Abstract

We have measured the optical absorption and scattering coefficient spectra of a multiple-scattering medium (i.e., a biological tissue-simulating phantom comprising a lipid colloid) containing methemoglobin by using frequency-domain techniques. The methemoglobin absorption spectrum determined in the multiple-scattering medium is in excellent agreement with a corrected methemoglobin absorption spectrum obtained from a steady-state spectrophotometer measurement of the optical density of a minimally scattering medium. The determination of the corrected methemoglobin absorption spectrum takes into account the scattering from impurities in the methemoglobin solution containing no lipid colloid. Frequency-domain techniques allow for the separation of the absorbing from the scattering properties of multiple-scattering media, and these techniques thus provide an absolute measurement of the optical absorption spectra of the methemoglobin/lipid colloid suspension. One accurately determines the absolute methemoglobin absorption spectrum in the frequency domain by extracting the scattering and absorption coefficients from the phase shift Φ and average light intensity DC (or Φ and the amplitude of the light-intensity oscillations AC) data with relationships provided by diffusion theory, but one determines it less accurately by using the Φ and modulation M (MAC/DC) data and the diffusion theory relationships. In addition to the greater uncertainty in the absorption and scattering coefficients extracted from the Φ and M data, the optical parameters extracted from the Φ and M data exhibit systematically inaccurate behavior that cannot be explained by random noise in the system. Possible reasons for the systematically lower accuracy of the methemoglobin absorption spectrum obtained from Φ and M data are discussed.

© 1995 Optical Society of America

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  1. Three special journal issues on biomedical optics: Appl. Opt. 28, 2207–2357 (1989); Appl. Opt. 32, 367–627 (1993); Opt. Eng. 32, 244–266 (1993).
    [PubMed]
  2. G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, R. F. Potter, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 3–642 (1993).
  3. B. Chance, ed., Photon Migration in Tissue (Plenum, New York, 1989), pp. 1–195.
  4. K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
    [CrossRef]
  5. B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
    [CrossRef] [PubMed]
  6. M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
    [CrossRef] [PubMed]
  7. M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
    [CrossRef] [PubMed]
  8. S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distribution in tissue during laser irradiation,” Laser Surg. Med. 6, 494–503 (1987).
    [CrossRef]
  9. E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.
  10. J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).
  11. B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
    [CrossRef] [PubMed]
  12. L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
    [CrossRef]
  13. A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).
  14. A. H. Hielscher, F. K. Tittel, S. L. Jacques, “Noninvasive monitoring of blood oxygenation by phase resolved transmission spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 275–288 (1993).
  15. W. Cui, L. E. Ostrander, “Effect of local changes on phase shift measurement using phase modulation spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 289–296 (1993).
  16. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
    [CrossRef] [PubMed]
  17. M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
    [CrossRef] [PubMed]
  18. S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
    [CrossRef] [PubMed]
  19. J. B. Fishkin, E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
    [CrossRef] [PubMed]
  20. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 2, p. 17.
  21. J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979), Chap. 2, p. 66.
  22. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  23. J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
    [CrossRef]
  24. B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
    [CrossRef]
  25. B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).
  26. R. Lemberg, J. W. Legge, Hematin Compounds and Bile Pigments (Interscience, New York, 1949), Chap. 6, p. 218.
  27. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  28. J. M. Beechem, E. Gratton, “Fluorescence spectroscopy data analysis environment: a second generation global analysis program,” in Time-Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 70–82 (1989).
  29. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  30. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  31. B. C. Wilson, M. S. Patterson, B. W. Pogue, “Instrumentation for in vivo tissue spectroscopy and imaging,” in Medical Lasers and Systems II, D. M. Harris, C. M. Penney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1892, 132–147 (1993).
  32. L. Stryer, Biochemistry (Freeman, New York, 1975), Chap. 7, p. 151.
  33. J. B. Fishkin, “Imaging and spectroscopy of tissuelike phantoms using photon density waves: theory and experiments,” Ph.D. dissertation (University of Illinois at Urbana–Champaign, Urbana, Ill., 1994), Chap. 5, pp. 107–115.

