Abstract

We calculate the time-resolved flux of photons transmitted across an optically turbid slab containing a partially absorbing inclusion. An analytical expression is obtained for the flux at a detector positioned opposite a point source (at a distance equal to the thickness of the slab) when the center of the inclusion lies on the line connecting those points. The calculation employs a discrete-time lattice random-walk model of photon transport. The resulting expression is used to assess the affects of time resolution on the detectability of the inclusion.

© 1996 Optical Society of America

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  1. R. Alfano, B. Chance, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. Soc. Photo-Opt. Instrum. Eng.1888 (1993).
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    [CrossRef] [PubMed]
  7. J. C. Hebden, “Evaluating the spatial resolution of a time resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
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  8. J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
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  18. R. Lakowitz, K. Berndt, “Frequency-domain measurements of photon migration in tissue,” Chem. Phys. Lett. 166, 246–252 (1990).
    [CrossRef]
  19. J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 65–86 (1993).
  20. B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 328–339 (1995).
  21. 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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).
  22. W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).
  23. A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
    [CrossRef]
  24. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
  25. A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
    [CrossRef] [PubMed]
  26. A.H. Gandjbakhche, R. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
  27. 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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).
  28. 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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).
  29. A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Scaling relationships for theory of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504–516 (1993).
    [CrossRef] [PubMed]
  30. J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
    [CrossRef] [PubMed]

1995

J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

1994

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

1993

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

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

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vis. 3, 263–283 (1993).
[CrossRef]

P. N. den Outer, Th. M. Niewenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

B. B. Das, K. M. Yoo, R. R. Alfano, “Ultrafast time gated imaging in thick tissues: a step toward optical mammography,” Opt. Lett. 18, 1092–1094 (1993).
[CrossRef] [PubMed]

J. C. Hebden, “Time resolved imaging of opaque and transparent spheres embedded in a highly scattering medium,” Appl. Opt. 32, 3837–3841 (1993).
[PubMed]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Scaling relationships for theory of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504–516 (1993).
[CrossRef] [PubMed]

S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, R. Nossal, “Numerical method for studying the detectability of inclusions hidden in optically turbid tissue,” Appl. Opt. 32, 617–627 (1993).
[CrossRef]

1992

J. C. Hebden, “Evaluating the spatial resolution of a time resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

1991

1990

R. Lakowitz, K. Berndt, “Frequency-domain measurements of photon migration in tissue,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time resolved transilluminations for medical diagnosis,” Opt. Lett. 15, 1179–1181 (1990).
[CrossRef] [PubMed]

1989

1987

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

Alfano, R. R.

Andersson-Engels, S.

Aronson, J.

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

Aronson, R.

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

Arridge, S. R.

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vis. 3, 263–283 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).

Barbour, B. L.

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

Barbour, R. L.

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

Berg, R.

Berndt, K.

R. Lakowitz, K. Berndt, “Frequency-domain measurements of photon migration in tissue,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

Boas, D. A.

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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).

Bonner, R. F.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Scaling relationships for theory of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504–516 (1993).
[CrossRef] [PubMed]

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

A.H. Gandjbakhche, R. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).

Burch, C. L.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Chance, B.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurements 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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).

Chang, J.

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).

Das, B. B.

Delpy, D. T.

J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

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

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vis. 3, 263–283 (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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).

den Outer, P. N.

Duncan, M. D.

Farrell, T. J.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 328–339 (1995).

Frisoli, J. K.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Gandjbakhche, A. H.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Scaling relationships for theory of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504–516 (1993).
[CrossRef] [PubMed]

Gandjbakhche, A.H.

A.H. Gandjbakhche, R. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).

Graber, H. L.

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

Graber, H.L.

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

Hall, D. J.

J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

Haselgrove, J. C.

Havlin, S.

S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, R. Nossal, “Numerical method for studying the detectability of inclusions hidden in optically turbid tissue,” Appl. Opt. 32, 617–627 (1993).
[CrossRef]

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

Hebden, J. C.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

J. C. Hebden, “Time resolved imaging of opaque and transparent spheres embedded in a highly scattering medium,” Appl. Opt. 32, 3837–3841 (1993).
[PubMed]

J. C. Hebden, “Evaluating the spatial resolution of a time resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

Hiraoka, M.

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

Jarlman, O.

Johnson, M. L.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Kaltenbach, J.-M.

J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 65–86 (1993).

Kaschke, M.

J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 65–86 (1993).

Kiefer, J. E.

Lagendijk, A.

Lakowitz, J. R.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Lakowitz, R.

R. Lakowitz, K. Berndt, “Frequency-domain measurements of photon migration in tissue,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

Leigh, J. S.

Lubowsky, J.

