Abstract

We present a method to extend rank-annihilation-factor analysis (RAFA) for the analysis of fluorescence from homogeneous turbid samples. The method is based on a fundamental relationship between the fluorescence of a dilute solution and that of a turbid solution. We have derived this relationship, known as the transfer function, for turbid materials using the two-flux Kubelka–Munk theory. The method is tested with spectroscopic data from optically thin and turbid samples of the media of a human aorta. At 450-nm excitation, agreement between the measured and predicted dilute-solution fluorescence spectra is within 5% at all emission wavelengths; at 340-nm excitation, agreement is within 20% at all wavelengths, with some residual Soret-band absorption. The simulations presented indicate that the transfer function is markedly more sensitive to absorption than to scattering properties.

© 1994 Optical Society of America

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  1. R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
    [CrossRef] [PubMed]
  2. C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
    [PubMed]
  3. R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
    [CrossRef] [PubMed]
  4. M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
    [CrossRef] [PubMed]
  5. R. R. Alfano, G. C. Tang, “Optical spectroscopic diagnosis of caner and normal breast tissues,” J. Opt. Soc. Am. 6, 1015–1023 (1989).
    [CrossRef]
  6. R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
    [PubMed]
  7. L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
    [CrossRef] [PubMed]
  8. W. F. Cheong, A. J. Welch, “A review of the optical properties of tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  9. J. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983) pp. 42–49.
  10. G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).
  11. Z. Z. Hugus, A. A. El-Awady, “The determination of the number of species present in a system: a new matrix rank treatment of spectrophotometric data,” J. Phys. Chem. 75, 2954–2957 (1977).
  12. C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
    [CrossRef]
  13. C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
    [CrossRef]
  14. A. Lorber, “Quantifying chemical composition from two-dimensional data arrays,” Anal. Chim. Acta 164, 293–297 (1984).
    [CrossRef]
  15. E. Malinowski, Factor Analysis in Chemistry (Wiley, New York, 1991), Chap. 6, pp. 188–199.
  16. M. Keijzer, R. R. Richards-Kortum, S. L. Jaques, M. S. Feld, “Fluorescence spetroscopy of turbid media: autofluorescene of human aorta,” Appl. Opt. 28, 4286–4292 (1989).
    [CrossRef] [PubMed]
  17. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948).
    [CrossRef] [PubMed]
  18. I. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) p. 202.
  19. D. G. Taylor, J. N. Demas, “Light-intensity measurements I: large-area bolometers with μWatt sensitivities and absolute calibration of the Rhodamine B quantum counter,” Anal. Chem. 51, 7112–7117 (1979).
    [CrossRef]
  20. S. Prahl, “Light transport in tissue” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988), pp. 75–90.
  21. M. J. C. Van Gemert, W. M. Star, “Relations between the Kubelka–Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).
  22. J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
    [CrossRef] [PubMed]
  23. R. A. J. Groenhius, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I: Theory,” Appl. Opt. 16, 2456–2462 (1983).
    [CrossRef]

1993 (1)

1991 (1)

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

1990 (3)

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

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

1989 (4)

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

R. R. Alfano, G. C. Tang, “Optical spectroscopic diagnosis of caner and normal breast tissues,” J. Opt. Soc. Am. 6, 1015–1023 (1989).
[CrossRef]

M. Keijzer, R. R. Richards-Kortum, S. L. Jaques, M. S. Feld, “Fluorescence spetroscopy of turbid media: autofluorescene of human aorta,” Appl. Opt. 28, 4286–4292 (1989).
[CrossRef] [PubMed]

1988 (1)

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

1987 (1)

M. J. C. Van Gemert, W. M. Star, “Relations between the Kubelka–Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

1986 (1)

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

1984 (1)

A. Lorber, “Quantifying chemical composition from two-dimensional data arrays,” Anal. Chim. Acta 164, 293–297 (1984).
[CrossRef]

1983 (1)

R. A. J. Groenhius, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I: Theory,” Appl. Opt. 16, 2456–2462 (1983).
[CrossRef]

1980 (1)

C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
[CrossRef]

1979 (1)

D. G. Taylor, J. N. Demas, “Light-intensity measurements I: large-area bolometers with μWatt sensitivities and absolute calibration of the Rhodamine B quantum counter,” Anal. Chem. 51, 7112–7117 (1979).
[CrossRef]

1978 (1)

C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
[CrossRef]

1977 (1)

Z. Z. Hugus, A. A. El-Awady, “The determination of the number of species present in a system: a new matrix rank treatment of spectrophotometric data,” J. Phys. Chem. 75, 2954–2957 (1977).