1994

1993

1991

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

1990

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

1989

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

Three special journal issues on biomedical optics: Appl. Opt. 28, 2207–2357 (1989); Appl. Opt. 32, 367–627 (1993); Opt. Eng. 32, 244–266 (1993).
[PubMed]

B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

1988

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

1987

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distribution in tissue during laser irradiation,” Laser Surg. Med. 6, 494–503 (1987).
[CrossRef]

1985

J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
[CrossRef]

1973

Alcala, J. R.

J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
[CrossRef]

Alfano, R. R.

K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

Barbieri, B.

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).

Beechem, J. M.

J. M. Beechem, E. Gratton, “Fluorescence spectroscopy data analysis environment: a second generation global analysis program,” in Time-Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 70–82 (1989).

Berndt, K. W.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

Berns, M. W.

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

Burns, D. M.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 2, p. 17.

Chance, B.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

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

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Cope, M.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).

Cui, W.

W. Cui, L. E. Ostrander, “Effect of local changes on phase shift measurement using phase modulation spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 289–296 (1993).

De Piccoli, F.

B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).

Delpy, D. T.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).

Duderstadt, J. J.

J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979), Chap. 2, p. 66.

Duncan, A.

A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).

Fantini, S.

Feather, J. W.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Feddersen, B. A.

B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

Fishkin, J. B.

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

J. B. Fishkin, E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef] [PubMed]

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

J. B. Fishkin, “Imaging and spectroscopy of tissuelike phantoms using photon density waves: theory and experiments,” Ph.D. dissertation (University of Illinois at Urbana–Champaign, Urbana, Ill., 1994), Chap. 5, pp. 107–115.

Fountain, M.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Franceschini, M. A.

Gratton, E.

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

J. B. Fishkin, E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef] [PubMed]

B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
[CrossRef]

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

J. M. Beechem, E. Gratton, “Fluorescence spectroscopy data analysis environment: a second generation global analysis program,” in Time-Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 70–82 (1989).

B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

Greenfeld, R.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Hale, G. M.

Haskell, R. C.

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, F. K. Tittel, S. L. Jacques, “Noninvasive monitoring of blood oxygenation by phase resolved transmission spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 275–288 (1993).

Holtom, G.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distribution in tissue during laser irradiation,” Laser Surg. Med. 6, 494–503 (1987).
[CrossRef]

A. H. Hielscher, F. K. Tittel, S. L. Jacques, “Noninvasive monitoring of blood oxygenation by phase resolved transmission spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 275–288 (1993).

Jameson, D. M.

J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
[CrossRef]

Kent, J.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Lakowicz, J. R.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

Legge, J. W.

R. Lemberg, J. W. Legge, Hematin Compounds and Bile Pigments (Interscience, New York, 1949), Chap. 6, p. 218.

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Lemberg, R.

R. Lemberg, J. W. Legge, Hematin Compounds and Bile Pigments (Interscience, New York, 1949), Chap. 6, p. 218.

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

Mantulin, W. W.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Maris, M. B.

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

Martin, W. R.

J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979), Chap. 2, p. 66.

McCully, K.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Moes, C. J. M.

Moulton, J. D.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

Nioka, S.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Ostrander, L. E.

W. Cui, L. E. Ostrander, “Effect of local changes on phase shift measurement using phase modulation spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 289–296 (1993).

Patterson, M. S.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

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

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, B. W. Pogue, “Instrumentation for in vivo tissue spectroscopy and imaging,” in Medical Lasers and Systems II, D. M. Harris, C. M. Penney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1892, 132–147 (1993).

Piston, D. W.

B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

Pogue, B. W.

B. C. Wilson, M. S. Patterson, B. W. Pogue, “Instrumentation for in vivo tissue spectroscopy and imaging,” in Medical Lasers and Systems II, D. M. Harris, C. M. Penney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1892, 132–147 (1993).

Prahl, S. A.

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distribution in tissue during laser irradiation,” Laser Surg. Med. 6, 494–503 (1987).
[CrossRef]

Pushka, W.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Querry, M. R.

Sevick, E. M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Stryer, L.

L. Stryer, Biochemistry (Freeman, New York, 1975), Chap. 7, p. 151.

Svaasand, L. O.

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

Tittel, F. K.

