Abstract

A procedure for the time-domain optical characterization of an inclusion in a scattering slab is investigated theoretically and experimentally. The method relies on the measurement of a contrast function, which is defined as the time-dependent relative change in the transmitted signal resulting from the presence of the inclusion. Analytical expressions for the contrast functions of absorptive and diffusive inclusions are obtained through a perturbation solution of the diffusion equation. This procedure is used successfully to determine the optical properties of absorptive, diffusive, and mixed inclusions located at midplane in a scattering slab by use of time-resolved transmittance measurements.

© 2000 Optical Society of America

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1999

1998

1997

1996

1995

1993

1989

Aronson, R.

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
[CrossRef]

H. L. Graber, R. L. Barbour, J. Chang, R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 669–681 (1995).

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Arridge, S. R.

J. C. Hebden, S. R. Arridge, “Imaging through scattering media by the use of an analytical model of perturbation amplitudes in the time domain,” Appl. Opt. 35, 6788–6796 (1996).
[CrossRef] [PubMed]

S. R. Arridge, “Photon-measurement density functions. Part 1: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Barbour, R. L.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

H. L. Graber, R. L. Barbour, J. Chang, R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 669–681 (1995).

Bassini, M.

Beaudry, P.

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

Beek, J. F.

Bethea, R. M.

R. M. Bethea, B. S. Duran, T. L. Boullion, Statistical Methods for Engineers and Scientists, Third Edition, Revised and Expanded (Marcel Dekker, New York, 1995).

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).
[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 Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 320–327 (1995).
[CrossRef]

Bonner, R. F.

A. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

Boullion, T. L.

R. M. Bethea, B. S. Duran, T. L. Boullion, Statistical Methods for Engineers and Scientists, Third Edition, Revised and Expanded (Marcel Dekker, New York, 1995).

Butkov, E.

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

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).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[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 Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 320–327 (1995).
[CrossRef]

Chang, J.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

H. L. Graber, R. L. Barbour, J. Chang, R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 669–681 (1995).

Chang, J.-H.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Chatigny, S.

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

Chernomordik, V.

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

Contini, D.

Cope, M.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Danlewski, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Delpy, D. T.

J. C. Hebden, D. J. Hall, M. Firbank, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Appl. Opt. 34, 8038–8047 (1995).
[CrossRef] [PubMed]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Dougherty, D. E.

Duran, B. S.

R. M. Bethea, B. S. Duran, T. L. Boullion, Statistical Methods for Engineers and Scientists, Third Edition, Revised and Expanded (Marcel Dekker, New York, 1995).

Eppstein, M. J.

Fantini, S.

Firbank, M.

Franceschini, M. A.

Fréchette, J.

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

Gandjbakhche, A.

Gandjbakhche, A. H.

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

Gilbert, C.

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

Graber, H. L.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

H. L. Graber, R. L. Barbour, J. Chang, R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 669–681 (1995).

Grosenick, D.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Hall, D. J.

Harvey, É.

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

Hebden, J. C.

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

J. C. Hebden, S. R. Arridge, “Imaging through scattering media by the use of an analytical model of perturbation amplitudes in the time domain,” Appl. Opt. 35, 6788–6796 (1996).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, M. Firbank, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Appl. Opt. 34, 8038–8047 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1.

Jacques, S. L.

Jiang, H.

Kaltenbach, J.-M.

J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modeling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

Kaschke, M.

S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, K. T. Moesta, “Assessment of the size, position, and optical properties on breast tumors in vivo by noninvasive optical methods,” Appl. Opt. 37, 1982–1989 (1998).
[CrossRef]

J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modeling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

Mailloux, A.

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

Martelli, F.

Moesta, K.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Moesta, K. T.

Morin, M.

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

Nossal, R.

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

A. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

O’Leary, M. 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).
[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 Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 320–327 (1995).
[CrossRef]

Osterberg, U. L.

Ostermeyer, M. R.

Painchaud, Y.

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

Patterson, M. S.

Paulsen, K. D.

Pei, Y.

Pickering, J. W.

Pogue, B. W.

Prahl, S. A.

Rinneberg, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Schlag, P.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Schlag, P. M.

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Sevick-Muraca, E. M.

Sterenborg, H. J. C. M.

Troy, T. L.

van der Zee, P.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

van Gemert, M. J. C.

van Wieringen, N.

Vernon, M. L.

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

Verreault, S.

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

Wabnitz, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

Walker, S. A.

Wang, Y.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Weiss, G. H.

Welch, A. J.

Wilson, B. C.

Yao, Y.

Yodh, A. G.

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).
[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 Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 320–327 (1995).
[CrossRef]

Zaccanti, G.

Zhu, W.

Appl. Opt.

