Abstract

A perturbation theory for the forward problem of optical transport in turbid media is developed. It is applicable to media with scattering and absorption inhomogeneities and steady-state and modulated light. Absorbing perturbations can be described by a volume distribution of virtual sources that primarily causes a monopole perturbation light field. Scattering objects have an additional contribution that, in the limiting case of sharply bounded objects, is represented by a surface distribution of virtual sources and causes a dipolelike perturbation pattern. Using the concept of virtual sources, we discuss a possible ambiguity between the perturbations from scattering and absorbing inhomogeneities and the implications for the source–detector placement in inverse problems. We show that the surface effects due to sharp boundaries of scattering objects pose both a numerical problem and a chance to improve the resolution of inverse algorithms.

© 1997 Optical Society of America

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    [CrossRef] [PubMed]

1995

S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
[CrossRef]

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

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

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

1994

1993

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

1992

S. L. Jacques,, “Simple optical theory for light dosimetry during PDT,” in Optical Methods for Tumor Treatment and Detection: Mechanisms and Techniques in Photodynamic Therapy, T. J. Dougherty, ed., Proc. SPIE 1645, 155–165(1992).
[CrossRef]

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1991

R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubovsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).

1989

Aronson, R.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubovsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).

Arridge, S. R.

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, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Barbour, R. L.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubovsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).

Benaron, D. A.

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

Boas, D. A.

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

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Chance, B.

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

S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

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

Chang, J.-H.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Cheong, W. F.

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

Delphy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Fantini, S.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Feng, T.-C.

Franceschini, M.

Graber, H. L.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubovsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).

Gratton, E.

Haskell, R. C.

He, L.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Heusmann, H.

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

Heywang-Köbrunner, S.

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques,, “Simple optical theory for light dosimetry during PDT,” in Optical Methods for Tumor Treatment and Detection: Mechanisms and Techniques in Photodynamic Therapy, T. J. Dougherty, ed., Proc. SPIE 1645, 155–165(1992).
[CrossRef]

Kang, K.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Kermit, E. L.

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

King, R. A.

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

Kölzer, J.

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

Lubovsky, J.

R. L. Barbour, H. L. Graber, R. Aronson, and J. Lubovsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 192–203 (1991).

Lubovsky, L.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Maier, J.

McAdams, M. S.

Nioka, S.

S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
[CrossRef]

O’Leary, M. A.

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

S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Otto, J.

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

Patterson, M. S.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

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

Puls, R.

H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
[CrossRef]

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Sevick, E.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.-T.

Van Houten, J. P.

D. A. Benaron, J. P. Van Houten, W. F. Cheong, E. L. Kermit, and R. A. King, “Early clinical results of time-of-flight optical tomography in a neonatal intensive care unit,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 582–596 (1995).
[CrossRef]

Walker, S.

Wang, Y.

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Weng, J.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Wilson, B. C.

Yodh, A. G.

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

S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
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H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
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B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
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D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Proc. SPIE

Y. Wang, J.-H. Chang, R. Aronson, and R. L. Barbour, H. L. Graber, and L. Lubovsky, “Imaging of scattering media by diffusion tomography: an iterative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
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S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delphy, “Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
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S. Zhao, M. A. O’Leary, S. Nioka, and B. Chance, “Breast tumor detection using continuous wave light sources,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 809–817(1995).
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H. Heusmann, J. Kölzer, R. Puls, and J. Otto, S. Heywang-Köbrunner, and W. Zinth, “Spectral transillumination of human breast tissue,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 798–808 (1995).
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M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Images of inhomogeneous turbid media using diffuse photon density waves,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, ed., Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 106–115.

B. W. Pogue and M. S. Patterson, “Perturbation calculations of photon density waves in an inhomogeneous tissue-simulating medium,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, ed., Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 74–77.

G. Arfken, Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985), Chap. 1, p. 1, and Chap. 16, p. 865.

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B. W. Pogue and M. S. Patterson, “Forward and inverse calculations for near-infrared imaging using a multigrid finite difference method,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, ed., Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 176–180.

S. Feng and F. Zeng, “Perturbation theory of photon migration in the presence of a single defect,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, ed., Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 217–228.