1948 (1)

Alfano, R. R.

R. R. Alfano, G. C. Tang, “Optical spectroscopic diagnosis of caner and normal breast tissues,” J. Opt. Soc. Am. 6, 1015–1023 (1989).
[CrossRef]

Balaban, R. S.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Blackman, R.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Bonner, R. F.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Boon, T. A.

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Boyce, G. A.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Breederveld, D.

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Cheong, W. F.

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

Christian, G. D.

C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
[CrossRef]

Christian, G. D. S.

C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
[CrossRef]

Cothren, R. M.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Cutruzzola, F. W.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

Davidson, E. R.

C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
[CrossRef]

C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
[CrossRef]

Deckelbaum, L. I.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Demas, J. N.

D. G. Taylor, J. N. Demas, “Light-intensity measurements I: large-area bolometers with μWatt sensitivities and absolute calibration of the Rhodamine B quantum counter,” Anal. Chem. 51, 7112–7117 (1979).
[CrossRef]

Doxtader, M.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

El-Awady, A. A.

Z. Z. Hugus, A. A. El-Awady, “The determination of the number of species present in a system: a new matrix rank treatment of spectrophotometric data,” J. Phys. Chem. 75, 2954–2957 (1977).

Enriquez, R.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

Feld, M. S.

J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
[CrossRef] [PubMed]

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

M. Keijzer, R. R. Richards-Kortum, S. L. Jaques, M. S. Feld, “Fluorescence spetroscopy of turbid media: autofluorescene of human aorta,” Appl. Opt. 28, 4286–4292 (1989).
[CrossRef] [PubMed]

Ferwerda, H. A.

R. A. J. Groenhius, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I: Theory,” Appl. Opt. 16, 2456–2462 (1983).
[CrossRef]

Fitzmaurice, M.

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Garrand, T. J.

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Gijsbers, G. H. M.

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Gindi, G. R.

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Granovsky, M.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Groenhius, R. A. J.

R. A. J. Groenhius, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I: Theory,” Appl. Opt. 16, 2456–2462 (1983).
[CrossRef]

Hayes, G. B.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Ho, C. N.

C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
[CrossRef]

C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
[CrossRef]

Hugus, Z. Z.

Z. Z. Hugus, A. A. El-Awady, “The determination of the number of species present in a system: a new matrix rank treatment of spectrophotometric data,” J. Phys. Chem. 75, 2954–2957 (1977).

Ishimaru, I.

I. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) p. 202.

Ivanc, T.

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Jaques, S. L.

Kapadia, C. R.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

Keijzer, M.

Kramer, J. R.

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Kubelka, P.

Laifer, L. I.

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Lakowicz, J.

J. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983) pp. 42–49.

Langelaar, J.

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Leon, M. B.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Lorber, A.

A. Lorber, “Quantifying chemical composition from two-dimensional data arrays,” Anal. Chim. Acta 164, 293–297 (1984).
[CrossRef]

Lu, D. Y.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Macy, W. W.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Malinowski, E.

E. Malinowski, Factor Analysis in Chemistry (Wiley, New York, 1991), Chap. 6, pp. 188–199.

O’Brien, K. M.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Petras, R. E.

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Prahl, S.

S. Prahl, “Light transport in tissue” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988), pp. 75–90.

Prevosti, L. G.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Ratliff, N. B.

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Rava, R.

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Rava, R. P.

J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
[CrossRef] [PubMed]

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Rettschnick, R. P. H.

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Richards-Kortum, R. R.

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

M. Keijzer, R. R. Richards-Kortum, S. L. Jaques, M. S. Feld, “Fluorescence spetroscopy of turbid media: autofluorescene of human aorta,” Appl. Opt. 28, 4286–4292 (1989).
[CrossRef] [PubMed]

Sivak, M.

