Abstract

In this work, the optical and thermal properties of tissuelike materials are measured by using frequency-domain infrared photothermal radiometry. This technique is better suited for quantitative multiparameter optical measurements than the widely used pulsed-laser photothermal radiometry (PPTR) because of the availability of two independent signal channels, amplitude and phase, and the superior signal-to-noise ratio provided by synchronous lock-in detection. A rigorous three-dimensional (3-D) thermal-wave formulation with a 3-D diffuse and coherent photon-density-wave source is applied to data from model phantoms. The combined theoretical, experimental, and computational methodology shows good promise with regard to its analytical ability to measure optical properties of turbid media uniquely, as compared with PPTR, which exhibits uniqueness problems. From data sets obtained by using calibrated test phantoms, the reduced optical scattering and absorption coefficients were found to be within 20% and 10%, respectively, of the values independently derived by using Mie theory and spectrophotometric measurements.

© 2001 Optical Society of America

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References

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  1. M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
    [CrossRef]
  2. G. Busse, H. G. Walther, “Photothermal nondestructive evaluation of materials with thermal waves,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, pp. 205–298.
  3. R. R. Anderson, H. Beck, U. Bruggemann, W. Farinelli, S. L. Jacques, J. A. Parrish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
    [CrossRef] [PubMed]
  4. I. A. Vitkin, B. C. Wilson, R. R. Anderson, “Pulsed photothermal radiometry applications in biological media,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 16.
  5. S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
    [CrossRef] [PubMed]
  6. F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
    [CrossRef]
  7. A. Ishimaru, Y. Kuga, R. L-T. Cheung, K. Shimizu, “Scattering and diffusion of a beam wave in randomly distributed scatterers,” J. Opt. Soc. Am. 73, 131–136 (1983).
    [CrossRef]
  8. A. Mandelis, “Diffusion waves and their uses,” Phys. Today 53, 29–34 (2000).
    [CrossRef]
  9. E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).
  10. A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer-Verlag, New York, 2001), Chap. 10.
  11. Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
    [CrossRef]
  12. M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–370 (1999).
    [CrossRef]
  13. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chap. 9.
  14. Ref. 3, p. 2261, Eq. (8).
  15. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  16. T. J. Farrell, M. S. Patterson, 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]
  17. A. Mandelis, C. Feng, “Theory of frequency-domain infrared radiometric detection of diffuse-photon-density- and photothermal waves in turbid media” (manuscript available from A. Mandelis, mandelis@mie.utoronto.ca).
  18. B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
    [CrossRef]
  19. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A.
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).
  21. W. M. Star, J. P. A. Marijnissen, “New trends in photobiology light dosimetry: status and prospects,” J. Photochem. Photobiol. B 1, 149–159 (1987).
    [CrossRef] [PubMed]
  22. A. Mandelis, “Signal-to-noise ratios in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency-, time- and hybrid (rate-window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
    [CrossRef]

2000 (1)

A. Mandelis, “Diffusion waves and their uses,” Phys. Today 53, 29–34 (2000).
[CrossRef]

1999 (1)

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–370 (1999).
[CrossRef]

1997 (1)

E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).

1994 (1)

A. Mandelis, “Signal-to-noise ratios in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency-, time- and hybrid (rate-window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
[CrossRef]

1993 (1)

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

1992 (3)

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, 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]

1989 (1)

1987 (2)

W. M. Star, J. P. A. Marijnissen, “New trends in photobiology light dosimetry: status and prospects,” J. Photochem. Photobiol. B 1, 149–159 (1987).
[CrossRef] [PubMed]

F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
[CrossRef]

1983 (2)

Amic, E.

E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).

Anderson, R. R.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

R. R. Anderson, H. Beck, U. Bruggemann, W. Farinelli, S. L. Jacques, J. A. Parrish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
[CrossRef] [PubMed]

F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
[CrossRef]

I. A. Vitkin, B. C. Wilson, R. R. Anderson, “Pulsed photothermal radiometry applications in biological media,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 16.

