Abstract

We present a novel technique, intrinsic Raman spectroscopy (IRS), to correct turbidity-induced Raman spectral distortions, resulting in the intrinsic Raman spectrum that would be observed in the absence of scattering and absorption. We develop an expression relating the observed and intrinsic Raman spectra through diffuse reflectance using the photon migration depiction of light transport. Numerical simulations are employed to validate the theoretical results and study the dependence of this expression on sample size and elastic scattering anisotropy.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  32. G. Zonios, L. T. Perelman, V. M. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, "Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo," Appl. Opt. 38, 6628-6637 (1999).
    [CrossRef]
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    [CrossRef]
  34. A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
    [CrossRef]
  35. T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2007

W.-C. Shih, K. L. Bechtel, and M. S. Feld, "Constrained regularization: Hybrid method for multivariate calibration," Anal. Chem. 79, 234-239 (2007).
[CrossRef]

2006

2005

S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
[CrossRef] [PubMed]

P. Matousek, I. P. Clark, E. R. C. Draper, M. D. Morris, A. E. Goodship, N. Everall, M. Towrie, W. F. Finney, and A. W. Parker, "Subsurface probing in diffusely scattering media using spatially offset Raman spectroscopy," Appl. Spectrosc. 59, 393-400 (2005).
[CrossRef] [PubMed]

P. J. Aarnoutse and J. A. Westerhuis, "Quantitative Raman reaction monitoring using the solvent as internal standard," Anal. Chem. 77, 1228-1236 (2005).
[CrossRef] [PubMed]

J. C. Finlay and T. H. Foster, "Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model," Appl. Opt. 44, 1917-1933 (2005).
[CrossRef] [PubMed]

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

M. A. Arnold and G. W. Small, "Noninvasive glucose sensing," Anal. Chem. 77, 5429-5439 (2005).
[CrossRef] [PubMed]

2003

G. L. Cote, R. M. Lec, and M. V. Pishko, "Emerging biomedical sensing technologies and their applications," IEEE Sens. J. 3, 251-266 (2003).
[CrossRef]

K. R. Diamond, T. J. Farrell, and M. S. Patterson, "Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence," Phys. Med. Biol. 48, 4135-4149 (2003).
[CrossRef]

N. C. Biswal, S. Gupta, N. Ghosh, and A. Pradhan, "Recovery of turbidity free fluorescence from measured fluorescence: an experimental approach," Opt. Express 11, 3320-3331 (2003).
[CrossRef] [PubMed]

T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

F. Fabbri, M. A. Franceschini, and S. Fantini, "Characterization of spatial and temporal variations in the optical properties of tissuelike media with diffuse reflectance imaging," Appl. Opt. 42, 3063-3072 (2003).
[CrossRef] [PubMed]

2002

S. Kuba, and H. Knozinger, "Time-resolved in situ Raman spectroscopy of working catalysts: sulfated and tungstated zirconia," J. Raman Spectrosc. 33, 325-332 (2002).
[CrossRef]

2001

2000

1999

O. S. Khalil, "Spectroscopic and clinical aspects of noninvasive glucose measurements," Clin. Chem. 45, 165-177 (1999).
[PubMed]

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

G. Zonios, L. T. Perelman, V. M. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, "Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo," Appl. Opt. 38, 6628-6637 (1999).
[CrossRef]

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

1998

B. W. Pogue and G. Burke, "Fiber-optic bundle design for quantitative fluorescence measurement from tissue," Appl. Opt. 37, 7429-7436 (1998).
[CrossRef]

N. N. Zhadin and R. R. Alfano, "Correction of the internal absorption effect in fluorescence emission and excitation spectra from absorbing and highly scattering media: Theory and experiment," J. Biomed. Opt. 3, 171-186 (1998).
[CrossRef]

1997

1996

1994

M. S. Patterson and B. W. Pogue, "Mathematical-model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissue," Appl. Opt. 33, 1963-1974 (1994).
[CrossRef] [PubMed]

D. N. Waters, "Raman spectroscopy of powders - effects of light absorption and scattering," Spectrochim. Acta, Part A 50, 1833-1840 (1994).
[CrossRef]

1993

1992

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

1990

B. C. Wilson and S. L. Jacques, "Optical reflectance and transmittance of tissues - principles and applications," IEEE J. Quantum Electron. 26, 2186-2199 (1990).
[CrossRef]

Aalders, M. C.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Aarnoutse, P. J.

