Abstract

We present a single-scattering model as well as a Monte Carlo model of the effect of glucose on polarized light in turbid media. Glucose alters the Mueller-matrix patterns of diffusely backscattered and forward-scattered light because glucose molecules rotate the polarization plane of linearly polarized light. For example, the angles of rotation in Mueller-matrix elements S21 and S12 are linearly related to the concentration of glucose and increase with the source–detector distance. In the nondiffusion regime, the two models agree well with each other. In the diffusion regime, the single-scattering model is invalid, but there still exists a linear relationship between the angles of rotation in the Mueller-matrix elements and the concentration of glucose, which is predicted by the Monte Carlo model.

© 2002 Optical Society of America

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References

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2000 (5)

1999 (3)

1998 (4)

1997 (6)

1995 (1)

L. H. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

1994 (2)

1993 (1)

G. X. Zhou, J. M. Schmitt, “Sensitive detection of optical rotation in liquids by reflection polarimetry,” Rev. Sci. Instrum. 64, 2801–2807 (1993).
[CrossRef]

1992 (1)

G. L. Cote, M. D. Fox, R. B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng. 39, 752–756 (1992).
[CrossRef] [PubMed]

Ablitt, B. P.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Ambirajan, A.

A. Ambirajan, D. C. Look, “A backward Monte Carlo study of the multiple scattering of a polarized laser beam,” J. Quantum Spectrosc. Radiat. Transfer 58, 171–192 (1997).
[CrossRef]

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, London, 1982).

Bartel, S.

Berger, M.

Bigio, I. J.

Bocker, D.

Bruulsema, J. T.

Cameron, B. D.

Chang, M.

C. Chou, Y. C. Huang, C. M. Feng, M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36(1), 356–359 (1997).
[CrossRef]

Chang, P. C. Y.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Chou, C.

C. Chou, C. Y. Han, W. C. Kuo, Y. C. Huang, C. M. Feng, J. C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt. 37, 3553–3557 (1998).
[CrossRef]

C. Chou, Y. C. Huang, C. M. Feng, M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36(1), 356–359 (1997).
[CrossRef]

Cope, M.

Cote, G. L.

M. J. Rakovic, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
[CrossRef]

B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. Kattawar, S. Rastegar, L. V. Wang, G. L. Cote, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
[CrossRef]

B. D. Cameron, G. L. Cote, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

G. L. Cote, M. D. Fox, R. B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng. 39, 752–756 (1992).
[CrossRef] [PubMed]

Eick, A. A.

Elick, A. A.

A. H. Hielscher, A. A. Elick, J. R. Mourant, I. J. Bigio, “Biomedical diagnostic with diffusely backscattered linearly and circularly polarized light,” in Biomedical Sensing, Imaging, and Tracking Technologies II, R. A. Lieberman, T. Vo-Dinh, G. G. Vurek, eds., Proc. SPIE2976, 298–305 (1997).
[CrossRef]

Essenpreis, M.

Fantini, S.

Farrell, T. J.

Feng, C. M.

C. Chou, C. Y. Han, W. C. Kuo, Y. C. Huang, C. M. Feng, J. C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt. 37, 3553–3557 (1998).
[CrossRef]

C. Chou, Y. C. Huang, C. M. Feng, M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36(1), 356–359 (1997).
[CrossRef]

Fox, M. D.

G. L. Cote, M. D. Fox, R. B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng. 39, 752–756 (1992).
[CrossRef] [PubMed]

Franceschini, M. A.

Freyer, J. P.

Gratton, E.

Han, C. Y.

Hayward, J. E.

Heinemann, L.

Hielscher, A. H.

Hopcraft, K. I.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Huang, Y. C.

C. Chou, C. Y. Han, W. C. Kuo, Y. C. Huang, C. M. Feng, J. C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt. 37, 3553–3557 (1998).
[CrossRef]

C. Chou, Y. C. Huang, C. M. Feng, M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36(1), 356–359 (1997).
[CrossRef]

Jacques, S. L.

L. H. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Jakeman, E.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Jiao, S. L.

Kattawar, G.

Kattawar, G. W.

Kehtarnavaz, N.

