β cos Δ ϕ )
= 1 + Ω ′ 2 e τ ( 1 + 6 R * Ω ′ e − τ / 2 cos 2 ( q 2 − 1 ) R δ ) 9 R * 2 1 + α ,
q > R b / R δ = ( 1 − g ) + σ μ ( 1 − g ) 3 ( 1 + σ μ ) ,
ω c > 2 3 σ ( 1 − g ) 2 ,
var ( V ) = ∑ i = 0 n T sin [ 2 π t i / T + ϕ r ] 2 I ( t ) = I 0 2 + I 0 M ∑ i = 0 n T ( sin [ 2 π t i / T + ϕ r ] ( sin [ 4 π t i / T + ϕ r ] + sin [ ϕ r ] ) ) = I 0 2
P U , V ( u , v | A , ϕ , Λ 2 ) = 1 2 π Λ 2 exp [ − ( u − A cos [ ϕ ] ) 2 + ( v − A sin [ ϕ ] ) 2 2 Λ 2 ] .
P Z , Ψ ( z , ψ | A , ϕ , Λ 2 ) = P U , V ( u , v | A , ϕ , Λ 2 ) | J u , v z , ψ | = z 2 π Λ 2 exp [ − 1 2 Λ 2 ( z 2 + A 2 − 2 z A cos [ ψ − ϕ ] ) ] ,
J D = [ 3 2 e − q R δ R * S 0 − 3 2 e − q R δ M q R * S 0 3 2 e − q R δ M S 0 0 − 1 + q 2 0 0 − 3 2 e − R δ R * S 0 3 2 e − R δ S 0 ] .
ℱ ( θ ) = [ 3 2 e ( 1 − 2 q ) R δ R * S 0 − 3 2 e ( 1 − 2 q ) R δ M q R * S 0 3 2 e ( 1 − 2 q ) R δ M S 0 − 3 2 e ( 1 − 2 q ) R δ M q R * S 0 1 + 3 2 e ( 1 − 2 q ) R δ M 2 ( − 1 + 2 q 2 ) R * S 0 − 1 R * − 3 2 e ( 1 − 2 q ) R δ M 2 q S 0 3 2 e ( 1 − 2 q ) R δ M S 0 − 1 R * − 3 2 e ( 1 − 2 q ) R δ M 2 q S 0 2 + 3 e ( 1 − 2 q ) R δ M 2 R * S 0 2 R * 2 ] .
u D = ∫ I D ( 1 + m D cos [ ω t − ϕ D ] ) cos [ ω t + δ ϕ ] d t = I D m D 2 cos [ ϕ D + δ ϕ ]
v D = ∫ I D ( 1 + m D cos [ ω t − ϕ D ] ) sin [ ω t + δ ϕ ] d t = I D m D 2 sin [ ϕ D + δ ϕ ] .
u ℬ ⊕ D = ∫ [ I D ( 1 + m D cos [ ω t − ϕ D ] ) + I B ( 1 + m B cos [ ω t − ϕ B ] ) ] × cos [ ω t + δ ϕ ] d t = I D m D 2 cos [ ϕ D + δ ϕ ] + I B m B 2 cos [ δ ϕ ]
v ℬ ⊕ D = I D m D 2 sin [ ϕ D + δ ϕ ] + I B m B 2 sin [ δ ϕ ] .
A D 2 = I D 2 m D 2 4 A ℬ ⊕ D 2 = I D 2 m D 2 4 + I B 2 m B 2 4 + I D I B m D m B 4 cos [ ϕ D ] = I D 2 m D 2 4 ( 1 + α 2 β 2 + 2 α β cos [ ϕ D ] ) .

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