P. J. Aarnoutse and J. A. Westerhuis, "Quantitative Raman reaction monitoring using the solvent as internal standard," Anal. Chem. 77, 1228-1236 (2005).
[CrossRef] [PubMed]

Alfano, R. R.

N. N. Zhadin and R. R. Alfano, "Correction of the internal absorption effect in fluorescence emission and excitation spectra from absorbing and highly scattering media: Theory and experiment," J. Biomed. Opt. 3, 171-186 (1998).
[CrossRef]

Andersson-Engels, S.

Arnold, M. A.

M. A. Arnold and G. W. Small, "Noninvasive glucose sensing," Anal. Chem. 77, 5429-5439 (2005).
[CrossRef] [PubMed]

Aruna, P.

Backman, V. M.

Bechtel, K. L.

W.-C. Shih, K. L. Bechtel, and M. S. Feld, "Constrained regularization: Hybrid method for multivariate calibration," Anal. Chem. 79, 234-239 (2007).
[CrossRef]

Biswal, N. C.

Burke, G.

Chan, E.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Clark, I. P.

Cote, G. L.

G. L. Cote, R. M. Lec, and M. V. Pishko, "Emerging biomedical sensing technologies and their applications," IEEE Sens. J. 3, 251-266 (2003).
[CrossRef]

Criswell, G.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Cross, F. W.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Dalgaard, T.

Dam, J. S.

Diamond, K.

Diamond, K. R.

K. R. Diamond, T. J. Farrell, and M. S. Patterson, "Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence," Phys. Med. Biol. 48, 4135-4149 (2003).
[CrossRef]

Dimou, A.

Doornbos, R. M. P.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Dorschel, K.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Draper, E. R. C.

Enejder, A. M. K.

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Everall, N.

Fabbri, F.

Fabricius, P. E.

Fantini, S.

Farrell, T. J.

K. R. Diamond, T. J. Farrell, and M. S. Patterson, "Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence," Phys. Med. Biol. 48, 4135-4149 (2003).
[CrossRef]

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Feld, M. S.

Field, M. S.

Finlay, J. C.

Finney, W. F.

Fitzmaurice, M.

Foster, T. H.

Franceschini, M. A.

Friebel, M.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Gardner, C.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Gardner, C. M.

Georgakoudi, I.

Ghosh, N.

Goodship, A. E.

Gupta, S.

Hahn, A.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Horowitz, G. L.

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Hull, E. L.

Hunter, M.

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Jacques, S. L.

C. M. Gardner, S. L. Jacques, and A. J. Welch, "Fluorescence spectroscopy of tissue: Recovery of intrinsic fluorescence from measured fluorescence," Appl. Opt. 35, 1780-1792 (1996).
[CrossRef] [PubMed]

B. C. Wilson and S. L. Jacques, "Optical reflectance and transmittance of tissues - principles and applications," IEEE J. Quantum Electron. 26, 2186-2199 (1990).
[CrossRef]

Khalil, O. S.

O. S. Khalil, "Spectroscopic and clinical aspects of noninvasive glucose measurements," Clin. Chem. 45, 165-177 (1999).
[PubMed]

Knozinger, H.

S. Kuba, and H. Knozinger, "Time-resolved in situ Raman spectroscopy of working catalysts: sulfated and tungstated zirconia," J. Raman Spectrosc. 33, 325-332 (2002).
[CrossRef]

Kox, M. H. F.

S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
[CrossRef] [PubMed]

Kuba, S.

S. Kuba, and H. Knozinger, "Time-resolved in situ Raman spectroscopy of working catalysts: sulfated and tungstated zirconia," J. Raman Spectrosc. 33, 325-332 (2002).
[CrossRef]

Lang, R.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Lec, R. M.

G. L. Cote, R. M. Lec, and M. V. Pishko, "Emerging biomedical sensing technologies and their applications," IEEE Sens. J. 3, 251-266 (2003).
[CrossRef]

Manoharan, R.

Matousek, P.

Morris, M. D.

Muller, G.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Muller, M. G.

Nichols, M. G.

Nijhuis, T. A.

S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
[CrossRef] [PubMed]

T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

Oh, J.

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Padgett, N.

Parker, A. W.

Partovi, F.

Patterson, M. S.

