Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence

S. C. Kanick; U. A. Gamm; M. Schouten; H. J. C. M. Sterenborg; D. J. Robinson; A. Amelink

doi:10.1364/BOE.2.001687

Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence

S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink

Biomedical Optics Express
Vol. 2,
Issue 6,
pp. 1687-1702
(2011)
•https://doi.org/10.1364/BOE.2.001687

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S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, "Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence," Biomed. Opt. Express 2, 1687-1702 (2011)

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Related Topics
Table of Contents Category
- Optics of Tissue and Turbid Media
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fiber optics (060.2310)
- Light propagation in tissues (170.3660)
- Backscattering (280.1350)
- Turbid media (290.7050)
- Spectroscopy, visible (300.6550)

About this Article
History
- Original Manuscript: March 24, 2011
- Revised Manuscript: May 19, 2011
- Manuscript Accepted: May 19, 2011
- Published: May 25, 2011

Accessible

Open Access

Abstract

This paper presents a relationship between the intensity collected by a single fiber reflectance device (R_SF) and the fiber diameter (d_fib) and the reduced scattering coefficient ( $μ_{s}^{'}$ ) and phase function (p(θ)) of a turbid medium. Monte Carlo simulations are used to identify and model a relationship between R_SF and dimensionless scattering ( $μ_{s}^{'} d_{fib}$ ). For $μ_{s}^{'} d_{fib} > 10$ we find that R_SF is insensitive to p(θ). A solid optical phantom is constructed with $μ_{s}^{'} \approx 220 {mm}^{- 1}$ and is used to convert R_SF of any turbid medium to an absolute scale. This calibrated technique provides accurate estimates of $μ_{s}^{'}$ over a wide range ([0.05 – 8] mm⁻¹) for a range of d_fib ([0.2 – 1] mm).