Kohl, M.

Koschinsky, T.

Kuo, W. C.

Lo, Y. H.

C. Pu, Z. H. Zhu, Y. H. Lo, “A surface-micromachined optical self-homodyne polarimetric sensor for noninvasive glucose monitoring,” IEEE Photon. Technol. Lett. 12, 190–192 (2000).
[CrossRef]

Look, D. C.

A. Ambirajan, D. C. Look, “A backward Monte Carlo study of the multiple scattering of a polarized laser beam,” J. Quantum Spectrosc. Radiat. Transfer 58, 171–192 (1997).
[CrossRef]

Maier, J. S.

Mehrubeoglu, M.

Mourant, J. R.

Northrop, R. B.

G. L. Cote, M. D. Fox, R. B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng. 39, 752–756 (1992).
[CrossRef] [PubMed]

Orskov, H.

Ostermeyer, M.

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Patterson, M. S.

Pu, C.

C. Pu, Z. H. Zhu, Y. H. Lo, “A surface-micromachined optical self-homodyne polarimetric sensor for noninvasive glucose monitoring,” IEEE Photon. Technol. Lett. 12, 190–192 (2000).
[CrossRef]

Rakovic, M. J.

Rastegar, S.

Sandahl-Christiansen, J.

Schmelzeisen-Redeker, G.

Schmitt, J. M.

G. X. Zhou, J. M. Schmitt, “Sensitive detection of optical rotation in liquids by reflection polarimetry,” Rev. Sci. Instrum. 64, 2801–2807 (1993).
[CrossRef]

Shen, D.

Shyu, J. C.

Stephens, D. V.

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Studinski, R. C. N.

R. C. N. Studinski, I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissuelike media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337 (2000).
[CrossRef] [PubMed]

Turpin, K. D.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vitkin, I. A.

R. C. N. Studinski, I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissuelike media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337 (2000).
[CrossRef] [PubMed]

Walker, J. G.

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Walker, S. A.

Wang, L. H.

L. H. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Wang, L. V.

Wang, L.-H.

Yao, G.

Zheng, L.

L. H. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Zhou, G. X.

G. X. Zhou, J. M. Schmitt, “Sensitive detection of optical rotation in liquids by reflection polarimetry,” Rev. Sci. Instrum. 64, 2801–2807 (1993).
[CrossRef]

Zhu, Z. H.

C. Pu, Z. H. Zhu, Y. H. Lo, “A surface-micromachined optical self-homodyne polarimetric sensor for noninvasive glucose monitoring,” IEEE Photon. Technol. Lett. 12, 190–192 (2000).
[CrossRef]

Appl. Opt. (6)

Comput. Methods Programs Biomed. (1)

L. H. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

C. Pu, Z. H. Zhu, Y. H. Lo, “A surface-micromachined optical self-homodyne polarimetric sensor for noninvasive glucose monitoring,” IEEE Photon. Technol. Lett. 12, 190–192 (2000).
[CrossRef]

IEEE Trans. Biomed. Eng. (2)

G. L. Cote, M. D. Fox, R. B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng. 39, 752–756 (1992).
[CrossRef] [PubMed]

B. D. Cameron, G. L. Cote, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

R. C. N. Studinski, I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissuelike media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337 (2000).
[CrossRef] [PubMed]

J. Quantum Spectrosc. Radiat. Transfer (1)

A. Ambirajan, D. C. Look, “A backward Monte Carlo study of the multiple scattering of a polarized laser beam,” J. Quantum Spectrosc. Radiat. Transfer 58, 171–192 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C. Chou, Y. C. Huang, C. M. Feng, M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36(1), 356–359 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Rev. Sci. Instrum. (1)

G. X. Zhou, J. M. Schmitt, “Sensitive detection of optical rotation in liquids by reflection polarimetry,” Rev. Sci. Instrum. 64, 2801–2807 (1993).
[CrossRef]

Waves Random Media (1)

B. P. Ablitt, K. I. Hopcraft, K. D. Turpin, P. C. Y. Chang, J. G. Walker, E. Jakeman, “Imaging and multiple scattering through media containing optically active particles,” Waves Random Media 9, 561–572 (1999).
[CrossRef]

Other (5)

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, London, 1982).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 79th ed. (CRC Press, Boca Raton, Fla., 1998), pp. 3–12 and 8–64.