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parametrization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, K. T. Moesta, “Assessment of the size, position, and optical properties on breast tumors in vivo by noninvasive optical methods,” Appl. Opt. 37, 1982–1989 (1998).
[CrossRef]

J. C. Hebden, D. J. Hall, M. Firbank, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Appl. Opt. 34, 8038–8047 (1995).
[CrossRef] [PubMed]

Y. Painchaud, A. Mailloux, M. Morin, S. Verreault, P. Beaudry, “Time-domain optical imaging: discrimination between scattering and absorption,” Appl. Opt. 38, 3686–3693 (1999).
[CrossRef]

A. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

J. C. Hebden, S. R. Arridge, “Imaging through scattering media by the use of an analytical model of perturbation amplitudes in the time domain,” Appl. Opt. 35, 6788–6796 (1996).
[CrossRef] [PubMed]

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

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[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

S. R. Arridge, “Photon-measurement density functions. Part 1: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
[CrossRef] [PubMed]

S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media by using the adding–doubling method,” Appl. Opt. 32, 559–568 (1993).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Lett.

Other

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

H. L. Graber, R. L. Barbour, J. Chang, R. Aronson, “Identification of the functional form of nonlinear effects of localized finite absorption in a diffusing medium,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 669–681 (1995).

M. Morin, S. Chatigny, A. Mailloux, Y. Painchaud, P. Beaudry, “Time-domain perturbation analysis of a scattering slab,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 67–78 (1999).
[CrossRef]

R. M. Bethea, B. S. Duran, T. L. Boullion, Statistical Methods for Engineers and Scientists, Third Edition, Revised and Expanded (Marcel Dekker, New York, 1995).

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 Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 320–327 (1995).
[CrossRef]

B. Chance, R. R. Alfano, B. J. Tromberg, eds., Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE3597, (1999).

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J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modeling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müeller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

A. H. Gandjbakhche, V. Chernomordik, R. F. Bonner, J. C. Hebden, R. Nossal, “Use of time-dependent contrast functions to discriminate between the scattering and absorption properties of abnormal regions hidden within a tissuelike phantom,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 211–218 (1997).

Y. Painchaud, A. Mailloux, É. Harvey, S. Verreault, J. Fréchette, C. Gilbert, M. L. Vernon, P. Beaudry, “Multiport time-domain laser mammography: results on solid phantom and volunteers,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 548–555 (1999).
[CrossRef]

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E. M. Sevick-Muraca, J. A. Izatt, M. N. Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 148–150.

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Figures (9)

Fig. 1
Fig. 1

On-axis time-resolved signal T hom(t) transmitted through a homogeneous scattering slab with parameters of μs = 1 mm-1, μ a = 0.003 mm-1, d = 50 mm, and n ref = 1.4.

Fig. 2
Fig. 2

Perturbation function f a for an absorptive pointlike inclusion located at three longitudinal positions within a homogeneous scattering slab with the same parameters as given for Fig. 1.

Fig. 3
Fig. 3

Perturbation function f s for a diffusive pointlike inclusion located at three longitudinal positions within a homogeneous scattering slab with the same parameters as given for Fig. 1.

Fig. 4
Fig. 4

Normalized absorptive contrast function for a pointlike inclusion at different depths within a scattering slab with the same parameters as given for Fig. 1.

Fig. 5
Fig. 5

Effect of the time shift tt + 1/cμs on the absorptive contrast function of a pointlike inclusion located at three longitudinal positions in a scattering slab with the same parameters as given for Fig. 1. The thin curves represent the uncorrected contrast functions.

Fig. 6
Fig. 6

Contrast function of a diffusive pointlike inclusion located at two longitudinal positions in a scattering slab with the same parameters as given for Fig. 1. The thin curves represent the uncorrected contrast functions.

Fig. 7
Fig. 7

Examples of the curve fittings obtained with (a) an absorptive and (b) a diffusive inclusion by use of a time interval that begins when the perturbed signal T per reaches 15% of its maximum value and stretches to the end of the detection time base.

Fig. 8
Fig. 8

Examples of the curve fittings obtained with (a) an absorptive and (b) a diffusive inclusion by use of a time interval that begins when the perturbed signal T per reaches 15% of its maximum value and ends when the signal falls below 50% of its maximum value.

Fig. 9
Fig. 9

(a) The solid curve represents the superposition of the signal transmitted through a diffusive inclusion (W s = 60 mm2 and z inc = 10 mm) and a mixed inclusion (W a = 0.34 mm2, W s = 108 mm2, and z inc = 25 mm) in a 50-mm-thick scattering slab (μ a = 0.002 mm-1 and μs = 1 mm-1). The dashed curve represents the signal that is transmitted through the homogeneous slab without an inclusion. (b) Contrast functions of the same diffusive inclusion (solid curve) and mixed inclusion (dashed curve).