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References

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Publication

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[Crossref]
K. Sokolov, M. Follen, and R. Richards-Kortum, “Optical spectroscopy for detection of neoplasia,” Curr. Opin. Chem. Biol. 6(5), 651–658 (2002).
[Crossref] [PubMed]
R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8(1), 7–16 (2003).
[Crossref] [PubMed]
I. Georgakoudi and J. Van Dam, “Characterization of dysplastic tissue morphology and biochemistry in Barrett’s esophagus using diffuse reflectance and light scattering spectroscopy,” Gastrointest. Endosc. Clin. N. Am. 13(2), 297–308 (2003).
[Crossref] [PubMed]
R. L. P. van Veen, A. Amelink, M. Menke-Pluymers, C. van der Pol, and H. J. C. M. Sterenborg, “Optical biopsy of breast tissue using differential path-length spectroscopy,” Phys. Med. Biol. 50(11), 2573–2581 (2005).
[Crossref] [PubMed]
M. Canpolat, M. Akyuz, G. A. Gokhan, E. I. Gurer, and R. Tuncer, “Intra-operative brain tumor detection using elastic light single-scattering spectroscopy: a feasibility study,” J. Biomed. Opt. 14(5), 054021 (2009).
[Crossref] [PubMed]
P. B. Garcia-Allende, V. Krishnaswamy, P. J. Hoopes, K. S. Samkoe, O. M. Conde, and B. W. Pogue, “Automated identification of tumor microscopic morphology based on macroscopically measured scatter signatures,” J. Biomed. Opt. 14(3), 034034 (2009).
[Crossref] [PubMed]
J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV-visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20(1), 119–131 (2009).
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[Crossref] [PubMed]
A. Amelink and H. J. C. M. Sterenborg, “Measurement of the local optical properties of turbid media by differential path-length spectroscopy,” Appl. Opt. 43(15), 3048–3054 (2004).
[Crossref] [PubMed]
A. Amelink, H. J. C. M. Sterenborg, M. P. Bard, and S. A. Burgers, “In vivo measurement of the local optical properties of tissue by use of differential path-length spectroscopy,” Opt. Lett. 29(10), 1087–1089 (2004).
[Crossref] [PubMed]
C. Lee, W. M. Whelan, and I. A. Vitkin, “Information content of point radiance measurements in turbid media: implications for interstitial optical property quantification,” Appl. Opt. 45(9), 2101–2114 (2009).
J. R. Mourant, J. Boyer, A. H. Hielscher, and I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source-detector separations,” Opt. Lett. 21(7), 546–548 (1996).
[Crossref] [PubMed]
A. Kienle, F. K. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26(20), 1571–1573 (2001).
[Crossref]
F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, and C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38(22), 4939–4950 (1999).
[Crossref]
F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source-detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16(12), 2935–2945 (1999).
[Crossref]
E. L. Hull and T. H. Foster, “Steady-state reflectance spectroscopy in the P3 approximation,” J. Opt. Soc. Am. A 18(3), 584–599 (2001).
[Crossref]
T. P. Moffitt and S. A. Prahl, “Sized-fiber reflectometry for measuring local optical properties,” IEEE J. Sel. Top. Quantum Electron. 7, 952–958 (2001).
[Crossref]
M. Johns, C. Giller, D. German, and H. Liu, “Determination of reduced scattering coefficient of biological tissue from a needle-like probe,” Opt. Express 13(13), 4828–4842 (2005).
[Crossref] [PubMed]
R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46 (29), 7317–7328 (2007).
[Crossref] [PubMed]
A. Kim, M. Roy, F. Dadani, and B. C. Wilson, “A fiberoptic reflectance probe with multiple source-collector separations to increase the dynamic range of derived tissue optical absorption and scattering coefficients,” Opt. Express 18(6), 5580–5594 (2010).
[Crossref] [PubMed]
S. C. Kanick, D. J. Robinson, H. J. C. M. Sterenborg, and A. Amelink, “Monte Carlo analysis of single fiber reflectance spectroscopy: photon path length and sampling depth,” Phys. Med. Biol. 54(22), 6991–7008 (2009).
[Crossref] [PubMed]
S. C. Kanick, C. van der Leest, J. G. Aerts, H. C. Hoogsteden, S. Kascakova, H. J. C. M. Sterenborg, and A. Amelink, “Integration of single-fiber reflectance spectroscopy into ultrasound-guided endoscopic lung cancer staging of mediastinal lymph nodes,” J. Biomed. Opt. 15(1), 017004 (2010).
[Crossref] [PubMed]
S. C. Kanick, C. van der Leest, R. S. Djamin, A. M. Janssens, H. C. Hoogsteden, H. J. C. M. Sterenborg, A. Amelink, and J. G. Aerts, “Characterization of mediastinal lymph node physiology in vivo by optical spectroscopy during endoscopic ultrasound-guided fine needle aspiration,” J. Thorac. Oncol. 5(7), 981–987 (2010).
B. W. Pogue and G. Burke, “Fiber-optic bundle design for quantitative fluorescence measurement from tissue,” Appl. Opt. 37(31), 7429–7436 (1998).
[Crossref]
T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” J. Opt. Soc. Am. B 7(6), 1077–1012 (2001).
K. R. Diamond, M. S. Patterson, and T. J. Farrell, “Quantification of fluorophore concentration in tissue-simulating media by fluorescence measurements with a single optical fiber,” Appl. Opt. 42(13), 2436–2442 (2003).
[Crossref] [PubMed]
H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, (1)23–34 (2007).
[Crossref]
M. Canpolat and J. R. Mourant, “Particle size analysis of turbid media with a single optical fiber in contact with the medium to deliver and detect white light,” Appl. Opt. 40(22), 3792–3799 (2001).
[Crossref]
A. Amelink, M. P. Bard, S. A. Burgers, and H. J. C. M. Sterenborg, “Single-scattering spectroscopy for the endoscopic analysis of particle size in superficial layers of turbid media,” Appl. Opt. 42(19), 4095–4101 (2003).
[Crossref] [PubMed]
T. P. Moffitt and S. A. Prahl, “The specular reflection problem with a single fiber for emission and collection,” SPIE Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, 5068, (2003).
P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Collection efficiency of a single optical fiber in turbid media,” Appl. Opt. 42(16), 3187–3197 (2003).
[Crossref] [PubMed]
S. C. Kanick, H. J. C. M. Sterenborg, and A. Amelink, “‘Empirical model of the photon path length for a single fiber reflectance spectroscopy device,” Opt. Express 17(2), 860–871 (2009).
[Crossref] [PubMed]
L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]
R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008).
[Crossref] [PubMed]
G. R. Kepner, “Saturation behavior: a general relationship described by a simple second-order differential equation,” Theor. Biol. Med. Model 7, 11 (2010).
[Crossref] [PubMed]
D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11(2), 431–441 (1963).
[Crossref]
A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt. 13(5), 054044 (2008).
[Crossref] [PubMed]
D. M. de Bruin, R. H. Bremmer, V. M. Kodach, R. de Kinkelder, J. van Marle, T. G. van Leeuwen, and D. J. Faber, “Optical phantoms of varying geometry based on thin building blocks with controlled optical properties,” J. Biomed. Opt. 15(2), 025001 (2010).
[Crossref] [PubMed]
B. K. Horn and R. W. Sjoberg, “Calculating the reflectance map,” Appl. Opt. 18(11), 1770–1779 (1979).
[Crossref] [PubMed]
P. Snabre and A. Arhaliass, “Anisotropic scattering of light in random media: incoherent backscattered spotlight,” Appl. Opt. 37(18), 4017–4026 (1998).
[Crossref]