A. H. Hielscher, F. K. Tittel, S. L. Jacques, “Noninvasive monitoring of blood oxygenation by phase resolved transmission spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 275–288 (1993).

Tromberg, B. J.

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

Tsay, T.

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

vandeVen, M.

B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).

vandeVen, M. J.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Whitlock, T. L.

A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).

Wilson, B. C.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

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

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, B. W. Pogue, “Instrumentation for in vivo tissue spectroscopy and imaging,” in Medical Lasers and Systems II, D. M. Harris, C. M. Penney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1892, 132–147 (1993).

Yoo, K. M.

K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 2, p. 17.

Anal. Biochem.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Anal. Biochem.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Anal. Instrum.

J. R. Alcala, E. Gratton, D. M. Jameson, “A multifrequency phase fluorometer using the harmonic content of a mode-locked laser,” Anal. Instrum. 14, 225–250 (1985).
[CrossRef]

Appl. Opt.

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

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissues,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Opt. Soc. Am. B

K. M. Yoo, F. Liu, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

J. Opt. Soc. Am. A

Laser Surg. Med.

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distribution in tissue during laser irradiation,” Laser Surg. Med. 6, 494–503 (1987).
[CrossRef]

Med. Biol. Eng. Comput.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

Opt. Eng.

L. O. Svaasand, B. J. Tromberg, R. C. Haskell, T. Tsay, M. W. Berns, “Tissue characterization and imaging using photon density waves,” Opt. Eng. 32, 258–266 (1993).
[CrossRef]

Photochem. Photobiol.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematopotphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

B. A. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

Three special journal issues on biomedical optics: Appl. Opt.

Three special journal issues on biomedical optics: Appl. Opt. 28, 2207–2357 (1989); Appl. Opt. 32, 367–627 (1993); Opt. Eng. 32, 244–266 (1993).
[PubMed]

Other

G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, R. F. Potter, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Proc. Soc. Photo-Opt. Instrum. Eng.IS11, 3–642 (1993).

B. Chance, ed., Photon Migration in Tissue (Plenum, New York, 1989), pp. 1–195.

E. Gratton, W. W. Mantulin, M. J. vandeVen, J. B. Fishkin, M. B. Maris, B. Chance, “The possibility of a near-infrared optical imaging system using frequency-domain methods,” in Proceedings of the Third International Conference on Peace through Mind/Brain Science (Hamamatsu, Hamamatsu City, Japan, 1990), pp. 183–189.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 2, p. 17.

J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979), Chap. 2, p. 66.

B. Barbieri, F. De Piccoli, M. vandeVen, E. Gratton, “What determines the uncertainty of phase and modulation measurements in frequency domain fluorometry,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 158–170 (1990).

R. Lemberg, J. W. Legge, Hematin Compounds and Bile Pigments (Interscience, New York, 1949), Chap. 6, p. 218.

J. M. Beechem, E. Gratton, “Fluorescence spectroscopy data analysis environment: a second generation global analysis program,” in Time-Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 70–82 (1989).

A. Duncan, T. L. Whitlock, M. Cope, D. T. Delpy, “A multiwavelength, wideband, intensity modulated optical spectrometer for near-infrared spectroscopy and imaging,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 248–257 (1993).

A. H. Hielscher, F. K. Tittel, S. L. Jacques, “Noninvasive monitoring of blood oxygenation by phase resolved transmission spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 275–288 (1993).

W. Cui, L. E. Ostrander, “Effect of local changes on phase shift measurement using phase modulation spectroscopy,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 289–296 (1993).

B. C. Wilson, M. S. Patterson, B. W. Pogue, “Instrumentation for in vivo tissue spectroscopy and imaging,” in Medical Lasers and Systems II, D. M. Harris, C. M. Penney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1892, 132–147 (1993).

L. Stryer, Biochemistry (Freeman, New York, 1975), Chap. 7, p. 151.

J. B. Fishkin, “Imaging and spectroscopy of tissuelike phantoms using photon density waves: theory and experiments,” Ph.D. dissertation (University of Illinois at Urbana–Champaign, Urbana, Ill., 1994), Chap. 5, pp. 107–115.

