Abstract

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green’s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

1998 (2)

1997 (4)

1996 (4)

For a brief review of optical imaging techniques, see S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16–22 (1996).

E. B. de Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996).
[CrossRef] [PubMed]

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

1995 (1)

1994 (1)

R. R. Alfano, X. Liang, L. Wang, P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
[CrossRef] [PubMed]

1993 (4)

A. O. Wist, P. P. Fatouros, S. L. Herr, “Increased spatial resolution in transillumination using collimated light,” IEEE Trans. Med. Imaging 12, 751–757 (1993).
[CrossRef] [PubMed]

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

E. Marshall, “Search for a killer: focus shifts from fat to hormones in a special report on breast cancer,” Science 259, 618–621 (1993).
[CrossRef] [PubMed]

M. R. Hee, J. Izzat, J. Jacobson, J. G. Fujimoto, E. A. Swanson, “Femtosecond transillumination optical coherence tomography,” Opt. Lett. 18, 950–952 (1993).
[CrossRef] [PubMed]

1992 (1)

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L curve,” SIAM (Soc. Ind. Appl. Math.) Rev. 34, 561–580 (1992).

1991 (2)

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

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

1990 (2)

1989 (1)

1929 (1)

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesion,” Surg. Gynecol. Obstet. 48, 721–730 (1929).

’t Hooft, G. W.

Alfano, R. R.

S. K. Gayen, M. E. Zevallos, M. Alrubaiee, J. M. Evans, R. R. Alfano, “Two-dimensional near-infrared transillumination imaging of biomedical media with a chromium-doped forsterite laser,” Appl. Opt. 37, 5327–5336 (1998).
[CrossRef]

Q. Fu, F. Seier, S. K. Gayen, R. R. Alfano, “High-average-power, kilohertz-repetition-rate, sub-100-fs Ti:sapphire amplifier system,” Opt. Lett. 22, 712–714 (1997).
[CrossRef] [PubMed]

For a brief review of optical imaging techniques, see S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16–22 (1996).

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

R. R. Alfano, X. Liang, L. Wang, P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
[CrossRef] [PubMed]

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

K. M. Yoo, R. R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Opt. Lett. 15, 320–322 (1990). For a discussion of the characteristics of photons transmitted through a turbid medium, see Refs. 1 and 12 and relevant references in those papers.
[CrossRef] [PubMed]

R. R. Alfano, A. Pradhan, G. C. Tang, S. J. Wahl, “Optical spectroscopic diagnosis of cancer and normal breast tissues,” J. Opt. Soc. Am. B 6, 1015–1023 (1989).
[CrossRef]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

Alrubaiee, M.

Arridge, S. R.

S. R. Arridge, W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Deply, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997); S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

S. R. Arridge, “The forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS 11 of SPIE Institute Series (SPIE, Bellingham, Wash., 1993).

Boas, D. A.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995), and relevant references therein.
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 320–327 (1997).

Brennan, J. F.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

Cai, W.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

Catarious, D.

A. H. Hielscher, A. Klose, D. Catarious, K. Hanson, “Tomographic imaging of biological tissue by time-resolved model-based iterative image reconstruction,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 156–161.

Chance, B.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995), and relevant references therein.
[CrossRef] [PubMed]

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 320–327 (1997).

Clark, N.

Colak, S. B.

Cutler, M.

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesion,” Surg. Gynecol. Obstet. 48, 721–730 (1929).

Das, B. B.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

Dasari, R. R.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

de Haller, E. B.

E. B. de Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996).
[CrossRef] [PubMed]

Deply, D. T.

J. C. Hebden, S. R. Arridge, D. T. Deply, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997); S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Evans, J. M.

Fatouros, P. P.

A. O. Wist, P. P. Fatouros, S. L. Herr, “Increased spatial resolution in transillumination using collimated light,” IEEE Trans. Med. Imaging 12, 751–757 (1993).
[CrossRef] [PubMed]

Feld, M. S.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

Fender, J. S.

Fishkin, J.