Beck, H.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A.

Brown, S. K.

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

Bruggemann, U.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

R. R. Anderson, H. Beck, U. Bruggemann, W. Farinelli, S. L. Jacques, J. A. Parrish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
[CrossRef] [PubMed]

Busse, G.

G. Busse, H. G. Walther, “Photothermal nondestructive evaluation of materials with thermal waves,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, pp. 205–298.

Cheung, R. L-T.

Deutsch, T. F.

F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
[CrossRef]

Farinelli, W.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, 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]

Ferwerda, H. A.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).

Groenhuis, R. A. J.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A.

Ishimaru, A.

Jacques, S. L.

Kuga, Y.

Long, F. H.

F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
[CrossRef]

Luck, J. M.

E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

Ma, T. C.

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

Majaron, B.

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

Mandelis, A.

A. Mandelis, “Diffusion waves and their uses,” Phys. Today 53, 29–34 (2000).
[CrossRef]

A. Mandelis, “Signal-to-noise ratios in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency-, time- and hybrid (rate-window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
[CrossRef]

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer-Verlag, New York, 2001), Chap. 10.

Mannik, L.

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

Marijnissen, J. P. A.

W. M. Star, J. P. A. Marijnissen, “New trends in photobiology light dosimetry: status and prospects,” J. Photochem. Photobiol. B 1, 149–159 (1987).
[CrossRef] [PubMed]

Milner, T. E.

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

Munidasa, M.

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

Nelson, J. S.

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

Nieuwenhuizen, Th. M.

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–370 (1999).
[CrossRef]

E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

Parrish, J. A.

Patterson, M. S.

T. J. Farrell, M. S. Patterson, 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]

Prahl, S. A.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).

Shimizu, K.

Star, W. M.

W. M. Star, J. P. A. Marijnissen, “New trends in photobiology light dosimetry: status and prospects,” J. Photochem. Photobiol. B 1, 149–159 (1987).
[CrossRef] [PubMed]

Tanenbaum, B. S.

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

Ten Bosch, J. J.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).

van Rossum, M. C. W.

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–370 (1999).
[CrossRef]

Verkruysse, W.

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).

Vitkin, I. A.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

I. A. Vitkin, B. C. Wilson, R. R. Anderson, “Pulsed photothermal radiometry applications in biological media,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 16.

Walther, H. G.

G. Busse, H. G. Walther, “Photothermal nondestructive evaluation of materials with thermal waves,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, pp. 205–298.

Wilson, B.

T. J. Farrell, M. S. Patterson, 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.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

I. A. Vitkin, B. C. Wilson, R. R. Anderson, “Pulsed photothermal radiometry applications in biological media,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 16.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. H. Long, R. R. Anderson, T. F. Deutsch, “Pulsed photothermal radiometry for depth profiling of layered media,” Appl. Phys. Lett. 51, 2076–2078 (1987).
[CrossRef]

J. Mater. Sci. Eng. A (1)

M. Munidasa, T. C. Ma, A. Mandelis, S. K. Brown, L. Mannik, “Non-destructive depth profiling of laser processed Zr-2.5Nb alloy by infrared photothermal radiometry,” J. Mater. Sci. Eng. A 159, 111–118 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Photochem. Photobiol. B (1)

W. M. Star, J. P. A. Marijnissen, “New trends in photobiology light dosimetry: status and prospects,” J. Photochem. Photobiol. B 1, 149–159 (1987).
[CrossRef] [PubMed]

J. Phys. (Paris) I (1)

E. Amic, J. M. Luck, Th. M. Nieuwenhuizen, “Multiple Rayleigh scattering of electromagnetic waves,” J. Phys. (Paris) I 7, 445–483 (1997).

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, 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]

Phys. Med. Biol. (1)

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

Phys. Today (1)

A. Mandelis, “Diffusion waves and their uses,” Phys. Today 53, 29–34 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–370 (1999).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Mandelis, “Signal-to-noise ratios in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency-, time- and hybrid (rate-window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
[CrossRef]

Other (9)

G. Busse, H. G. Walther, “Photothermal nondestructive evaluation of materials with thermal waves,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, pp. 205–298.