2010 (5)

S. C. Kanick, C. van der Leest, J. G. Aerts, H. C. Hoogsteden, S. Kascakova, H. J. C. M. Sterenborg, and A. Amelink, “Integration of single-fiber reflectance spectroscopy into ultrasound-guided endoscopic lung cancer staging of mediastinal lymph nodes,” J. Biomed. Opt. 15(1), 017004 (2010).
[Crossref] [PubMed]

S. C. Kanick, C. van der Leest, R. S. Djamin, A. M. Janssens, H. C. Hoogsteden, H. J. C. M. Sterenborg, A. Amelink, and J. G. Aerts, “Characterization of mediastinal lymph node physiology in vivo by optical spectroscopy during endoscopic ultrasound-guided fine needle aspiration,” J. Thorac. Oncol. 5(7), 981–987 (2010).

G. R. Kepner, “Saturation behavior: a general relationship described by a simple second-order differential equation,” Theor. Biol. Med. Model 7, 11 (2010).
[Crossref] [PubMed]

D. M. de Bruin, R. H. Bremmer, V. M. Kodach, R. de Kinkelder, J. van Marle, T. G. van Leeuwen, and D. J. Faber, “Optical phantoms of varying geometry based on thin building blocks with controlled optical properties,” J. Biomed. Opt. 15(2), 025001 (2010).
[Crossref] [PubMed]

A. Kim, M. Roy, F. Dadani, and B. C. Wilson, “A fiberoptic reflectance probe with multiple source-collector separations to increase the dynamic range of derived tissue optical absorption and scattering coefficients,” Opt. Express 18(6), 5580–5594 (2010).
[Crossref] [PubMed]

2009 (6)

S. C. Kanick, H. J. C. M. Sterenborg, and A. Amelink, “‘Empirical model of the photon path length for a single fiber reflectance spectroscopy device,” Opt. Express 17(2), 860–871 (2009).
[Crossref] [PubMed]

C. Lee, W. M. Whelan, and I. A. Vitkin, “Information content of point radiance measurements in turbid media: implications for interstitial optical property quantification,” Appl. Opt. 45(9), 2101–2114 (2009).