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Figures (9)

Fig. 1
Fig. 1

Time evolution of the intensity from a sinusoidally intensity-modulated source. The detected photon-density wave retains the same modulation frequency as the source photon-density wave but is delayed because of the phase velocity of the wave in the medium. The reduced amplitude of the detected wave arises from attenuation related to scattering and absorption processes. The demodulation is the ratio AC/DC at the detector normalized to the modulation of the source.

Fig. 2
Fig. 2

Typical geometry used to generate and detect a diffusive photon-density wave. Ω ^ d is the principal direction in which photons can enter the detector optical fiber. We assume that a Dirac-delta function δ(r) accurately describes the light source when r ≫1/μs′.

Fig. 3
Fig. 3

Schematic of the frequency-domain spectrophotometer used for measurements of the optical properties of turbid media. S1, S2, frequency synthesizers(PTS 500, Programmed Test Sources, Inc., and Marconi Instruments Signal Generator 2022A, respectively); A1, Hewlett-Packard 8447E amplifier; A2, Electronic Navigation Industry 603L rf amplifier. The mode-locker driver is from Coherent Model 7600. CD, cavity dumper (Coherent 7200). Synthesizers S1 and S2 are phase locked to the data acquisition, processing, and display portion of the instrument. Modulation frequencies range from 19.05 to 304.8 MHz. The cross-correlation frequency is 40 Hz.

Fig. 4
Fig. 4

Apparent absorption spectrum of a 2.5-μM solution of methemoglobin in a 50-mM sodium phosphate buffer of 7.23 pH. A transmission geometry in a sample-holding cuvette of 1-cm width and Eq. (1) allowed for the determination of this spectrum through measurement of the optical density of the medium.

Fig. 5
Fig. 5

Frequency-domain-determined scattering and absorption of a Liposyn III blank or reference medium. The solids content of this medium is 1.54% Liposyn. We determined the absolute absorption coefficients μa (●) and absolute reduced scattering coefficients μs′ (○) by simultaneously fitting DCrel and Φrel data, obtained at two relative distances (i.e., r = 2.5 and 3.0 cm relative to r0 = 2.0 cm) at multiple modulation frequencies ranging from 19.05 to 304.80 MHz, to Eqs. (5) and (7), respectively. The uncertainties in the μa and μs′ values recovered from the data analysis are of the order of 2 × 10−5 and 0.1 cm−1, respectively. Absorption of water (+) is as given by Hale and Querry.29 The Mie theory calculations of van Staveren et al.30 (solid curve) are for a medium consisting of a solids content of 1.54% Intralipid.

Fig. 6
Fig. 6

(a) Frequency-domain-determined scattering and absorption of the 2.5-μM methemoglobin/1.50% Liposyn/7.23 pH aqueous buffer medium. Absolute absorption coefficients μa (●) and absolute reduced scattering coefficients μs′ (○) were determined by simultaneously fitting DCrel and Φrel data, obtained at two relative distances (i.e., r = 2.5 and 3.0 cm relative to r0 = 2.0 cm) at multiple modulation frequencies ranging from 19.05 to 304.80 MHz, to Eqs. (5) and (7), respectively. The uncertainties in the μa and μs′ values recovered from the data analysis are of the order of 5 × 10−4 and 0.1 cm−1, respectively. The dashed curve is the same curve as shown in Fig. 4. The solid curve is the Rayleigh-scattering-corrected methemoglobin absorption spectrum that we obtained by subtracting scattering values determined by Eq. (15) from the dashed curve. (b) Same sample as in (a) except that we determined the medium optical parameters represented by the circles by simultaneously fitting ACrel and Φrel data to Eqs. (6) and (7), respectively. The uncertainties recovered from the data analysis here are the same as in (a). (c) Same sample as in (a) except that we determined the medium optical parameters represented by the circles by simultaneously fitting Φrel and Mrel data to Eqs. (7) and (8), respectively. The uncertainties in the μa and μs′ values recovered from the data analysis are of the order of 8 × 10−4 and 0.2 cm−1, respectively.

