Abstract

A method to determine the absorption and reduced scattering coefficients of rectangular parallelepiped highly scattering media from frequency-domain photon migration measurements is presented. An analytical model for photon diffusion propagation in the rectangular parallelepiped media is established using the method of images and extrapolated boundary conditions. This present technique has simplicity, accuracy, and rapid computability as compared with the Monte Carlo or finite element methods. The theoretical predictions are verified with experimental measurements using a white polyacetal resin, and the errors introduced by using the slab geometry for the optical property determination are identified.

© 2007 Optical Society of America

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, 1997).
  2. D. A. Boas, "Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications," Ph.D. dissertation (University of Pennsylvania, 1996).
  3. A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics, T. Vo-Dinh, ed. (CRC, 2003), pp. 21-1-21-45.
  4. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. McAdams, and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
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    [CrossRef] [PubMed]
  7. S. R. Arridge and M. Schwiger, "Photon-measurement density functions. Part 2: Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
    [CrossRef] [PubMed]
  8. E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, "Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head," Appl. Opt. 36, 21-31 (1997).
    [CrossRef] [PubMed]
  9. 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]
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    [CrossRef] [PubMed]
  11. B. W. Pogue and M. S. Patterson, "Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory," Phys. Med. Biol. 39, 1157-1180 (1994).
    [CrossRef] [PubMed]
  12. S. R. Arridge, "Photon-measurement density functions. Part 1: Analytical forms," Appl. Opt. 34, 7395-7409 (1995).
    [CrossRef] [PubMed]
  13. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 1. Theory," Appl. Opt. 36, 4587-4599 (1997).
    [CrossRef] [PubMed]
  14. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results," Appl. Opt. 36, 4600-4612 (1997).
    [CrossRef] [PubMed]
  15. F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
    [CrossRef]
  16. S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
    [CrossRef] [PubMed]
  17. F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
    [CrossRef]
  18. A. Kienle, "Light diffusion through a turbid parallelepiped," J. Opt. Soc. Am. A 22, 1883-1888 (2005).
    [CrossRef]
  19. J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, and B. J. Tromberg, "Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject," Appl. Opt. 36, 10-20 (1997).
    [CrossRef] [PubMed]
  20. T. Xu, C. Zhang, X. Wang, L. Zhang, and J. Tian, "Measurement and analysis of light distribution in Intralipid-10% at 650 nm," Appl. Opt. 42, 5777-5784 (2003).
    [CrossRef] [PubMed]
  21. G. Mitic, J. Kolzer, J. Otto, E. Piles, G. Solkner, and W. Zinth, "Time-gate transillumination of biological tissues and tissuelike phantoms," Appl. Opt. 33, 6699-6708 (1994).
    [CrossRef] [PubMed]
  22. O. Coquoz, L. O. Svaasand, and B. J. Tromberg, "Optical property measurements of turbid media in a small-volume cuvette with frequency-domain photon migration," Appl. Opt. 40, 6281-6291 (2001).
    [CrossRef]
  23. T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
    [CrossRef]
  24. J. Brandrup and E. H. Immergut, Polymer Handbook, 3rd ed. (Wiley, 1989).
  25. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2000).
  26. H. Xu and M. S. Patterson, "Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference," Opt. Express 14, 6485-6501 (2006).
    [CrossRef] [PubMed]
  27. A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
    [CrossRef]
  28. A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
    [CrossRef] [PubMed]
  29. H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
    [CrossRef] [PubMed]
  30. I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
    [CrossRef] [PubMed]

2006

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

H. Xu and M. S. Patterson, "Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference," Opt. Express 14, 6485-6501 (2006).
[CrossRef] [PubMed]

2005

A. Kienle, "Light diffusion through a turbid parallelepiped," J. Opt. Soc. Am. A 22, 1883-1888 (2005).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

2004

A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
[CrossRef] [PubMed]

2003

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
[CrossRef]

T. Xu, C. Zhang, X. Wang, L. Zhang, and J. Tian, "Measurement and analysis of light distribution in Intralipid-10% at 650 nm," Appl. Opt. 42, 5777-5784 (2003).
[CrossRef] [PubMed]

2002

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
[CrossRef]

2001

1997

1996

A. Kienle and M. S. Patterson, "Determination of the optical properties of turbid media from a single Monte Carlo simulation," Phys. Med. Biol. 41, 2221-2227 (1996).
[CrossRef] [PubMed]

1995

1994

1992

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]

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

1989

Anderson, E. R.