Tables (2)

Tables Icon

Table 1 Optical Characterization of Inclusions Located in the Middle of a Scattering Slab

Tables Icon

Table 2 Simultaneous Optical Characterization and Localization of Inclusions in a Scattering Slaba

Equations (48)

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

1ct+μar-·Drϕr, t=Sr, t,
D=13μs,
jr, t=-Dϕr, t,
δϕr, t=δϕar, t+δϕDr, t,
δϕar, t=- δμarpGr, t; rp, tpϕrp, tpdVpdtp,
δϕDr, t=- δDrppGr, t; rp, tp·pϕrp, tpdVpdtp,
Gslabr, t; rp, tp=m=- Gr, t; rm+rp, tp-Gr, t; rm-rp, tp,
Gr, t; rp, tp=c4πDct-tp3/2 exp-|r-rp|24Dct-tp-μact-tput-tp
|r-rp|=x-xp2+y-yp2+z-zp21/2
rm+rp=rp+2md+2zez,  rm-rp=rp+2md+2ze-ze-zpz,
ϕslabr, t=Gslabr, t; r0, 0,
Thomx, y, t=-D ϕslabr, tzz=d.
Thom0, 0, t=exp-μactut24πDc3/2t5/2m=- z1,m exp-z1,m24Dct-z2,m exp-z2,m24Dct,
z1,m=1-2md-4mze-z0,  z2,m=1-2md-4m-2ze+z0.
δϕar, t=- δμarpGslabr, t; rp, tp×Gslabrp, tp; r0, 0dVpdtp,
δTax, y, t=-D δϕar, tzz=d.
δTa0, 0, t=-Wafat,
fat=c exp-μactut4π4πDct3/2k=-m=0 jm,kt,
jm,kt=hm,k4ze+zinc, 2ze+z0, t+hm,k2ze+zinc, 2ze+z0, t+hm,k-zinc, -z0, t+hm,k2ze-zinc, -z0, t-hm,k2ze+zinc, -z0, t-hm,k4ze+zinc, -z0, t-hm,k-zinc, 2ze+z0, t-hm,k2ze-zinc, 2ze+z0, t,
hm,kξ, η, t=1fm2ξ+12Dct2+gkηfmξ+fmξgkη×exp-fmξ+gkη24Dct,
fmξ=2m+1d+4mze+ξ,
gkη=|2kd+4kze-zinc-η|,
Wa=δμaVinc
δϕDr, t=- δDrppGslabr, t; rp, tp·pGslabrp, tp; r0, 0dVpdtp,
p=xxp+yyp+zzp.
δTDx, y, t=-D δϕDr, tzz=d.
δTD0, 0, t=-Wsfst,
fst=-c exp-μact6μs24πDct5/2k=-m=- Jm,k++t-Jm,k+-t+Jm,k-+t-Jm,k--t,
Jm,kt=rmwk-2 exp-rm+wk24Dct×zinc-zkrm+wk×rm+wk22Dct+rmwk+wkrm-1-rmzinc-zkrm+wk42Dct2-rm+wk22Dct×2-rmwk-3 wkrm+3wkrm2,
rm=|zinc-dm|,
wk=|zinc-zk|,
dm+=2m+1d+4mze,  dm-=2m-1d+2ze,
zk+=2kd+2ze+z0,  zk-=2kd+2ze-2ze-z0,
Ws=δμsVinc1+δμs/μs.
δD=13μs+δμs-13μs=-δμs3μsμs+δμs.
Tper0, 0, t=Thom0, 0, t+δTa0, 0, t+δTD0, 0, t.
ηt=Thom0, 0, t-Tper0, 0, tThom0, 0, t.
ηt=WafatThomt+WsfstThomt.
ηt=Waηat+Wsηst,
ηat=fatThomt
ηst=fstThomt
ηat=ct2πk=-m=0 jm,ktm=- z1,m exp-z1,m24Dct-z2,m exp-z2,m24Dct.
ηat=fat+1/cμsThomt=exp-μa/μsct5/22πt+1/cμs3/2×k=-m=0 jm,kt+1/cμsm=- z1,m exp-z1,m24Dct-z2,m exp- z2,m24Dct.
ηst=fst+1/cμsThomt=-exp-μa/μst5/24πμst+1/cμs5/2×k=-m=-Jm,k++-Jm,k+-+Jm,k-+-Jm,k--t+1/cμsm=- z1,m exp-z1,m24Dct-z2,m exp-z2,m24Dct,
χ2=t1t2ηexp-ηtheory2dt,
t1t2 ηatηexpt-Waηat-Wsηstdt=0,  t1t2 ηstηexpt-Waηat-Wsηstdt=0.
Wa=t1t2 ηatηexptdt t1t2 ηs2tdt-t1t2 ηstηexptdt t1t2 ηatηstdtt1t2 ηa2tdt t1t2 ηs2tdt-t1t2 ηatηstdt2,  Ws=t1t2 ηstηexptdt t1t2 ηa2tdt-t1t2 ηatηexptdt t1t2 ηatηstdtt1t2 ηa2tdt t1t2 ηs2tdt-t1t2 ηatηstdt2.
σηexp2σThom/Thom,

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