Abstract

The ultimate success of near-infrared optical tomography rests on the precise measurement of light propagation within tissues or random media, the accurate prediction of these measurements from a light propagation model, and an efficient three-dimensional solution of the inverse imaging problem. To date, optical tomography algorithms have focused on frequency-domain photon migration (FDPM) measurements of phase-delay and amplitude attenuation, which are reported relative to the incident light, even though phase-delay and amplitude of incident light are nearly impossible to measure directly. In this contribution, we examine referenced, fluorescence-enhanced frequency-domain photon migration measured at excitation and/or emission wavelengths and report on a measurement strategy to minimize measurement and calibration error for efficient coupling of data to a distorted Born iterative imaging algorithm. We examine three referencing approaches and develop associated inversion algorithms for (1) normalizing detected emission FDPM data to the predicted emission wave arising from a homogeneous medium, (2) referencing detected emission FDPM data to that detected at a reference point, and (3) referencing detected emission FDPM data to detected excitation FDPM data detected at a reference point. Our results show the latter approach to be practical while reducing the nonlinearity of the inverse problem. Finally, in light of our results, we demonstrate the method for eliminating the influence of source strength and instrument functions for effective fluorescence-enhanced optical tomography using FDPM.

© 2002 Optical Society of America

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2001

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

J. Lee, E. Sevick-Muraca, “Fluorescence-enhanced absorption imaging using frequency-domain photon migration: tolerance to measurement error,” J. Biomed. Opt. 6(1), 58–67 (2001).
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterbeg, K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometric analysis for finite-element image and reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

2000

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

D. J. Hawrysz, Eva M. Sevick-Muraca, “Development towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2(5), 382–417 (2000).
[CrossRef]

1999

D. Grosenick, H. Wabnitz, H. Rinnenberg, K. Moesta, P. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt. 38, 2927–2943 (1999).
[CrossRef]

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

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

T. McBride, B. Pogue, E. Gerety, S. Poplack, U. Osterberg, K. Paulsen, “Spectroscopic diffuse optical tomography for the quantitative assessment of hemoglobin concentration and oxygen saturation in breast tissue,” Appl. Opt. 38, 5480–5490 (1999).
[CrossRef]

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

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

R. Mayer, J. Reynolds, E. Sevick-Muraca, “Measurement of the fluorescence lifetime in scattering media by frequency-domain photon migration,” Appl. Opt. 38, 4930–4938 (1999).
[CrossRef]

B. Pogue, T. McBride, J. Prewitt, U. Osterberg, K. Paulsen, “Spatially varying regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
[CrossRef]

1998

1997

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

J. Fishikin, O. Coquoz, E. Anderson, M. Brenner, B. Tromberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
[CrossRef]

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and quantum efficiency form multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef] [PubMed]

J. Chang, H. Graber, R. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
[CrossRef]

1996

1995

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

1994

Alfano, R. R.

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of AmericaWashington, D.C., 2000), pp. 345–347.

Amir, A. H.

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

Anderson, E.

Arridge, S. R.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

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

Barbour, R.

Becker, A.

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

K. Licha, A. Becker, “New contrast agent for optical imaging: acid cleavable conjugates of cyannine dyes with biomolecules,” in Biomedical Imaging: Reporters, Dyes, and Instrumentation, D. J. Bornhop, C. H. Contag, eds., Proc. SPIE3600, 29–35 (1999).

Boas, D. A.

Bogdanov, A.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

Brenner, M.

Chance, B.

Chang, J.

Chen, A. U.

Chernomordik, V.

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

Chernomorik, V.

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

Colak, S. B.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Coquoz, O.

Dehghani, H.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Delpy, D. T.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Dougerty, D. E.

Dougherty, D. E.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

Duderstadt, J. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Eppstein, M. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

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

D. J. Hawrysz, M. J. Eppstein, E. M. Sevick-Muraca, “Measurement and model error assessment of a single pixel, frequency domain apparatus and diffusion model for imaging applications,” in Photon Migration, Diffuse Spectroscopy, and Optical Coherence Tomography: Imaging and Functional Assessment, S. Anderson-Engels, J. G. Fujimoto, eds., Proc. SPIE4160, 153–162 (2000).
[CrossRef]

Fantini, S.

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

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Feng, T.

Fishikin, J.

Franceschini, M.

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

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Fry, M. E.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Gaida, G.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

Gannot, I.

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

Gannot, L.

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

Geimer, S.

Gerety, E.