Aronson, R.

Arridge, S. R.

Boas, D. A.

D. A. Boas, "Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications," Ph.D. dissertation (University of Pennsylvania, 1996).

A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics, T. Vo-Dinh, ed. (CRC, 2003), pp. 21-1-21-45.

Brandrup, J.

J. Brandrup and E. H. Immergut, Polymer Handbook, 3rd ed. (Wiley, 1989).

Brenner, M.

Chance, B.

Contini, D.

Cope, M.

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, "Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head," Appl. Opt. 36, 21-31 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Coquoz, O.

Del Bianco, S.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

Delpy, D. T.

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, "Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head," Appl. Opt. 36, 21-31 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Eda, H.

A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
[CrossRef] [PubMed]

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.

Firbank, M.

Fishkin, J. B.

Gao, F.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Haruna, M.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Haskell, R. C.

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

Immergut, E. H.

J. Brandrup and E. H. Immergut, Polymer Handbook, 3rd ed. (Wiley, 1989).

Ishikawa, T.

T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, 1997).

Kienle, A.

A. Kienle, "Light diffusion through a turbid parallelepiped," J. Opt. Soc. Am. A 22, 1883-1888 (2005).
[CrossRef]

A. Kienle and M. S. Patterson, "Determination of the optical properties of turbid media from a single Monte Carlo simulation," Phys. Med. Biol. 41, 2221-2227 (1996).
[CrossRef] [PubMed]

Klose, A. D.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

Koike, Y.

T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
[CrossRef]

Kolzer, J.

Martelli, F.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results," Appl. Opt. 36, 4600-4612 (1997).
[CrossRef] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 1. Theory," Appl. Opt. 36, 4587-4599 (1997).
[CrossRef] [PubMed]

McAdams, M.

Mitic, G.

Ntziachristos, V.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

Ohmi, M.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Okada, E.

Okumura, T.

T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
[CrossRef]

Ondoera, Y.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Otto, J.

Patterson, M. S.

H. Xu and M. S. Patterson, "Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference," Opt. Express 14, 6485-6501 (2006).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, "Determination of the optical properties of turbid media from a single Monte Carlo simulation," Phys. Med. Biol. 41, 2221-2227 (1996).
[CrossRef] [PubMed]

B. W. Pogue and M. S. Patterson, "Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory," Phys. Med. Biol. 39, 1157-1180 (1994).
[CrossRef] [PubMed]

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]

Piles, E.

Pogue, B. W.

B. W. Pogue and M. S. Patterson, "Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory," Phys. Med. Biol. 39, 1157-1180 (1994).
[CrossRef] [PubMed]

Sase, I.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

Sassaroli, A.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
[CrossRef]

Schweiger, M.

Schwiger, M.

Seiyama, A.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
[CrossRef] [PubMed]

Seki, J.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

Solkner, G.

Svaasand, L. O.

Tagaya, A.

T. Okumura, T. Ishikawa, A. Tagaya, and Y. Koike, "Optical design of liquid crystal display backlighting with highly scattering optical transmission polymer," J. Opt. A 5, S269-S275 (2003).
[CrossRef]

Takatsuki, A.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
[CrossRef] [PubMed]

Tanikawa, Y.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Tian, J.

Tromberg, B. J.

Tsay, T.-T.

Tuchin, V.

V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2000).

Wang, X.

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.

Xu, H.

Xu, T.

Yamada, Y.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
[CrossRef]

Yanagida, T.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

A. Takatsuki, H. Eda, T. Yanagida, and A. Seiyama, "Absorber's effect projected directly above improves spatial resolution in near-infrared backscattering imaging," Jpn. J. Physiol. 54, 79-86 (2004).
[CrossRef] [PubMed]

Yodh, A. G.

A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics, T. Vo-Dinh, ed. (CRC, 2003), pp. 21-1-21-45.