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

Fu, Q.

Fujimoto, J. G.

Gayen, S. K.

Gratton, E.

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

Grunbaum, F.

J. Singer, F. Grunbaum, P. Kohn, J. Zubelli, “Image reconstruction of the interior of the bodies that diffuse radiation,” Science 248, 990–992 (1990).
[CrossRef] [PubMed]

Hansen, P. C.

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L curve,” SIAM (Soc. Ind. Appl. Math.) Rev. 34, 561–580 (1992).

Hanson, K.

A. H. Hielscher, A. Klose, D. Catarious, K. Hanson, “Tomographic imaging of biological tissue by time-resolved model-based iterative image reconstruction,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 156–161.

Hebden, J. C.

J. C. Hebden, S. R. Arridge, D. T. Deply, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997); S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Hee, M. R.

Herr, S. L.

A. O. Wist, P. P. Fatouros, S. L. Herr, “Increased spatial resolution in transillumination using collimated light,” IEEE Trans. Med. Imaging 12, 751–757 (1993).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, A. Klose, D. Catarious, K. Hanson, “Tomographic imaging of biological tissue by time-resolved model-based iterative image reconstruction,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 156–161.

Ho, P. P.

R. R. Alfano, X. Liang, L. Wang, P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
[CrossRef] [PubMed]

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

Izzat, J.

Jacobson, J.

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

H. Jiang “Three-dimensional optical image reconstruction: finite element approach,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 168–170.

Klose, A.

A. H. Hielscher, A. Klose, D. Catarious, K. Hanson, “Tomographic imaging of biological tissue by time-resolved model-based iterative image reconstruction,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 156–161.

Kohn, P.

J. Singer, F. Grunbaum, P. Kohn, J. Zubelli, “Image reconstruction of the interior of the bodies that diffuse radiation,” Science 248, 990–992 (1990).
[CrossRef] [PubMed]

Lax, M.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

Liang, X.

R. R. Alfano, X. Liang, L. Wang, P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
[CrossRef] [PubMed]

Lionheart, W. R. B.

Liu, C.

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

Liu, F.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef] [PubMed]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

Manoharan, R.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

Mantolin, W.

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

Maris, M.

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
[CrossRef]

Marshall, E.

E. Marshall, “Search for a killer: focus shifts from fat to hormones in a special report on breast cancer,” Science 259, 618–621 (1993).
[CrossRef] [PubMed]

Matson, C. L.

McMackin, L.

Melissen, J. B. M.

Moes, C. J. M.

O’Leary, M. A.

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[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 320–327 (1997).

Ornstein-Carndona, J.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
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Pradhan, A.

Prahl, S. A.

Romer, T. J.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

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M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
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E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
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L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

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M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
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A. O. Wist, P. P. Fatouros, S. L. Herr, “Increased spatial resolution in transillumination using collimated light,” IEEE Trans. Med. Imaging 12, 751–757 (1993).
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M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995), and relevant references therein.
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M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 320–327 (1997).

Yoo, K. M.

Zeng, Fan An

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

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W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
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J. Singer, F. Grunbaum, P. Kohn, J. Zubelli, “Image reconstruction of the interior of the bodies that diffuse radiation,” Science 248, 990–992 (1990).
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Appl. Opt. (4)

Bioimaging (1)

E. Gratton, W. Mantolin, M. vande Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to optical tomography,” Bioimaging 1, 40–46 (1993), pp. 35–64.
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IEEE Trans. Med. Imaging (1)

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

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Phys. Med. Biol. (1)

J. C. Hebden, S. R. Arridge, D. T. Deply, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997); S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
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Proc. Natl. Acad. Sci. USA (1)

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
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Science (4)

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[CrossRef] [PubMed]

R. R. Alfano, X. Liang, L. Wang, P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
[CrossRef] [PubMed]

J. Singer, F. Grunbaum, P. Kohn, J. Zubelli, “Image reconstruction of the interior of the bodies that diffuse radiation,” Science 248, 990–992 (1990).
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M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 320–327 (1997).