Graber, H.

Gratton, E.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Grosenick, D.

H., H. J.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Hamilton, L. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Haskell, R.

Hattery, D.

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

Hattery, V. D.

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

Hawrysz, D. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

D. J. Hawrysz, Eva M. Sevick-Muraca, “Development towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2(5), 382–417 (2000).
[CrossRef]

D. J. Hawrysz, M. J. Eppstein, E. M. Sevick-Muraca, “Measurement and model error assessment of a single pixel, frequency domain apparatus and diffusion model for imaging applications,” in Photon Migration, Diffuse Spectroscopy, and Optical Coherence Tomography: Imaging and Functional Assessment, S. Anderson-Engels, J. G. Fujimoto, eds., Proc. SPIE4160, 153–162 (2000).
[CrossRef]

Hebden, J. C.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Hess, H.

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Hielschert, A.

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

Hillman, E. M. C.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Holboke, M. J.

M. J. Holboke, A. G. Yodh, “Parallel three-dimensional diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 177–179.

Hooft, G. W.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Hutchinson, C.

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Jacques, S.

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

Jess, H.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Jiang, S.

Kaschke, M.

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

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

Kuijpers, F. A.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Kuwana, E.

E. Kuwana, E. M. Sevick-Muraca, “Generation and propagation of fluorescence light from fluorophores exhibiting multiexponential decay kinetics in multiply scattering media,” in Optical Diagnostics and Sensing of Biological Fluids and Glucose and Cholesterol Monitoring, A. V. Priezzhev, G. L. Cote, eds., Proc. SPIE4263, 183–194 (2001).
[CrossRef]

Lax, M.

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of AmericaWashington, D.C., 2000), pp. 345–347.

Lee, J.

J. Lee, E. Sevick-Muraca, “Fluorescence-enhanced absorption imaging using frequency-domain photon migration: tolerance to measurement error,” J. Biomed. Opt. 6(1), 58–67 (2001).
[CrossRef] [PubMed]

Li, X.

Li, X. D.

Licha, K.

K. Licha, A. Becker, “New contrast agent for optical imaging: acid cleavable conjugates of cyannine dyes with biomolecules,” in Biomedical Imaging: Reporters, Dyes, and Instrumentation, D. J. Bornhop, C. H. Contag, eds., Proc. SPIE3600, 29–35 (1999).

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

Loew, M.

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

Lopez, G.

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Mahmood, U.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

Mantulin, W.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Mayer, R.

McAdams, M.

McBride, T.

McBride, T. O.

Moesta, K.

D. Grosenick, H. Wabnitz, H. Rinnenberg, K. Moesta, P. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt. 38, 2927–2943 (1999).
[CrossRef]

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Moesta, T.

O’Leary, M.

Osterbeg, U. L.

Osterberg, U.

Paithankar, D. Y.

Patterson, M. S.

Paulsen, K.

Paulsen, K. D.

Pogue, B.

Pogue, B. W.

Poplack, S.

Prewitt, J.

Reynolds, J.

R. Mayer, J. Reynolds, E. Sevick-Muraca, “Measurement of the fluorescence lifetime in scattering media by frequency-domain photon migration,” Appl. Opt. 38, 4930–4938 (1999).
[CrossRef]

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Riefke, B.

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

Rinnenberg, H.

Schlag, M.

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Schlag, P.

Schmidt, F. E. W.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Schneider, G.

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

Schweiger, M.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Seeber, M.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Semmler, W.

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

Sevick-Muraca, E.

J. Lee, E. Sevick-Muraca, “Fluorescence-enhanced absorption imaging using frequency-domain photon migration: tolerance to measurement error,” J. Biomed. Opt. 6(1), 58–67 (2001).
[CrossRef] [PubMed]

R. Mayer, J. Reynolds, E. Sevick-Muraca, “Measurement of the fluorescence lifetime in scattering media by frequency-domain photon migration,” Appl. Opt. 38, 4930–4938 (1999).
[CrossRef]

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

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

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and quantum efficiency form multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, D. Y. Paithankar, “Fluorescence imaging system and measurement,” U.S. patent5,865,754, February2, 1999.