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

Smith, P. D.

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

Star, W. M.

M. J. C. Van Gemert, W. M. Star, “Relations between the Kubelka–Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

Stetz, M. L.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Tang, G. C.

R. R. Alfano, G. C. Tang, “Optical spectroscopic diagnosis of caner and normal breast tissues,” J. Opt. Soc. Am. 6, 1015–1023 (1989).
[CrossRef]

Taylor, D. G.

D. G. Taylor, J. N. Demas, “Light-intensity measurements I: large-area bolometers with μWatt sensitivities and absolute calibration of the Rhodamine B quantum counter,” Anal. Chem. 51, 7112–7117 (1979).
[CrossRef]

Ten Bosch, J. J.

R. A. J. Groenhius, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I: Theory,” Appl. Opt. 16, 2456–2462 (1983).
[CrossRef]

Tong, L.

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Tong, L. L.

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

Van Gemert, M. J. C.

M. J. C. Van Gemert, W. M. Star, “Relations between the Kubelka–Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Welch, A. J.

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

Wu, J.

Anal. Chem. (3)

C. N. Ho, G. D. Christian, E. R. Davidson, “Application of the method of rank annihilation to quantitative analysis of multicomponent fluorescence data from the video fluorometer,” Anal. Chem. 50, 1108–1113 (1978).
[CrossRef]

C. N. Ho, G. D. S. Christian, E. R. Davidson, “Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,” Anal. Chem. 52, 1071–1079 (1980).
[CrossRef]

D. G. Taylor, J. N. Demas, “Light-intensity measurements I: large-area bolometers with μWatt sensitivities and absolute calibration of the Rhodamine B quantum counter,” Anal. Chem. 51, 7112–7117 (1979).
[CrossRef]

Anal. Chim. Acta (1)

A. Lorber, “Quantifying chemical composition from two-dimensional data arrays,” Anal. Chim. Acta 164, 293–297 (1984).
[CrossRef]

Appl. Opt. (3)

Circulation (1)

L. I. Laifer, K. M. O’Brien, M. L. Stetz, G. R. Gindi, T. J. Garrand, L. I. Deckelbaum, “Biochemical basis for the difference between normal and atherosclerotic arterial fluorescence,” Circulation 80, 1893–1901 (1989).
[CrossRef] [PubMed]

Gastroenterology (1)

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99, 150–157 (1990).
[PubMed]

Gastrointest. Endosc. (1)

R. M. Cothren, R. R. Richards-Kortum, M. Sivak, M. Fitzmaurice, R. P. Rava, G. A. Boyce, G. B. Hayes, M. Doxtader, R. Blackman, T. Ivanc, M. S. Feld, R. E. Petras, “Gastrointestinal tissue diagnosis by laser-induced fluorescence spectroscopy at endoscopy,” Gastrointest. Endosc. 36, 105–111 (1990).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

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

IEEE Trans. Biomed. Eng. (1)

R. R. Richards-Kortum, R. Rava, M. Fitzmaurice, L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

J. Am. Coll. Cardiol. (1)

M. B. Leon, D. Y. Lu, L. G. Prevosti, W. W. Macy, P. D. Smith, M. Granovsky, R. F. Bonner, R. S. Balaban, “Human arterial surface fluorescence: atherosclerotic plaque identification and effects of laser atheroma ablation,” J. Am. Coll. Cardiol. 12, 94–102 (1988).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

R. R. Alfano, G. C. Tang, “Optical spectroscopic diagnosis of caner and normal breast tissues,” J. Opt. Soc. Am. 6, 1015–1023 (1989).
[CrossRef]

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Lasers Life Sci. (2)

M. J. C. Van Gemert, W. M. Star, “Relations between the Kubelka–Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

G. H. M. Gijsbers, D. Breederveld, M. J. C. van Gemert, T. A. Boon, J. Langelaar, R. P. H. Rettschnick, “In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative,” Lasers Life Sci. 1, 29–48 (1986).