A. H. Hielscher, A. A. Elick, J. R. Mourant, I. J. Bigio, “Biomedical diagnostic with diffusely backscattered linearly and circularly polarized light,” in Biomedical Sensing, Imaging, and Tracking Technologies II, R. A. Lieberman, T. Vo-Dinh, G. G. Vurek, eds., Proc. SPIE2976, 298–305 (1997).
[CrossRef]

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

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Figures (9)

Fig. 1
Fig. 1

Geometry of a single-scattering event.

Fig. 2
Fig. 2

Single-scattering profiles of the backscattering Mueller-matrix patterns from a turbid medium.

Fig. 3
Fig. 3

Comparison of results of a Monte Carlo model of a backscattering Mueller matrix from turbid media with and without glucose. The size of each intensity map is 4 cm × 4 cm. Absorption coefficient μa, 0.01 cm-1; scattering coefficient μs, 1 cm-1; concentration of glucose α, 300 g/dL. The symbols to describe Sij consist of double-polarization states with the input polarization state denoted by the left-hand letter and the output polarization state denoted by the right-hand letter. O, unpolarized light; H, horizontally linear polarization; V, vertically linear polarization; P, linear polarization oriented in the +45° direction; M, linear polarization oriented in the -45° direction; R, right-circular polarization; L, left-circular polarization.

Fig. 4
Fig. 4

Results of single scattering (solid curves) and Monte Carlo (scattered symbols) models of the azimuthal dependence of backward Mueller-matrix pattern elements (a) S12 and (b) S21. The source–detector distances are 0.4 cm and 1.0 cm. Absorption coefficient μa, 0.01 cm-1; scattering coefficient μs, 1 cm-1; concentration of glucose, 300 g/dL.

Fig. 5
Fig. 5

Rotation angles θ¯1 and θ¯2 for changes in backward Mueller-matrix elements S12 (a) and (b) S21 with changes in the source–detector distance. Solid curves, results from the single-scattering model; symbols, results from the Monte Carlo model. μs, 10 cm-1; μa, 0.1 cm-1; thickness of the sample h, 1 cm; α, concentrations of glucose.

Fig. 6
Fig. 6

Distribution of backscattered light intensities on scattering events of light (μa, 0.1 cm-1; μs, 10 cm-1; thickness of the turbid medium, 1 cm).

Fig. 7
Fig. 7

Monte Carlo simulated rotation of (a) matrix element S12, θ¯1 and (b) matrix element S21, θ¯2. μs, 10 cm-1; μa, 0.1 cm-1; thickness of the sample h, 1 cm.

Fig. 8
Fig. 8

Rotation angles θ¯2 of changes in backward Mueller-matrix element S21 with changes in the concentration of glucose. Solid curves, results from the single-scattering model; symbols, results from the Monte Carlo model. Source-detector distances ρ are shown. μs, 10 cm-1; μa, 0.1 cm-1; thickness of the sample h, 1 cm.

Fig. 9
Fig. 9

Monte Carlo simulated rotation angle of backward Mueller-matrix element S21 for high scattering in a turbid medium containing glucose; μs is 100 cm-1, μa is 10 cm-1, and the thickness of the sample h is 0.04 cm. Solid curves, linear fit.

Equations (16)