E. Kuwana, E. M. Sevick-Muraca, “Generation and propagation of fluorescence light from fluorophores exhibiting multiexponential decay kinetics in multiply scattering media,” in Optical Diagnostics and Sensing of Biological Fluids and Glucose and Cholesterol Monitoring, A. V. Priezzhev, G. L. Cote, eds., Proc. SPIE4263, 183–194 (2001).
[CrossRef]

D. J. Hawrysz, M. J. Eppstein, E. M. Sevick-Muraca, “Measurement and model error assessment of a single pixel, frequency domain apparatus and diffusion model for imaging applications,” in Photon Migration, Diffuse Spectroscopy, and Optical Coherence Tomography: Imaging and Functional Assessment, S. Anderson-Engels, J. G. Fujimoto, eds., Proc. SPIE4160, 153–162 (2000).
[CrossRef]

Sevick-Muraca, Eva M.

D. J. Hawrysz, Eva M. Sevick-Muraca, “Development towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2(5), 382–417 (2000).
[CrossRef]

Svaasand, L.

Tittel, F.

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

Tromberg, B.

Troy, T.

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Troy, T. L.

Tshay, T.

Tung, C. H.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

van der Linden, E. S.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

van der Mark, M. B.

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

van Germert, M. J. C.

A. J. Welch, M. J. C. van Germert, Optical–Thermal Response of Laser-Irradiated Tissue (Plenum, Welch Press, New York, 1995).

Veenstra, H.

Wabnitz, H.

Walker, S.

Wang, L.

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

Weissleder, R.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

Welch, A. J.

A. J. Welch, M. J. C. van Germert, Optical–Thermal Response of Laser-Irradiated Tissue (Plenum, Welch Press, New York, 1995).

Xu, M.

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of AmericaWashington, D.C., 2000), pp. 345–347.

Yodh, A. G.

X. Li, B. Chance, A. G. Yodh, “Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption,” Appl. Opt. 37, 6833–6844 (1998).
[CrossRef]

M. O’Leary, D. A. Boas, X. D. Li, B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
[CrossRef] [PubMed]

M. J. Holboke, A. G. Yodh, “Parallel three-dimensional diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 177–179.

Appl. Opt.

T. McBride, B. Pogue, E. Gerety, S. Poplack, U. Osterberg, K. Paulsen, “Spectroscopic diffuse optical tomography for the quantitative assessment of hemoglobin concentration and oxygen saturation in breast tissue,” Appl. Opt. 38, 5480–5490 (1999).
[CrossRef]

J. Fishikin, O. Coquoz, E. Anderson, M. Brenner, B. Tromberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
[CrossRef]

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

D. Grosenick, H. Wabnitz, H. Rinnenberg, K. Moesta, P. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt. 38, 2927–2943 (1999).
[CrossRef]

X. Li, B. Chance, A. G. Yodh, “Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption,” Appl. Opt. 37, 6833–6844 (1998).
[CrossRef]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and quantum efficiency form multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef] [PubMed]

J. Chang, H. Graber, R. Barbour, “Improved reconstruction algorithm for luminescence optical tomography when background lumiphore is present,” Appl. Opt. 37, 3547–3552 (1998).
[CrossRef]

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

R. Mayer, J. Reynolds, E. Sevick-Muraca, “Measurement of the fluorescence lifetime in scattering media by frequency-domain photon migration,” Appl. Opt. 38, 4930–4938 (1999).
[CrossRef]

B. Pogue, T. McBride, J. Prewitt, U. Osterberg, K. Paulsen, “Spatially varying regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
[CrossRef]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterbeg, K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometric analysis for finite-element image and reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. Chernomordik, V. D. Hattery, L. Gannot, A. H. Amir, “Inverse method 3-D reconstruction of localized in vivo fluorescence—application to Sjogren syndrome,” IEEE J. Sel. Top. Quantum Electron. 54, 930–935 (1999).
[CrossRef]

S. B. Colak, M. B. van der Mark, G. W. Hooft, H. J. H., E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

IEEE Trans. Med. Imaging

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “3-D Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

Int. J. Imaging Syst. Technol.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delpy, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Inverse Probl.

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

J. Biomed. Opt.

K. Moesta, S. Fantini, H. Hess, M. Franceschini, M. Kaschke, M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

J. Lee, E. Sevick-Muraca, “Fluorescence-enhanced absorption imaging using frequency-domain photon migration: tolerance to measurement error,” J. Biomed. Opt. 6(1), 58–67 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nat. Biotechnol.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 4, 375–378 (1999).
[CrossRef]

Neoplasia

D. J. Hawrysz, Eva M. Sevick-Muraca, “Development towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2(5), 382–417 (2000).
[CrossRef]

Opt. Lett.