A. Mandelis, C. Feng, “Theory of frequency-domain infrared radiometric detection of diffuse-photon-density- and photothermal waves in turbid media” (manuscript available from A. Mandelis, mandelis@mie.utoronto.ca).

B. Majaron, W. Verkruysse, B. S. Tanenbaum, T. E. Milner, J. S. Nelson, “Pulsed photothermal profiling of hypervascular lesions: some recent advances,” in Lasers in Surgery: Advanced Characterization, Therapeutics and Systems X, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, N. Kollias, H. Lui, R. S. Malek, G. M. Peavy, H.-D. Reidenbach, L. Reinisch, D. S. Robinson, L. P. Tate, E. A. Towers, T. A. Woodward, eds., Proc. SPIE3907, 114–125 (2000).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chap. 9.

Ref. 3, p. 2261, Eq. (8).

I. A. Vitkin, B. C. Wilson, R. R. Anderson, “Pulsed photothermal radiometry applications in biological media,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 16.

A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer-Verlag, New York, 2001), Chap. 10.

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Figures (8)

Fig. 1
Fig. 1

Schematic of a 3-D turbid medium excited optically by a collimated Gaussian laser beam of spot size W.

Fig. 2
Fig. 2

Frequency-domain photothermal radiometric instrumentation.

Fig. 3
Fig. 3

Least-residual contour surface for reference medium with high absorption and no scatters (stock b). A local minimum marked by “×” yields the optimum (μ¯IR=480 cm-1, α=0.9×10-7 m2/s) pair. This number indicates the best solution to fit the experimental data in stock b.

Fig. 4
Fig. 4

3-D contour plot for phantom 1: (a) g=0.965 and (b) g=0.984. The minimum set of values obtained for g=0.965 is (μa=118 cm-1, μ¯IR=600 cm-1, μs=318 cm-1) and for g=0.984 is (μa=118 cm-1, μ¯IR=600 cm-1, μs=303 cm-1).

Fig. 5
Fig. 5

Amplitude and phase fits for phantom 1 from the minimum solution obtained by the 3-D contour in Fig. 4(a).

Fig. 6
Fig. 6

3-D contour plot for phantom 4: (a) g=0.965 and (b) g=0.984. The minimum set of values obtained for g=0.965 is (μa=116 cm-1, μ¯IR=600 cm-1, μs=351 cm-1) and for g=0.984 is (μa=120 cm-1, μ¯IR=600 cm-1, μs=326 cm-1).

Fig. 7
Fig. 7

Amplitude and phase fits for phantom 4 from the minimum solution obtained by the 3-D contour in Fig. 4(b).

Fig. 8
Fig. 8

Percent deviation (from independently derived values) of μa and μs as determined from the 3-D FD-PTR analysis.

Tables (1)

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Table 1 Results of the Multiparameter Fit for Various Phantoms, Indicating Values Independently Measured with a Spectrophotometer, Calculated with Mie Theory, and PTR Derived

Equations (33)

