Abstract

We demonstrate the effectiveness of intrinsic Raman spectroscopy (IRS) at reducing errors caused by absorption and scattering. Physical tissue models, solutions of varying absorption and scattering coefficients with known concentrations of Raman scatterers, are studied. We show significant improvement in prediction error by implementing IRS to predict concentrations of Raman scatterers using both ordinary least squares regression (OLS) and partial least squares regression (PLS). In particular, we show that IRS provides a robust calibration model that does not increase in error when applied to samples with optical properties outside the range of calibration.

© 2008 Optical Society of America

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    [CrossRef]
  2. 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]
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    [CrossRef] [PubMed]
  4. J. Wu, M. S. Feld, and R. P. Rava, "Analytical model for extracting intrinsic fluorescence in turbid media," Appl. Opt. 32, 3585-3595 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. 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]
  7. 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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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  14. S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
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  15. A. M. K. Enejder, Doctoral Thesis, Department of Physics, Lund Institute of Technology (1997).
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  17. S. Wold, H. Martin, and H. Wold, Lecture Notes in Mathematics (Springer-Verlag, Heidelberg, 1983).
  18. W.-C. Shih, K. L. Bechtel, and M. S. Feld, "Constrained regularization: Hybrid method for multivariate calibration," Anal. Chem. 79, 234-239 (2007).
    [CrossRef]
  19. 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]
  20. 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 Invivo," 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]

2005

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]

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]

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]

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]

2003

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]

2002

M. Tsuboi, "Raman scattering anisotropy of biological systems," J. Biomed. Opt. 7, 435-441 (2002).
[CrossRef] [PubMed]

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

1999

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]

1998

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

1993

I. E. Frank and J. H. Friedman, "A Statistical View of Some Chemometrics Regression Tools," Technometrics 35, 109-135 (1993).
[CrossRef]

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

1992

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[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 Invivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

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.

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.

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.

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]

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]

Fabricius, P. E.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, "A Diffusion-Theory Model of Spatially Resolved, Steady-State Diffuse Reflectance for the Noninvasive Determination of Tissue Optical-Properties Invivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Feld, M. S.

Finlay, J. C.

Fitzmaurice, M.

Flock, S. T.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[CrossRef] [PubMed]

Foster, T. H.

Frank, I. E.

I. E. Frank and J. H. Friedman, "A Statistical View of Some Chemometrics Regression Tools," Technometrics 35, 109-135 (1993).
[CrossRef]

Friedman, J. H.

I. E. Frank and J. H. Friedman, "A Statistical View of Some Chemometrics Regression Tools," Technometrics 35, 109-135 (1993).
[CrossRef]

Georgakoudi, I.

Ghosh, N.

Gupta, S.

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.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[CrossRef] [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]

Manoharan, R.

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]

Patterson, M. S.

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 Invivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Pedersen, C. B.

Perelman, L. T.

Pradhan, A.

Rava, R. P.

Sasic, S.

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]

Scecina, T. G.

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]

Star, W. M.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

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]

Tinnemans, S. J.

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]

Tsuboi, M.

M. Tsuboi, "Raman scattering anisotropy of biological systems," J. Biomed. Opt. 7, 435-441 (2002).
[CrossRef] [PubMed]

Van Dam, J.

Vangemert, M. J. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[CrossRef] [PubMed]

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).
[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]

Weckhuysen, B. M.

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]

Westerhuis, J. A.

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]

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, "A Diffusion-Theory Model of Spatially Resolved, Steady-State Diffuse Reflectance for the Noninvasive Determination of Tissue Optical-Properties Invivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Wilson, B. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[CrossRef] [PubMed]

Wu, J.

Zhadin, N. N.

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]

Zhang, Q. G.

Zonios, G.

Anal. Chem.

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]

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

Appl. Opt.

J. Biomed. Opt.

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]

M. Tsuboi, "Raman scattering anisotropy of biological systems," J. Biomed. Opt. 7, 435-441 (2002).
[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]

J. Raman Spectrosc.

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]

Lasers Surg. Med.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. Vangemert, "Optical-Properties of Intralipid - a Phantom Medium for Light-Propagation Studies," Lasers Surg. Med. 12, 510-519 (1992).
[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 Invivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Opt. Express

Phys. Chem. Chem. Phys.

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]

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]

Technometrics

I. E. Frank and J. H. Friedman, "A Statistical View of Some Chemometrics Regression Tools," Technometrics 35, 109-135 (1993).
[CrossRef]

Other

S. Wold, H. Martin, and H. Wold, Lecture Notes in Mathematics (Springer-Verlag, Heidelberg, 1983).

A. M. K. Enejder, Doctoral Thesis, Department of Physics, Lund Institute of Technology (1997).

W. -C. Shih, K. L. Bechtel, and M. S. Feld, " Quantitative biological Raman spectroscopy," V. V. Tuchin, Taylor and Francis, eds., in Handbook of Optical Sensing of Glucose in biological fluids and tissues, 2008) Chap. 12.

V. V. Tuchin, Tissue optics: light scattering methods and instruments for medical diagnosis (SPIE Press, Bellingham, Wash., 2000).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of experimental setup. F1: laser line filter (MaxLine, Semrock); S1-S2: shutters; BS: MgF2 plate used as beamsplitter; M1-M2: gold plated mirrors; L1-L2: beam shaping lenses; M3: paraboloidal mirror; F2: notch filter; L3: coupling lens; FB: fiber bundle.

Fig. 2.
Fig. 2.

OLS model components for experiment 1.

Fig. 3.
Fig. 3.

(a). Raman spectra (b). Relative DRS spectra normalized to 4% intralipid with no absorber present.

Fig. 4.
Fig. 4.

The ratio of observed to actual values of an analyte at constant concentration showing significant deviation from 1 resulting from turbidity distortions, plotted as a function of µa and µs .

Fig. 5.
Fig. 5.

(NOBS /NREF µt versus Rd for experiments 1 and 2, showing reproducible curvature.

Fig. 6.
Fig. 6.

Boxplot showing reduction in mean and standard deviation of prediction error by application of IRS. Values were derived from 500 unique splittings of 50 samples into 36 calibration and 14 prediction sample sets.

Fig. 7.
Fig. 7.

(a). 50 samples split into 36 calibration and 14 prediction samples based on optical property values. (b). Standard error of cross-validation (SECV) and standard error of prediction (SEP) for samples split into calibration and prediction sets based on optical property values.

Equations (2)

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Ram INT = μ t f ( R d ) Ram OBS ,
N OBS = f ( R d ) μ t N REF .

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