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

MΘ=aΘbΘ00bΘaΘ0000dΘ-eΘ00eΘdΘ.
aΘ=316π1+cos2Θ, bΘ=316π-1+cos2Θ, dΘ=38πcosΘ, eΘ=0.
Rϕ=10000cos2ϕ-sin2ϕ00sin2ϕcos2ϕ00001.
Rθ=10000cos2θ-sin2θ00sin2θcos2θ00001,
Ibsρ, ϕ=μs-h0dz1/r2exp-μT|z|+r×R2ϕRθ2MΘR1θ31RϕP0,
Ifsρ, ϕ=μs-h0dz1/r2exp-μT|z|+r×R2-ϕRθ2MΘRθ1R1ϕP0.
Sρ, ϕ=μs-h0dz1/r2exp-μT|z|+r×R2ϕTθ,1, θ2, ΘR1ϕ,
Tijθ1, θ2, Θ=ab cos 2θ1-b sin 2θ10b cos 2θ2a cos 2θ2 cos 2θ1-d sin 2θ2 sin 2θ1-d sin 2θ2 sin 2θ1-a sin 2θ2 sin 2θ1e sin 2θ2b sin 2θ2a sin 2θ2 cos 2θ1+d cos 2θ2 sin 2θ1-a sin 2θ2 sin 2θ1+d cos 2θ2 cos 2θ1-e cos 2θ20e sin 2θ1e cos 2θ1d,
Sijρ, ϕ=μs-h0dzr2exp-μT|z|+rFij, F11=aΘ, F12=bΘcos2ϕ, F13=-bΘsin2ϕ, F14=0, F21=F12, F22=aΘcos2ϕcos2ϕ-dΘsin2ϕ×sin2ϕ=aΘ-dΘ2+aΘ+dΘ2cos4ϕ, F23=-aΘcos2ϕsin2ϕ-dΘcos2ϕsin2ϕ=-aΘ+dΘsin4ϕ, F24=eΘsin2ϕ, F31=-F13, F32=-F23, F33=-aΘsin2ϕsin2ϕ+dΘcos2ϕcos2ϕ=-aΘ+dΘ2+aΘ+dΘ2cos4ϕ, F34=-eΘcos2ϕ, F41=0, F42=F24, F43=-F34, F44=dΘ.
S12ρ, ϕ=μs cos2ϕ-h0dz1/r2×exp-μT|z|+rcos2θ1bΘ-μs sin2ϕ-h0dz1/r2×exp-μT|z|+rsin2θ1bΘ, S13ρ, ϕ=μs sin2ϕ-h0dz1/r2×exp-μT|z|+rcos2θ1bΘ+μs cos2ϕ-h0dz1/r2×exp-μT|z|+rsin2θ1bΘ, S21ρ, ϕ=μs cos2ϕ-h0dz1/r2×exp-μT|z|+rcos2θ2bΘ-μs sin2ϕ-h0dz1/r2×exp-μT|z|+rsin2θ2bΘ, S31ρ, ϕ=μs sin2ϕ-h0dz1/r2×exp-μT|z|+rcos2θ2bΘ+μs cos2ϕ-h0dz1/r2×exp-μT|z|+rsin2θ2bΘ.
S12ρ, ϕ=K1ρ, α, μT, μscos2ϕ+2θ¯1, S13ρ, ϕ=K1ρ, α, μT, μssin2ϕ+2θ¯1, S21ρ, ϕ=K2ρ, α, μT, μscos2ϕ+2θ¯2, S31ρ, ϕ=K2ρ, α, μT, μssin2ϕ+2θ¯2,
K1ρ, ϕ, α, μT, μs=-h0dzr2exp-μT|z|+r×sin2θ1bΘ2+-h0dzr2exp-μT|z|+r×cos2θ1bΘ21/2, K2ρ, ϕ, α, μT, μs=-h0dzr2exp-μT|z|+r×sin2θ2bΘ2+-h0dzr2exp-μT|z|+r×cos2θ2bΘ21/2,
tan2θ¯1=-h0dz1/r2exp-μT|z|+rsin2θ1bΘ-h0dz1/r2exp-μT|z|+rcos2θ1bΘ, tan2θ¯2=-h0dz1/r2exp-μT|z|+rsin2θ2bΘ-h0dz1/r2exp-μT|z|+rcos2θ2bΘ.
S12ρ, ϕ=K1ρ, α, μT, μscos2ϕ, S13ρ, ϕ=K1ρ, α, μT, μssin2ϕ, S21ρ, ϕ=K2ρ, α, μT, μscos2ϕ, S31ρ, ϕ=K2ρ, α, μT, μssin2ϕ,
2π0πaΘsinΘdΘ=1.
ρΘ, ϕ=aΘ+bΘS2 cos2ϕ+S3 sin2ϕ/S1,

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