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Figures (5)

Fig. 1
Fig. 1

Perturbation of the diffuse light field in an infinite background medium, caused by the doubled absorption in a sphere, calculated on a line through a point source and a sphere. The algorithm calculates the total fluence perturbation ϕPert (solid curve) as a sum of the contributions from the surface integral (short-dashed curve) and the volume integral (long-dashed curve) in Eq. (15). For comparison, results from a spherical harmonics expansion method16,17) are marked with symbols. Sphere: radius = 0.2 cm, 739 voxels, μa = 0.2 cm-1, μs=10 cm-1; background medium: μa=0.1cm-1, μs=10 cm-1; point source at x=-1 cm; S = 1 W.

Fig. 2
Fig. 2

Perturbation fluence from a sphere with increased scattering. Same as Fig. 1, but the sphere has doubled scattering: μa=0.1cm-1, μs=20cm-1.

Fig. 3
Fig. 3

Measurement configurations for imaging.

Fig. 4
Fig. 4

Ambiguity between scattering and absorbing inhomogeneities for dc light. The scattering object i in (a) is a 1 cm × 1 cm × 1 cm cube with increased scattering μs=12cm-1 but the same absorption as the background medium (μa0 =0.1cm-1, μs0=10cm-1). The absorbing object in (b) is composed of the cube i with increased absorption μa =0.12cm-1, a 0.1-cm-thick slab ii with decreased absorption μa=0.002cm-1 on the front side of i, and a 0.1-cm-thick slab iii with increased absorption μa=0.26cm-1 on the back side; the scattering is the same as in the background. For both situations, 1-W source at x=-2.5 cm;voxel length, 1 mm. The perturbation for the scattering (solid curve) and for the absorbing inhomogeneities (dashed curve) in (c) is almost the same.

Fig. 5
Fig. 5

(a) Volume and surface contributions for the scattering object i from Fig. 4, calculated with different discretizations. (b) The total perturbation is the sum of the volume and the surface contributions in (a).

Equations (23)

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[D(r)ϕ(r)]-μa(r)ϕ(r)-iωcϕ(r)=-S(r),
D2ϕ(r)-μaϕ(r)-iωcϕ(r)=-S(r).
3μt·J+2ϕ+k2ϕ=-3μtS.
k02=-3μt0μa0+iωc,
Δk2=-3Δμaμt0+μa0Δμt+ΔμaΔμt+Δμtiωc
(2+k02)ϕ=-3μtS-3μt·J-Δk2ϕ.
(2+k02)ϕ=-3μt0μtμt0S+SVirt(ϕ),
SVirt(ϕ)=SϕVirt+SJVirt,
SϕVirt=13μt0Δk2ϕ,
SJVirt=μtμt0·J,
ϕ(r)=ϕ0(r)+ϕPert(r),
ϕ0(r)=Vsdr[μt(r)/μt0]S(r)Gˆ(|r-r|),
ϕPert(r)=VobjdrSVirt[ϕ(r)]Gˆ(|r-r|),
ϕ1(r)=ϕ0(r)+VobjdrSVirt[ϕ0(r)]Gˆ(|r-r|).
ϕn(r)=ϕ0(r)+VobjdrSVirt[ϕn-1(r)]Gˆ(|r-r|).
ϕn,i=ϕ0,i+jNVSjVirt(ϕn-1)Gˆij.
Gˆii=VidrGˆ(|ri-r|).
Gˆii=3μt0-34πk2R3[1-(1-ikR)exp(ikR)].
1μt0Vobjdrμt(r)J(r)Gˆ(|r-r|)
1μt0Vobjinsidedrμt(r)J(r)Gˆ(|r-r|)+1μt0SobjdAΔμt(r)n(r)·J(r)Gˆ(|r-r|).
ϕPert(r)=Δμa+Δμsμs0SobjdA·J(r)Gˆ(|r-r|)-Δμa+Δμsμa0μs0+ΔμaΔμsμs0×Vobjdrϕ(r)Gˆ(|r-r|).
ϕPert=fμa0μs0SdA·JGˆ-fμa0VdVϕGˆ;
ϕPert=fSdA·JGˆ-fμa0VdVϕGˆ.

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