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

Mahon, R.

Niewenhuizen, Th. M.

Nossal, R.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Scaling relationships for theory of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504–516 (1993).
[CrossRef] [PubMed]

S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, R. Nossal, “Numerical method for studying the detectability of inclusions hidden in optically turbid tissue,” Appl. Opt. 32, 617–627 (1993).
[CrossRef]

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

A.H. Gandjbakhche, R. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).

Nowaczyk, K.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

O’Leary, M. A.

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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).

Patterson, M. S.

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

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 328–339 (1995).

Pogue, B. W.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 328–339 (1995).

Reintjes, J.

Schotland, J. C.

Schweiger, M.

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vis. 3, 263–283 (1993).
[CrossRef]

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

Sevick, E. M.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Svanberg, S.

Szmacinski, H.

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

Tankersley, L. L.

Trus, B.

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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).

Wang, Y.

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

Weiss, G. H.

S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, R. Nossal, “Numerical method for studying the detectability of inclusions hidden in optically turbid tissue,” Appl. Opt. 32, 617–627 (1993).
[CrossRef]

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).

Wilson, B. C.

Yodh, A. G.

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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).

Yoo, K. M.

Zhu, W.

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

Appl. Opt.

Chem. Phys. Lett.

R. Lakowitz, K. Berndt, “Frequency-domain measurements of photon migration in tissue,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

J. Math. Imag. Vis.

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vis. 3, 263–283 (1993).
[CrossRef]

J. Opt. Soc. Am. A

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 309–333 (1987).
[CrossRef]

P. N. den Outer, Th. M. Niewenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

Med. Phys.

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

J. C. Hebden, “Evaluating the spatial resolution of a time resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “Spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon pathlength distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

Other

G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).

E. M. Sevick, C. L. Burch, J. K. Frisoli, M. L. Johnson, K. Nowaczyk, H. Szmacinski, J. R. Lakowitz, “The physical basis of photon migration imaging using frequency-domain measurements,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 485–512 (1993).

H. L. Graber, J. Chang, J. Lubowsky, J. Aronson, B. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 372–386 (1993).

A.H. Gandjbakhche, R. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).

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. Soc. Photo-Opt. Instrum. Eng.1431, 204–215 (1991).

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. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 87–120 (1993).

R. Alfano, B. Chance, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. Soc. Photo-Opt. Instrum. Eng.1888 (1993).

R. Alfano, ed., Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, Proc. Soc. Photo-Opt. Instrum. Eng.2135 (1994).

J.-M. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 65–86 (1993).

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 328–339 (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. Soc. Photo-Opt. Instrum. Eng.2389, 320–327 (1995).

W. Zhu, Y. Wang, J. Chang, H.L. Graber, R. L. Barbour, “A total least squares approach for the solution of the perturbation equation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2389, 420–427 (1995).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of photon random walks on a lattice in the presence of a target absorbing site. The absorbing site represents a voxel, Σ s * on a side, centered about the lattice point (0, 0, s). Examples of different types of photon paths are shown: those in which photons pass several times through the target, paths for which the photons pass only once through the target, and those in which photons do not see the target at all before being detected. The boundaries at z = 0 and z = N are considered to be totally absorbing.

Fig. 2.
Fig. 2.

Contrast Cn) as a function of excess number of steps Δn, or excess transit time [ Δ t = Δ n / Σ s * c ; see Eqs. (35)], for two different values of the absorptivity η (N = 10).

Fig. 3.
Fig. 3.

Contrast C(Z) as a function of the fractional depth, Z, for three different values of Δn. Here η = 1 and N = 20.

Fig. 4.
Fig. 4.

Contrast Cn) of an absorbing site in the center of a slab as a function of excess transit time Δn, for three different slab thicknesses. The absorptivity of the inclusion, which is located at the midplane, is η = 1.

Fig. 5.
Fig. 5.

Results shown in Fig. 4, expressed as functions of the thickness-scaled excess transit time Δn* = Δn/(N + 1).

Equations (36)