Fig. 7
Fig. 7

(a) Same sample as in Fig. 6(a) except that the DCrel and Φrel data simultaneously fit to Eqs. (5) and (7), respectively, were obtained at a single relative distance (i.e., r = 2.5 cm relative to r0 = 2.0 cm) and a single modulation frequency ω/2π. At a wavelength of 532 nm, ω/2π = 228.6 MHz, and at wavelengths of 570–700 nm, ω/2π = 114.30 MHz. The uncertainties in the μa and μs′ values recovered from the data analysis are of the order of 16 × 10−4 and 0.3 cm−1, respectively. (b) Same as Fig. 6(a). Shown for comparison.

Fig. 8
Fig. 8

(a) Plots of Eqs. (11)(14) with frequency-domain data: DCrel = 0.278, ACrel = 0.271, Φrel = 10.74°, and Mrel = 0.975. The data were obtained from the 2.5-μM methemoglobin/1.50% Liposyn/7.23 pH aqueous buffer medium at λ = 605 nm, ω/2π = 95.25 MHz and at r = 2.5 cm relative to r0 = 2.0 cm. (b) Same as (a) except that ω/2π = 190.50 MHz and DCrel = 0.279, ACrel = 0.260, Φrel = 20.56°, and Mrel = 0.932.

Fig. 9
Fig. 9

Plots of Eqs. (11) and (13) with frequency-domain data obtained from the 2.5-μM methemoglobin/1.50% Liposyn/7.23 pH aqueous buffer medium at λ = 605 nm and at r = 2.5 cm relative to r0 = 2.0 cm. These data are as follows: DCrel = 0.278; at ω/2π = 95.25 MHz, Φrel = 10.74°; at ω/2π = 114.30 MHz, Φrel = 12.71°; at ω/2π = 152.40 MHz, Φrel = 16.53°; at ω/2π = 190.50 MHz, Φrel = 20.56°; at ω/2π = 247.65 MHz, Φrel = 25.89°. The Φrel curves [i.e., the curves generated by Eq. (13)] become more horizontal with increasing modulation frequency.

Equations (15)

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[ μ a ] app μ a + μ s 1 L log e I 0 I [ C ] ,
U ( r , t ) = S 4 π v D r exp [ - r ( μ a D ) 1 / 2 ] + S A 4 π v D r × exp { - r ( v 2 μ a 2 + ω 2 v 2 D 2 ) 1 / 4 cos [ 1 2 tan - 1 ( ω v μ a ) ] } × exp { i r ( v 2 μ a 2 + ω 2 v 2 D 2 ) 1 / 4 × sin [ 1 2 tan - 1 ( ω v μ a ) ] - i ( ω t + ) } .
D 1 3 ( μ a + μ s )
μ s ( 1 - g ) μ s
D C rel D C ( r ) D C ( r 0 ) = r 0 r exp [ - r ( r - r 0 ) ( μ a D ) 1 / 2 ] ,
A C rel A C ( r ) A C ( r 0 ) = r 0 r exp { - ( r - r 0 ) ( v 2 μ a 2 + ω 2 v 2 D 2 ) 1 / 4 × cos [ 1 2 tan - 1 ( ω v μ a ) ] } ,
Φ rel Φ ( r ) - Φ ( r 0 ) = ( r - r 0 ) ( v 2 μ a 2 + ω 2 v 2 D 2 ) 1 / 4 × sin [ 1 2 tan - 1 ( ω v μ a ) ] .
M rel A C rel / D C rel .
sin β 2 = ( 1 - cos β 2 ) 1 / 2 ,             cos β 2 = ( 1 + cos β 2 ) 1 / 2 ,
β tan - 1 ( ω v μ a ) .
μ s = 1 3 μ a [ ln ( r / r 0 D C rel ) r - r 0 ] 2 - μ a ;
μ s = 2 3 μ a [ ln ( r / r 0 A C rel ) r - r 0 ] 2 { [ 1 + ( ω v μ a ) 2 ] 1 / 2 + 1 } - 1 - μ a ;
μ s = 2 3 μ a [ Φ rel r - r 0 ] 2 { [ 1 + ( ω v μ a ) 2 ] 1 / 2 - 1 } - 1 - μ a ;
μ s = 1 3 μ a [ ln ( M rel ) r - r 0 ] 2 × ( 1 - 1 2 { [ 1 + ( ω v μ a ) 2 ] 1 / 2 + 1 } 1 / 2 ) - 2 - μ a ;
μ s = α λ 4 ,

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