Photochem. Photobiol.

E. Sevick-Muraca, G. Lopez, J. Reynolds, T. Troy, C. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol.

A. Hielschert, S. Jacques, L. Wang, F. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Other

K. Licha, A. Becker, “New contrast agent for optical imaging: acid cleavable conjugates of cyannine dyes with biomolecules,” in Biomedical Imaging: Reporters, Dyes, and Instrumentation, D. J. Bornhop, C. H. Contag, eds., Proc. SPIE3600, 29–35 (1999).

E. M. Sevick-Muraca, D. Y. Paithankar, “Fluorescence imaging system and measurement,” U.S. patent5,865,754, February2, 1999.

A. Becker, G. Schneider, B. Riefke, K. Licha, W. Semmler, “Localization of near-infrared contrast agents in tumor by intravital microscopy,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 112–118 (1999).
[CrossRef]

M. J. Holboke, A. G. Yodh, “Parallel three-dimensional diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 177–179.

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier diffuse optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics (Optical Society of AmericaWashington, D.C., 2000), pp. 345–347.

D. J. Hawrysz, M. J. Eppstein, E. M. Sevick-Muraca, “Measurement and model error assessment of a single pixel, frequency domain apparatus and diffusion model for imaging applications,” in Photon Migration, Diffuse Spectroscopy, and Optical Coherence Tomography: Imaging and Functional Assessment, S. Anderson-Engels, J. G. Fujimoto, eds., Proc. SPIE4160, 153–162 (2000).
[CrossRef]

D. Hattery, V. Chernomorik, I. Gannot, M. Loew, A. H. Gandjbakhche, “Fluorescence measurement of localized, deeply embedded physiological processes,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 377–382 (2000).
[CrossRef]

A. J. Welch, M. J. C. van Germert, Optical–Thermal Response of Laser-Irradiated Tissue (Plenum, Welch Press, New York, 1995).

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

E. Kuwana, E. M. Sevick-Muraca, “Generation and propagation of fluorescence light from fluorophores exhibiting multiexponential decay kinetics in multiply scattering media,” in Optical Diagnostics and Sensing of Biological Fluids and Glucose and Cholesterol Monitoring, A. V. Priezzhev, G. L. Cote, eds., Proc. SPIE4263, 183–194 (2001).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Spatial 2-D distribution of absorption due to fluorophore assuming 100:1 uptake. The distribution was used to generate synthetic data for recovery with use of referencing to the detected emission wave (Fig. 2) and the detected excitation wave (Fig. 3).

Fig. 2
Fig. 2

2-D recovery of absorption due to fluorophore for the distribution illustrated in Fig. 1 with use of the emission wave detected at a reference position. Reconstruction was obtained after 100 iterations with the regularization parameter λ set to 100. The SNR was set to 35 dB.

Fig. 3
Fig. 3

2-D recovery of absorption owing to fluorophore for distribution illustrated in Fig. 1 with use of the excitation wave detected at a reference position. Reconstruction was obtained after 100 iterations with the regularization parameter λ set to 0.0001. The SNR was set to 35 dB.

Fig. 4
Fig. 4

3-D simulation geometry of a 8×4×8 cm3 volume with four sources located one element from the surface and with twelve detectors on the surface.

Fig. 5
Fig. 5

(a) Original μaxf map of a 100:1 partitioning of fluorescent dye in 1×1×1 cm3 inclusion. (b) Reconstructed μaxf map after 30 iterations.

Fig. 6
Fig. 6

SSE versus iteration number.

Fig. 7
Fig. 7

Schematic of measurement setup (adapted from Mayer et al.23).

Fig. 8
Fig. 8

Homogeneous-background measurement of RPS and ACR with the excitation wave used as the reference signal. (a) RPS, (b) ACR. ICG concentration of 0.02 µM is added to 1% Intralipid solution.

Fig. 9
Fig. 9

Homogeneous-background measurement of RPS ACR with the emission wave used as the reference signal. (a) RPS, and (b) ACR. ICG concentration of 0.02 µM is added to 1% Intralipid solution.

Fig. 10
Fig. 10

Placement of sources and detectors in reflectance and transillumination geometries for the reconstructed image presented in Fig. 11.

Fig. 11
Fig. 11

Reconstruction of μaxf with the excitation wave used as a reference. The image was acquired after 27 iterations with regularization parameters for ACR, λAC=1.0, and for RPS, λθ=0.02. (a) Optical property maps of true μaxf distribution (b) and reconstructed μaxf distribution. Peak values of μaxf reached 0.1205 cm-1. (c) Iteration versus SSE.