Photochem. Photobiol. (1)

R. R. Richards-Kortum, R. P. Rava, R. E. Petras, M. Fitzmaurice, L. L. Tong, M. Sivak, M. S. Feld, “Clinical applications of fluorescence excitation emission matrices: diagnosis of colonic adenomas,” Photochem. Photobiol. 53, 777–786 (1991).
[PubMed]

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J. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983) pp. 42–49.

I. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) p. 202.

S. Prahl, “Light transport in tissue” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988), pp. 75–90.

E. Malinowski, Factor Analysis in Chemistry (Wiley, New York, 1991), Chap. 6, pp. 188–199.

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Figures (6)

Fig. 1
Fig. 1

Geometry for the fluorecence model. H in represents the probability that an excitation photon (solid arrows) will reach a thin layer dz, located at depth z below the sample surface. Similarly, H out represents the probability that a fluorescence photon (dashed arrows) generated in the layer dz will reach the front surface of the sample.

Fig. 2
Fig. 2

Method of calculating H out. Fluorescence is assumed to be emitted equally in the +z direction (dashed arrows) and −z direction (solid arrows). The series approximation of Ref. 10 is used to describe the fraction of fluorescence generated at z that reaches the front surface. R z = R z j ) and T z = T z j ) indicate the reflection and transmission coefficients, respectively, at the emission wavelength of the layer of tissue of thickness z above the fluorescing layer. R L Tur z indicates the reflection coefficient at the emission wavelength of the layer of tissue of thickness L Turz below the fluorescing layer.

Fig. 3
Fig. 3

Emission spectra of 4-μm-thick (dilute) and 250-μm-thick (turbid) sections of media at the 340-nm excitation. Fluorescence intensity has been normalized as to excitation intensity and sample thickness. (The same set of arbitrary units is maintained throughout the paper.)

Fig. 4
Fig. 4

Measurements from a 250-μm-thick section of aortic media: (a) Diffuse reflectance and transmission spectra over the range 300–700 nm, (b) the corresponding Kubelka-Munk absorption and scattering coefficients, (c) the corresponding transport optical properties μ a and μ s ′ where g = 0.88.

Fig. 5
Fig. 5

Comparison of measured and calculated data: (a) the transfer function for the 340-nm excitation; (b) measured turbid- and dilute-emission spectra at the 340-nm excitation wavelength compared with the calculated dilute-emission spectrum based on the transfer function (a); (c) measured turbid- and dilute-emission spectra at the 340-nm excitation compared with the calculated dilute-emission spectrum where all data has been normalized to a value of 1 at 460 nm, indicated by the arrow; (d) measured turbid- and dilute-emission spectra at the 450-nm excitation compared with the calculated dilute-emission spectrum.

Fig. 6
Fig. 6

Sensitivity of the transfer function to the scattering and absorption coefficients: (a) the transfer function as a function of S KM while A KM is held constant (see text): the arrow indicates the value of S KM for aorta at 340 nm; (b) the transfer function as a function of A KM while S KM is held constant: the arrow indicates the value of A KM for aorta at 340 nm. Note the difference of a factor of 10 in the y axes.

Equations (20)