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2Ψd(r; ω)-μeff2Ψd(r; ω)=-3μs(μt+gμa)I(r)exp(-μtz),
μt=μa+μs.
μeff=3μaμtr,μtrμa+μs.
Ψd(r; ω)=Ψd(r)exp(iωt).
I(r)=P(1-R)πW2exp[-(2r2/W2)+iωt],
Ψd(r, 0; ψ)-AzΨd(r, z; ω)z=0
=-3μsgAI(r),
Ψd(r, L; ω)+AzΨd(r, z; ω)z=L
=3μsgAI(r)exp(-μtL),
A2D1+r211-r21,D=13μtr,
Ψc(r, z; ω)=[P(1-R)/πW2]exp(-2r2/W2-μtz)
Ψt(r, z; ω)=Ψd(r, z; ω)+Ψc(r, z; ω).
Ψ˜t(λ, z; ω)=0Ψt(r, z; ω)J0(λr)r dr,
Ψ˜t(λ, z; ω)=Ψ˜c(λ, z; ω)+Ψ˜d(λ, z; ω)=[F1-γF2 exp(-βL)]exp(-βz)+[F2-γF1 exp(-βL)]exp[-β(L-z)](1+Aβ)[1-γ2 exp(-2βL)]+1-1Dμt+gμaμt-gμsμsμt2-β2exp(-μtz)I˜(λ, ω),
γ1-Aβ1+Aβ,β2(λ)λ2+(μa/D).
F1=31D1+μtAμt2-β2μt+gμaμt-gμs-2gμtr×μsI˜(λ, ω),
F2=31D1-μtAμt2-β2μt+gμaμt-gμs+2gμtr×μs exp(-μtL)I˜(λ, ω).
Q(r, z; ω)=ηNRμaΨt(r, z; ω),
2T(r; ω)-σt2T(r; ω)=-Q(r, z; ω)/k,
σt=iω/α
T˜(λ, z; ω)=0T(r, z; ω)J0(λr)r dr.
T˜(λ, z; ω)=B1exp(-βz)+ktβ-h1-exp(-2qL)×1h+ktq{exp[-(β+q)L]-exp(-2qL)}exp(qz)+1h-ktq×{1-exp[-(β+q)L]}exp(-qz)+B2exp(βz)-ktβ+h1-exp(-2qL)×1h+ktq{exp[-(q-β)L]-exp(-2qL)}exp(qz)+1h-ktq×{1-exp[-(q-β)L]}exp(-qz)+B3exp(-μtz)+ktμt-h1-exp(-2qL)×1h+ktq{exp[-(μt+q)L]-exp(-2qL)}exp(qz)+1h-ktq×{1-exp[-(μt+q)L]}exp(-qz),
B1(λ, ω)=ηNRμakt(β2-q2)b1(λ, ω),
B2(λ, ω)=-ηNRμakt(β2-q2)b2(λ, ω),
B3(λ, ω)=-ηNRμakt(μt2-q2)b3(λ, ω),
b1(λ, ω)1H(λ, ω)[-F1+γF2 exp(-βL)],
b2(λ, ω)1H(λ, ω)[F2-γF1 exp(-βL)]exp(-βL),
b3(λ, ω)1-μsD(μt2-β2)μt+gμaμt-gμsI˜(λ, ω),
H(λ, ω)(1+Aβ)[1-γ2 exp(-2βL)].
S(r, ω)=Cμ¯IR0LT(r, z; ω)exp(-μ¯IRz)dz,
U˜(λ, ω)=Cμ¯IR0LT˜(λ, z; ω)exp(-μ¯IRz)dz.
U˜(λ, ω)=Cμ¯IRB11-exp[-(β+μ¯IR)L]β+μ¯IR+ktβ-h1-exp(-2qL)×1-exp[-(μ¯IR-q)L](h+ktq)(μ¯IR-q){exp[-(β+q)L]-exp(-2qL)}+1-exp[-(μ¯IR+q)L](h-ktq)(μ¯IR+q)×{1-exp[-(β+q)L]}+B21-exp[-(μ¯IR-β)L]μ¯IR-β-ktβ+h1-exp(-2qL)×1-exp[-(μ¯IR-q)L](h+ktq)(μ¯IR-q){exp[-(q-β)L]-exp(-2qL)}+1-exp[-(μ¯IR+q)L](h-ktq)(μ¯IR+q)×{1-exp[-(q-β)L]}+B31-exp[-(μ¯IR+μt)L]μ¯IR+μt+ktμt-h1-exp(-2qL)×1-exp[-(μ¯IR-q)L](h+ktq)(μ¯IR-q){exp[-(μt+q)L]-exp(-2qL)}+1-exp[-(μIR+q)L](h-ktq)(μ¯IR+q)×{1-exp[-(μt+q)L]},
q2(λ, ω)λ2+σt2(ω),

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