K. R. Diamond, T. J. Farrell, and M. S. Patterson, "Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence," Phys. Med. Biol. 48, 4135-4149 (2003).
[CrossRef]

R. Weersink, M. S. Patterson, K. Diamond, S. Silver, and N. Padgett, "Noninvasive measurement of fluorophore concentration in turbid media with a simple fluorescence/reflectance ratio technique," Appl. Opt. 40, 6389-6395 (2001).
[CrossRef]

M. S. Patterson and B. W. Pogue, "Mathematical-model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissue," Appl. Opt. 33, 1963-1974 (1994).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Pedersen, C. B.

Perelman, L. T.

Pfefer, J.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Pishko, M. V.

G. L. Cote, R. M. Lec, and M. V. Pishko, "Emerging biomedical sensing technologies and their applications," IEEE Sens. J. 3, 251-266 (2003).
[CrossRef]

Pogue, B. W.

Pradhan, A.

Rava, R. P.

Richards-Kortum, R.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
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A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
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A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Shih, W. C.

A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

Shih, W.-C.

W.-C. Shih, K. L. Bechtel, and M. S. Feld, "Constrained regularization: Hybrid method for multivariate calibration," Anal. Chem. 79, 234-239 (2007).
[CrossRef]

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Small, G. W.

M. A. Arnold and G. W. Small, "Noninvasive glucose sensing," Anal. Chem. 77, 5429-5439 (2005).
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R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
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S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
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T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

Towrie, M.

Van Dam, J.

Visser, T.

S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
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T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

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A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Waters, D. N.

D. N. Waters, "Raman spectroscopy of powders - effects of light absorption and scattering," Spectrochim. Acta, Part A 50, 1833-1840 (1994).
[CrossRef]

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S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
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T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

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Welch, A. J.

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[CrossRef]

P. J. Aarnoutse and J. A. Westerhuis, "Quantitative Raman reaction monitoring using the solvent as internal standard," Anal. Chem. 77, 1228-1236 (2005).
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C. M. Gardner, S. L. Jacques, and A. J. Welch, "Fluorescence spectroscopy of tissue: Recovery of intrinsic fluorescence from measured fluorescence," Appl. Opt. 35, 1780-1792 (1996).
[CrossRef] [PubMed]

M. G. Muller, I. Georgakoudi, Q. G. Zhang, J. Wu, and M. S. Feld, "Intrinsic fluorescence spectroscopy in turbid media: disentangling effects of scattering and absorption," Appl. Opt. 40, 4633-4646 (2001).
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R. Weersink, M. S. Patterson, K. Diamond, S. Silver, and N. Padgett, "Noninvasive measurement of fluorophore concentration in turbid media with a simple fluorescence/reflectance ratio technique," Appl. Opt. 40, 6389-6395 (2001).
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G. Zonios, L. T. Perelman, V. M. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, "Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo," Appl. Opt. 38, 6628-6637 (1999).
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M. G. Nichols, E. L. Hull, and T. H. Foster, "Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems," Appl. Opt. 36, 93-104 (1997).
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Appl. Spectrosc.

Clin. Chem.

O. S. Khalil, "Spectroscopic and clinical aspects of noninvasive glucose measurements," Clin. Chem. 45, 165-177 (1999).
[PubMed]

IEEE J. Quantum Electron.

B. C. Wilson and S. L. Jacques, "Optical reflectance and transmittance of tissues - principles and applications," IEEE J. Quantum Electron. 26, 2186-2199 (1990).
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G. L. Cote, R. M. Lec, and M. V. Pishko, "Emerging biomedical sensing technologies and their applications," IEEE Sens. J. 3, 251-266 (2003).
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A. M. K. Enejder, T. G. Scecina, J. Oh, M. Hunter, W. C. Shih, S. Sasic, G. L. Horowitz, and M. S. Feld, "Raman spectroscopy for noninvasive glucose measurements," J. Biomed. Opt. 10, 031114 (2005).
[CrossRef] [PubMed]

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, "Optical properties of circulating human blood in the wavelength range 400-2500 NM," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

N. N. Zhadin and R. R. Alfano, "Correction of the internal absorption effect in fluorescence emission and excitation spectra from absorbing and highly scattering media: Theory and experiment," J. Biomed. Opt. 3, 171-186 (1998).
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S. Kuba, and H. Knozinger, "Time-resolved in situ Raman spectroscopy of working catalysts: sulfated and tungstated zirconia," J. Raman Spectrosc. 33, 325-332 (2002).
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Lasers Surg. Med.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, "Propagation of fluorescent light," Lasers Surg. Med. 21, 166-178 (1997).
[CrossRef] [PubMed]

Med. Phys.