Zaccanti, G.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method," Phys. Rev. E. 67, 056623-1-14 (2003).
[CrossRef]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Analytical approximate solutions of the time-domain diffusion equation in layered slabs," J. Opt. Soc. Am. A 71, 71-80 (2002).
[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results," Appl. Opt. 36, 4600-4612 (1997).
[CrossRef] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 1. Theory," Appl. Opt. 36, 4587-4599 (1997).
[CrossRef] [PubMed]

Zhang, C.

Zhang, L.

Zhao, H.

H. Zhao, F. Gao, Y. Tanikawa, Y. Ondoera, M. Ohmi, M. Haruna, and Y. Yamada, "Imaging of in vivo chicken leg using time-resolved near-infrared optical tomography," Phys. Med. Biol. 47, 1979-1993 (2002).
[CrossRef] [PubMed]

Zinth, W.

Appl. Opt.

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]

G. Mitic, J. Kolzer, J. Otto, E. Piles, G. Solkner, and W. Zinth, "Time-gate transillumination of biological tissues and tissuelike phantoms," Appl. Opt. 33, 6699-6708 (1994).
[CrossRef] [PubMed]

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

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 1. Theory," Appl. Opt. 36, 4587-4599 (1997).
[CrossRef] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results," Appl. Opt. 36, 4600-4612 (1997).
[CrossRef] [PubMed]

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

S. R. Arridge and M. Schwiger, "Photon-measurement density functions. Part 2: Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
[CrossRef] [PubMed]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, "Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head," Appl. Opt. 36, 21-31 (1997).
[CrossRef] [PubMed]

O. Coquoz, L. O. Svaasand, and B. J. Tromberg, "Optical property measurements of turbid media in a small-volume cuvette with frequency-domain photon migration," Appl. Opt. 40, 6281-6291 (2001).
[CrossRef]

T. Xu, C. Zhang, X. Wang, L. Zhang, and J. Tian, "Measurement and analysis of light distribution in Intralipid-10% at 650 nm," Appl. Opt. 42, 5777-5784 (2003).
[CrossRef] [PubMed]

J. Biomed. Opt.

I. Sase, A. Takatsuki, J. Seki, T. Yanagida, and A. Seiyama, "Noncontact backscatter-mode near-infrared time-resolved imaging system: preliminary study for functional brain mapping," J. Biomed. Opt. 11, 054006 (2006).
[CrossRef] [PubMed]

J. Comput. Phys.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

J. Opt. A

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Figures (9)

Fig. 1
Fig. 1

Geometry of the rectangular parallelepiped medium.

Fig. 2
Fig. 2

Two-dimensional arrangement of the positive and negative sources for the method of images and extrapolated boundaries.

Fig. 3
Fig. 3

Experimental setup. PMT, photomultiplier tube; LPF, low-pass filter.

Fig. 4
Fig. 4

Experimental positioning and the geometry of the rectangular parallelepiped medium.

Fig. 5
Fig. 5

Contour plot of the measured intensity of the diffuse photon density wave at the surface ( z = 50   mm ) when the source was placed far from the side boundary at ( 252.5 , 100 , 0 )   mm . Left, intensity profile at x = 254   mm along the y axis. Bottom, intensity profile at y = 102.5   mm along the x axis. Dots and the dotted curve are the measured and calculated results, respectively. Modulation frequency, 50   MHz .

Fig. 6
Fig. 6

Contour plot of the measured intensity of the diffuse photon density wave at the surface ( z = 50   mm ) when the source was placed near the side boundary at ( 252.5 , 20 , 0 )   mm . Left, intensity profile at x = 252.5   mm along the y axis. Bottom, intensity profile at y = 20   mm along the x axis. Dots and the dotted curve are the measured and calculated results, respectively. Modulation frequency, 50   MHz .

Fig. 7
Fig. 7

Relative error for the slab and the rectangular parallelepiped geometry versus the source position along the y axis. ( x s , z s ) = ( 252.5 , 0 )   mm .

Fig. 8
Fig. 8

Experimental positioning and the geometry of the cubic medium.

Fig. 9
Fig. 9

Measured intensity and phase distributions of the diffuse photon density wave at the bottom and the side surfaces. Modulation frequency, 100   MHz .