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EEM Dil i j = ( Ω 4 π ) S Total ( λ i , λ j ) I ( λ i ) L dil = ( Ω 4 π ) k = 1 N 2.3 C k k ( λ i ) ϕ k ( λ j ) , = ( Ω 4 π ) k = 1 N μ a k ( λ i ) ϕ k ( λ j ) ,
d S Tur Front ( λ i , λ j , z ) = I ( λ i ) H in [ op . prop . ( λ i ) , z , L Tur ] × [ k = 1 N 2.3 C k k ( λ i ) ϕ k ( λ j ) d z ] × H out [ op . prop . ( λ j ) , z , L Tur ] ,
S Tur Front ( λ i , λ j ) = 0 L Tur d S Tur Front ( λ i , λ j , z ) = I ( λ i ) 0 L Tur d z H in [ op . prop . ( λ i ) , z , L Tur ] × [ k = 1 N 2.3 C k k ( λ i ) ϕ k ( λ j ) ] × H out [ op . porp . ( λ j ) , z , L Tur ] .
S Tur Front ( λ j , λ j ) = I ( λ i ) [ k = 1 N 2.3 C k k ( λ i ) ϕ k ( λ j ) ] × 0 L Tur d z H in [ op . porp . ( λ i ) , z , L Tur ] × H out [ op . prop . ( λ j ) , z , L Tur ] .
EEM Tur i j = S Tur Front ( λ i , λ j , L Tur ) I ( λ i ) L Tur ( Ω 2 π ) .
EEM Tur i j = 2 EEM Dil i j L Tur 0 L Tur d z H in [ op . prop . ( λ i ) , z , L Tur ] × H out [ op . prop . ( λ j ) , z , L Tur ] = EEM Dil i j 2 TF [ op . prop . ( λ i , λ j ) , z , L Tur ] L Tur .
H in ( λ i , z , L Tur ) = 2 C ( λ i , L Tur ) e κ i z + 2 B ( λ i , L Tur ) e - κ i z ,
C ( λ i , L Tur ) = - ( 1 - β i ) e - κ i L Tur ( 1 + β i ) 2 e κ i L Tur - ( 1 - β i ) 2 e - κ i L Tur - ( 1 - β i ) e - κ i L Tur D i ( L Tur ) , B ( λ i , L ) = ( 1 + β i ) e κ i L Tur D i ( L Tur ) , β i = [ A KM ( λ i ) A KM ( λ i ) + 2 S KM ( λ i ) ] 1 / 2 , κ i = { A KM ( λ i ) [ A KM ( λ i ) + 2 S KM ( λ i ) ] } 1 / 2 .
H out [ op . prop . ( λ j ) , z , L Tur ] = 1 / 2 [ T z + R L Tur - z T z + ( R z R L Tur - z ) 2 T z + ] + 1 / 2 [ R L Tur - z T z + R L Tur - z R z R L Tur - z T z + R L Tur - z ( R z R L tur - z ) 2 T z + ] = 1 2 T z ( 1 - R L Tur - z R z ) + 1 2 T z R L Tur - z ( 1 - R L Tur - z R z ) ,
R z ( λ j ) = ( 1 - β j 2 ) ( e κ j z - e - κ j z ) D j ( z ) , T z ( λ j ) = 4 β j D j ( z ) .
H out = [ ( 1 + β j ) e κ j ( L Tur - z ) - ( 1 - β j ) e - κ j ( L Tur - z ) ] D j ( L Tur ) .
TF KM ( λ i , λ j , L Tur ) = 2 D i ( L Tur ) D j ( L Tur ) [ - p 1 q 1 ( e - q 1 L Tur - 1 ) + p 2 q 1 ( e q 1 L Tur - 1 ) + - p 3 q 2 ( e - q 2 L Tur - 1 ) + p 4 q 2 ( e q 2 L Tur - 1 ) ] ,
p 1 = ( β i + 1 ) ( β j + 1 ) e ( κ i + κ j ) L Tur , p 2 = ( β i - 1 ) ( β j - 1 ) e - ( κ i + κ j ) L Tur , p 3 = ( β i + 1 ) ( β j - 1 ) e ( κ i - κ j ) L Tur , p 4 = ( β i - 1 ) ( β j + 1 ) e - ( κ i - κ j ) L Tur , q 1 = κ i + κ j , q 2 = κ i - κ j .
TF KM ( λ i , λ j ) = 2 ( β i + 1 ) ( β j + 1 ) ( κ i + κ j ) .
TF KM ( λ i , λ j ) = 1 2 [ A KM ( λ i ) + A KM ( λ j ) ] .
EEM Dil i j = ( Ω 4 π ) S Total ( λ i , λ j ) I ( λ i ) L dil = ( Ω 4 π ) k = 1 N 2.3 C k k ( λ i ) ϕ k ( λ j ) = ( Ω 4 π ) k = 1 N μ a k ( λ i ) ϕ k ( λ j ) ,
EEM Dil = X Φ T ,
EEM Mix = EEM Mix - C A ( EEM A ) ,
det EEM Mix = det EEM Mix - C A EEM A = 0
C A = 1 Tr ( a b T S - 1 )

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