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Chem. Chem. Phys.

T. A. Nijhuis, S. J. Tinnemans, T. Visser, and B. M. Weckhuysen, "Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry," Phys. Chem. Chem. Phys. 5, 4361-4365 (2003).
[CrossRef]

S. J. Tinnemans, M. H. F. Kox, T. A. Nijhuis, T. Visser, and B. M. Weckhuysen, "Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard," Phys. Chem. Chem. Phys. 7, 211-216 (2005).
[CrossRef] [PubMed]

Phys. Med. Biol.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

K. R. Diamond, T. J. Farrell, and M. S. Patterson, "Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence," Phys. Med. Biol. 48, 4135-4149 (2003).
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D. N. Waters, "Raman spectroscopy of powders - effects of light absorption and scattering," Spectrochim. Acta, Part A 50, 1833-1840 (1994).
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Other

S. L. Jacques, "Diffuse reflectance from a semiinfinite medium," http://omlc.ogi.edu/news/may99/rd/index.html, (1999).

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M.-A. Mycek and B. W. Pogue, Handbook of biomedical fluorescence (Marcel Dekker, New York, NY, 2003).

A. Ishimaru, Wave propagation and scattering in random media (Academic Press, New York, 1978).

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Figures (8)

Fig. 1.
Fig. 1.

RamOBS versus Rd for various turbidities. Each symbol represents one µa series. For each µa series, progressive values of µs (cm-1) are used: 18.4, 36.8, 50.6, 62.6, 73.6, 87.4, 99.4. As noted in the text, the same data is replotted in Fig. 2 from left to right data points. Semi-infinite sample geometry was employed with g=0.8.

Fig. 2.
Fig. 2.

(RamOBSµt ) versus Rd for various turbidities. The fit to the curve provides the calibration function, f(Rd), which can be used to correct for sampling volume variations. Semi-infinite sample geometry was employed with g=0.8.

Fig. 3.
Fig. 3.

Diffuse reflectance from the 49 samples versus µs /µa for a 2 cm (r) by 2 cm (z) cylinder with three collection spot radii: 2, 1, and 0.5 cm. g was kept constant (0.8).

Fig. 4.
Fig. 4.

Diffuse reflectance from the 49 samples versus µs /µa for a 1 cm (r) by 2 cm (z) cylinder with three collection spot radii: 1, 0.5, and 0.2 cm. g was kept constant (0.8).

Fig. 5.
Fig. 5.

Diffuse reflectance from the 49 samples versus µs /µa for a 0.5 cm (r) by 1 cm (z) cylinder with three collection spot radii: 0.5, 0.25, and 0.1 cm. g was kept constant (0.8).

Fig. 6.
Fig. 6.

(RamOBSµt ) versus Rd for different sample sizes: 0.5 cm (r)×0.5 cm (z); 1 cm (r)×1 cm (z); 1.5 cm (r)×1.5 cm (z); 2 cm (r)×2 cm (z). (Fixed g (0.8) for all cases.) The collection spot radius was chosen to match the radial dimension of each sample.

Fig. 7.
Fig. 7.

(RamOBSµt ) versus Rd for four g’s: 0.99, 0.95, 0.9, and 0.7. (Fixed sample size 2 cm (r) by 2 cm (z) and collection radius 2 cm for all cases).

Fig. 8.
Fig. 8.

Combined effect of the sample size and scattering anisotropy on the curvature.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

R d = n = 1 f n ( g ) a n ,
R d = 0 a n k ( g ) e k ( g ) n d n = 1 1 ln a k ( g ) ,
Ram OBS = n = 1 f n ( g ) { m = 0 n 1 a x m μ sR μ t a R n m 1 }
= Ram INT μ t l R d , x R d , R a x a R ,
Ram INT = ( μ t l ) Ram OBS a x a R R d , x R d , R .
Ram INT = k ( g ) ( μ t l ) Ram OBS R d , x R d , R .
Ram INT = μ t f ( R d ) Ram OBS .

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