Tables (2)

Tables Icon

Table 1 Absorption and Reduced Scattering Coefficients of the White Polyacetal Resin

Tables Icon

Table 2 Absorption and Reduced Scattering Coefficients of the White Polyacetal Resin

Equations (74)

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l x
l y
l z
z b
( x s , y s , 0 ) m m
z 0
z 0
z 0 = ( μ a + μ s ) 1 ,
μ a
μ s
z b
z b = 1 + R e f f 1 R e f f 2 D v .
D = v / [ 3 ( μ a + μ s ) ]
R e f f
R e f f = 1.440 n r e l 2 + 0.710 n r e l 1 + 0.668 + 0.0636 n r e l ,
n r e l = n medium / n air
n medium
n air
ϕ ( r , ω ) = v S 4 π D l = m = n = [ exp ( j k r 1 ) r 1 exp ( j k r 2 ) r 2 exp ( j k r 3 ) r 3 + exp ( j k r 4 ) r 4 exp ( j k r 5 ) r 5 + exp ( j k r 6 ) r 6 + exp ( j k r 7 ) r 7 exp ( j k r 8 ) r 8 ] .
r i
r 1 = [ ( x x 1 l ) 2 + ( y y 1 m ) 2 + ( z z 1 n ) 2 ] 1 / 2 , r 2 = [ ( x x 1 l ) 2 + ( y y 1 m ) 2 + ( z z 2 n ) 2 ] 1 / 2 , r 3 = [ ( x x 1 l ) 2 + ( y y 2 m ) 2 + ( z z 1 n ) 2 ] 1 / 2 , r 4 = [ ( x x 1 l ) 2 + ( y y 2 m ) 2 + ( z z 2 n ) 2 ] 1 / 2 , r 5 = [ ( x x 2 l ) 2 + ( y y 1 m ) 2 + ( z z 1 n ) 2 ] 1 / 2 , r 6 = [ ( x x 2 l ) 2 + ( y y 1 m ) 2 + ( z z 2 n ) 2 ] 1 / 2 , r 7 = [ ( x x 2 l ) 2 + ( y y 2 m ) 2 + ( z z 1 n ) 2 ] 1 / 2 , r 8 = [ ( x x 2 l ) 2 + ( y y 2 m ) 2 + ( z z 2 n ) 2 ] 1 / 2 ,
x 1 l = 2 l l x + 4 l z b + x s , y 1 m = 2 m l y + 4 m z b + y s , z 1 n = 2 n l x + 4 n z b + z 0 , x 2 l = 2 l l x + ( 4 l 2 ) z b x s , y 2 m = 2 m l y + ( 4 m 2 ) z b y s , z 2 n = 2 n l x + ( 4 n 2 ) z b z 0 ,
k = ( v μ a + j ω D ) 1 / 2 .
660   nm
100   MHz
11   cm
3 .8   mW
62 .5   μm
1   mm
1   kHz
550   mm × 200   mm × 50   mm
( x s , y s , 0 )
x s
252.5   mm
( x s , y s , 50 )   mm
z = 50   mm
( 252 .5, 100, 0 )   mm
( 252 .5, 20, 0 )  mm
f ( μ a , μ s ) = i = 1 5 j = 1 5 ( | ϕ measured ( r s , r d i , j ) | | ϕ calculated ( r s , r d i , j , μ a , μ s ) | σ i , j amplitude ) 2 + i = j 5 j = 1 5 ( Arg [ ϕ measured ( r s , r d i , j ) ] Arg [ ϕ calculated ( r s , r d i , j , μ a , μ s ) ] σ i , j phase ) 2 .
r s
r d i , j
ϕ measured ( r s , r d i , j )
ϕ calculated ( r s , r d i , j , μ a , μ s )
μ a
μ s
| ϕ |
| ϕ |
σ i , j amplitude
σ i , j phase
± 0.001 cm 1
± 1 cm 1
y s
100   mm
10   mm
30   mm
50   mm × 50   mm × 50   mm
( 25, 25, 0 )   mm
100   MHz
z = 50   mm
x = 0   mm
10   cm 1
30   mm
( z = 50   mm )
( 252.5 , 100 , 0 )   mm
x = 254   mm
y = 102.5   mm
50   MHz
( z = 50   mm )
( 252.5 , 20 , 0 )   mm
x = 252.5   mm
y = 20   mm
50   MHz
( x s , z s ) = ( 252.5 , 0 )   mm
100   MHz

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