Tables (1)

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Table 1 Optical Properties for 3-D Simulation

Equations (32)

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·[Dx(r)Φx(r, ω)]+-μax(r)+iωcΦx(r, ω)=-Sx(r),
·[Dm(r)Φm(r, ω)]+-μam(r)+iωc×Φm(r, ω)=-Sm(r)=-ϕμaxf(r)1-iωτ(r)Φx(r, ω).
2Φm(r)+km2(r)Φm(r)=-Sm(r)Dm(r)-Dm(r)·Φm(r)Dm(r),
km2(r)=1Dm(r) -μam(r)+i ωc.
2Gf(r, r)+km2(r)Gf(r, r)=-δ(r-r).
(U2G-G2U)d3r=S(UG-GU)·dS,
Φ˜m(rd, rs)=Ω Gf(rd, r)Sm(r, rs)dΩ=ΩGf(rd, r) ϕμaxf(r)Dom(1-iωτo)×Φx(r, rs)dΩ,
Φ˜m(rd, rs)=j=1NGf(rj, rd)Φx(rj, rs) ϕμaxf(rj)ΔDom(1-iωτ),
Φ˜m(rd, rs)1Φ˜m(rd, rs)2Φ˜m(rd, rs)M=F11F1NF21F2NFM1FMNX(r1)X(r2)X(rN),
Fij=Gf(rdi, rj)Φx(rsi, rj)ϕΔDom(1-iωτo)
X(rj)=μaxf(rj),
Φm(rs, rd)Φbm(rs, rr)exp=1[Φbm(rs, rr)]apriori Ω ϕDm(1-iωτ)×Gf(rd, r)Φx(rs, r)μaxf(r)dΩ.
Φm(rs, rd)Φm(rs, rr)=1Φm(rs, rr) Ω ϕDm(1-iωτ)×Gf(rd, r)Φx(rs, r)μaxf(r)dΩ.
f(x)=ΩΦx(rs, r)Gf(r, rd) ϕμaxf(r)Dm(1-iωτ) dΩ=Kj=1NΦx(rs, rj)Gf(rj, rd)μaxf(rj),
g(x)=ΩΦx(rs, r)Gf(r, rr) ϕμaxf(r)Dm(1-iωτ) dΩ=Kj=1NΦx(rs, rj)Gf(rj, rd)μaxf(rj),
Φm(rs, rd)Φm(rs, rr)exp=f(xg(x),
Φm(rs, rd)Φm(rs, rr)exp=f(x)g(x)=f(xo)g(xo)+f(x)g(x)x=xo(x-xo).
f(x)g(x)x=xo=f(x)g(x)μaxf(rj)=(f(xo))μajg(xo)-(g(xo))μajf(xo)[g(xo)]2,
(f(xo))μaj=μajK[Φx(rs, r1)Gf(r1, rd)μaxf(r1)++Φx(rs, rn)Gf(rn, rd)μaxf(rn)]=KΦx(rs, rj)Gf(rj, rd),
Φm(rs, rd)Φm(rs, rr)exp-f(xo)g(xo)=J·(x-xo)=J11J1NJM1JMN·(x-xo),
J11=AB-CDj=1NΦx(rs1, rj)Gr(rj, rr)μaxf(rj)2,
A=Φx(rs1, r1)Gf(r1, rd1),
B=j=1NΦx(rs1, rj)Gf(rj, rr)μaxfo(rj),
C=Φx(rs1, r1)Gf(r1, rr),
D=j=1NΦx(rs1, rj)Gf(rj, rd1)μaxfo(rj).
Φm(rs, rd)Φx(rs, rr)exp=1Φx(rs, rr) Ω ϕDm(1-iωτ)×Gf(rd, r)Φx(rs, r)μaxf(r)dΩ,
Gf(r, rd)=Gf(rd, r).
θ(rd1, rd2)=θ(rd1)-θ(rd2)+(θinstr1-θinstr2).
θ(rd2, rd1)=θ(rd2)-θ(rd1)+(θinstr1-θinstr2).
M(rd1, rd2)=MAC1Lf1Ginstr1MAC2Lf2Ginstr2
M(rd2, rd1)=MAC1Lf2Ginstr1MAC2Lf1Ginstr2,
Ginstr1Ginstr2=[M(rd1, rd2)M(rd2, rd1)]1/2.

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