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J n ( r ) = 1 6 q n 1 ( x , y , N 1 r 0 ) ,
q n ( r r 0 ) = p n ( r r 0 ) j = 0 n m = 1 η ( 1 η ) m 1    × f j ( s , m r 0 ) p n j ( r s ) .
g ^ ξ = n = 0 g n exp ( n ξ ) ,
q ^ ξ ( r r 0 ) = p ^ ξ ( r r 0 ) η p ^ ξ ( r s ) m = 1 ( 1 η ) m 1 f ^ ξ ( s , m r 0 ) ,
λ ( θ ) = j p ( j ) exp ( i j θ ) .
λ ( θ ) = 1 3 ( cos   θ 1 + cos   θ 2 + cos   θ 3 ) .
p n ( r r 0 ) = 1 2 π 2 π π π π j = 1 N λ n ( θ 1 , θ 2 , π j N ) sin ( π j z 0 N ) sin ( π j z N )           × exp { i [ ( x 0 x ) θ 1 + ( y 0 y ) θ 2 ] } 1 2 .
λ n ( θ ) = exp [ n    ln   λ ( θ ) ] ,
λ ( θ ) 1 1 6 ( θ 2 + π 2 j 2 N 2 ) ,
λ n ( θ ) exp [ n 6 ( θ 2 + π 2 j 2 N 2 ) ] .
π π exp ( n θ 2 6 ) dθ =  exp ( n θ 2 6 )    2 π exp ( n θ 2 6 ) ,
π exp ( n θ 2 6 ) = 1 n π n exp ( ϕ 2 6 ) 0 ,                                           as  n .
p n ( r r 0 ) 3 π n exp ( 3 ρ ρ 0 2 2 n ) j = 1 exp ( n π 2 j 2 6 N 2 ) × sin ( π j z 0 N ) sin ( π j z N ) .
p ^ ξ ( r r 0 ) 3 π j = 1 ln [ 1 1 exp ( ξ π 2 j 2 / 6 N 2 ) ]              × sin ( π j z 0 N ) sin ( π j z N ) .
p n ( s r 0 ) = j = 0 n f j ( s , 1 r 0 ) p n j ( s s ) , r 0 s .
f ^ ξ ( s , 1 r 0 ) = p ^ ξ ( s r 0 ) p ^ ξ ( s s ) .
f n ( s , m + 1 r 0 ) = j = 0 n f j ( s , m r 0 ) f n j ( s , 1 s ) ,
f ^ ξ ( s , m + 1 r 0 ) = f ^ ξ ( s , m r 0 ) f ^ ξ ( s , 1 s ) ,
f ^ ξ ( s , m r 0 ) = f ^ ξ ( s , 1 r 0 ) [ f ^ ξ ( s , 1 s ) ] m 1 .
p n ( s s ) = δ n , 0 + j = 0 n f j ( s , 1 s ) p n j ( s s ) ,
f ^ ξ ( s , 1 s ) = 1 1 p ^ ξ ( s s ) ,
q ^ ξ ( r r 0 ) = p ^ ξ ( r r 0 ) η p ^ ξ ( r s ) p ^ ξ ( s r 0 ) 1 + η [ p ^ ξ ( s s ) 1 ] ,
p ^ ξ ( s s ) exp ( ξ ) j = 1 exp ( π 2 j 2 / 6 N 2 ) sin 2 ( π j s N )      = A ( N , s ) exp ( ξ ) .
A ( N , s ) A ( N ) 0.35 N 0.05 ( N 10 ) .
η 1 + η [ p ^ ξ ( s s ) 1 ] η { 1 η [ A ( N ) exp ( ξ ) 1 ] + } .
q n p n η W n η 2 [ W n A ( N ) W n 1 ] + ,
η 1 + η [ p ^ ξ ( s s ) 1 ]    1 A ( N ) exp ( ξ ) { 1 1 η A ( N ) exp ( ξ ) ( 1 η) 2 A ( N )           × exp ( ξ ) [ 1 exp ( ξ ) A ( N ) ] + } ,
q n p n W n + 1 A ( N ) + ( 1 η ) A 2 ( N ) W n + 2 ( 1 η ) 2 A 2 ( N )    × [ W n + 2 W n + 3 A ( N ) ] + .
η p ^ ξ ( s s ) 1 η ,
q n p n η 1 η + η A ( N ) W n + 1 ,
p n ( r r 0 ) 3 2 [ 2 π ( n 2 ) ] 3 / 2 k = { exp [ 3 [ ( 2 k + 1 ) N 2 ] 2 2 ( n 2 ) ]       exp [ 3 ( 2 k + 1 ) 2 N 2 2 ( n 2 ) ] } .
α ± ( k ) = 3 2 2 k N + s ± 1 , β ± ( m ) = 3 2 ( 2 m + 1 ) N ± s 1 ,
F n ( x , y ) = ( 1 x + 1 y ) exp [ ( x + y ) 2 n 2 ] .
W n = 9 16 π 5 / 2 ( n 2 ) 3 / 2    × k = m = { F n [ α ( k ) , β ( m ) ] + F n [ α + ( k ) , β + ( m ) ]    F n [ α + ( k ) , β ( m ) ] F n [ α ( k ) , β + ( m ) ] } .
N = Σ s * L 2 , n = Σ s * c t , s = Σ s * z 2 ,
C ( n ) = 1 q n p n ,

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