A. H. Hielscher, A. Klose, D. Catarious, K. Hanson, “Tomographic imaging of biological tissue by time-resolved model-based iterative image reconstruction,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 156–161.

H. Jiang “Three-dimensional optical image reconstruction: finite element approach,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of 1998 OSA Trends in Optics and Photonics (1998), pp. 168–170.

M. S. Feld, R. Manoharan, J. Salenius, J. Ornstein-Carndona, T. J. Romer, J. F. Brennan, R. R. Dasari, Y. Wang, “Detection and characterization of human tissue lesions with near-infrared Raman spectroscopy,” in Advances in Fluorescence Sensing Technology II, J. R. Lakowicz, ed., Proc. SPIE2388, 99–104 (1995).
[CrossRef]

W. Cai, B. B. Das, F. Liu, Fan An Zeng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Proceedings of Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–248 (1997).

G. J. Muller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zeeet, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS 11 of SPIE Institute Series (SPIE, Bellingham, Wash., 1993).

S. R. Arridge, “The forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS 11 of SPIE Institute Series (SPIE, Bellingham, Wash., 1993).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram of the experimental arrangement used for time-sliced transmitted intensity measurements. (b) Geometric arrangement used to describe the reconstruction algorithm showing the object and image planes and the object in an arbitrary position in cylindrical coordinates. (c) Object location in a lateral plane parallel to and 15 mm away from the exit plane. The 10-mm side of the sample was inclined at an angle of approximately 15° with the vertical (x axis). This is the object position that was used in the experiment.

Fig. 2
Fig. 2

Experimentally measured 2-D intensity distribution of light transmitted through the scattering medium with the object for a gate position of (a) 700 ps and (b) 1500 ps. (c) The object was located approximately on the axis of the cylindrical cell at a distance of 15 mm from the exit plane.

Fig. 3
Fig. 3

L curve used for choosing the regularization parameters for IIR with simulated data. The object was located at a distance of 15 mm from the exit plane.

Fig. 4
Fig. 4

Images reconstructed from simulated data when the object was located at a distance of 15 mm (z = 45 mm) from the exit plane. The sequence of circles represents images at 3-mm intervals along the cylinder axis. The linear intensity scale spans the range 0–20. The maximum value of Δμ a (r) is 0.04 mm-1 and the size of the object is 3 × 3 × 3 mm3.

Fig. 5
Fig. 5

Images reconstructed from experimental data with the object located at a distance of 15 mm (z = 45 mm) from the exit plane. The sequence of circles represents images at 3-mm intervals along the cylinder axis.

Fig. 6
Fig. 6

Images reconstructed from simulated data when the object was located at a distance of (a) 30 mm (z = 30 mm) and (b) 45 mm (z = 15 mm) from the exit plane. The sequence of circles represents images at 3-mm intervals along the cylinder axis.

Fig. 7
Fig. 7

Images reconstructed from simulated data when the object was located at a distance of 15 mm (z = 45 mm) from the exit plane. Image reconstruction was carried out with data collected using the direct arrangement of both the source and the detector, as well as reversing their positions in the z direction.

Equations (7)

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t+μarc-DrcIr, t=Sr, t,
Y=WX,
W3-Dρd, ρ, z, φ-φdt=ΔVGρ0ρd, tGz0z0, 0, t×0dτ 14πDct-τ×exp-ρ2-ρd2+2ρρd cosφ-φd4Dct-τ×Gz0z, z0, t-τGρ0ρ, τGz0z, 0, τ.
Gz0z, 0, t=4πDct-1/2 exp-z2/4Dct+i4πDct-1/2 exp-z-zi2/4Dct,
Gρ0ρ, t=14πDct exp-ρ24Dct,
Gρ0ρ, t=12Dct  fρsexp-ρ2+ρs24DctI02ρρs4Dctρsdρs,
Xk=YkTW2-DkW2-DkTW2-Dk+Λk-1,  k=1, 2,  K.

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