S. C. Kanick, D. J. Robinson, H. J. C. M. Sterenborg, and A. Amelink, “Monte Carlo analysis of single fiber reflectance spectroscopy: photon path length and sampling depth,” Phys. Med. Biol. 54(22), 6991–7008 (2009).
[Crossref] [PubMed]

M. Canpolat, M. Akyuz, G. A. Gokhan, E. I. Gurer, and R. Tuncer, “Intra-operative brain tumor detection using elastic light single-scattering spectroscopy: a feasibility study,” J. Biomed. Opt. 14(5), 054021 (2009).
[Crossref] [PubMed]

P. B. Garcia-Allende, V. Krishnaswamy, P. J. Hoopes, K. S. Samkoe, O. M. Conde, and B. W. Pogue, “Automated identification of tumor microscopic morphology based on macroscopically measured scatter signatures,” J. Biomed. Opt. 14(3), 034034 (2009).
[Crossref] [PubMed]

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV-visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20(1), 119–131 (2009).
[Crossref] [PubMed]

2008 (2)

A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt. 13(5), 054044 (2008).
[Crossref] [PubMed]

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008).
[Crossref] [PubMed]

2007 (2)

R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46 (29), 7317–7328 (2007).
[Crossref] [PubMed]

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, (1)23–34 (2007).
[Crossref]

2005 (2)

R. L. P. van Veen, A. Amelink, M. Menke-Pluymers, C. van der Pol, and H. J. C. M. Sterenborg, “Optical biopsy of breast tissue using differential path-length spectroscopy,” Phys. Med. Biol. 50(11), 2573–2581 (2005).
[Crossref] [PubMed]

M. Johns, C. Giller, D. German, and H. Liu, “Determination of reduced scattering coefficient of biological tissue from a needle-like probe,” Opt. Express 13(13), 4828–4842 (2005).
[Crossref] [PubMed]

2004 (2)

A. Amelink, H. J. C. M. Sterenborg, M. P. Bard, and S. A. Burgers, “In vivo measurement of the local optical properties of tissue by use of differential path-length spectroscopy,” Opt. Lett. 29(10), 1087–1089 (2004).
[Crossref] [PubMed]

A. Amelink and H. J. C. M. Sterenborg, “Measurement of the local optical properties of turbid media by differential path-length spectroscopy,” Appl. Opt. 43(15), 3048–3054 (2004).
[Crossref] [PubMed]

2003 (5)

K. R. Diamond, M. S. Patterson, and T. J. Farrell, “Quantification of fluorophore concentration in tissue-simulating media by fluorescence measurements with a single optical fiber,” Appl. Opt. 42(13), 2436–2442 (2003).
[Crossref] [PubMed]

P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Collection efficiency of a single optical fiber in turbid media,” Appl. Opt. 42(16), 3187–3197 (2003).
[Crossref] [PubMed]

A. Amelink, M. P. Bard, S. A. Burgers, and H. J. C. M. Sterenborg, “Single-scattering spectroscopy for the endoscopic analysis of particle size in superficial layers of turbid media,” Appl. Opt. 42(19), 4095–4101 (2003).
[Crossref] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8(1), 7–16 (2003).
[Crossref] [PubMed]

I. Georgakoudi and J. Van Dam, “Characterization of dysplastic tissue morphology and biochemistry in Barrett’s esophagus using diffuse reflectance and light scattering spectroscopy,” Gastrointest. Endosc. Clin. N. Am. 13(2), 297–308 (2003).
[Crossref] [PubMed]

2002 (1)

K. Sokolov, M. Follen, and R. Richards-Kortum, “Optical spectroscopy for detection of neoplasia,” Curr. Opin. Chem. Biol. 6(5), 651–658 (2002).
[Crossref] [PubMed]

2001 (5)

T. P. Moffitt and S. A. Prahl, “Sized-fiber reflectometry for measuring local optical properties,” IEEE J. Sel. Top. Quantum Electron. 7, 952–958 (2001).
[Crossref]

T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” J. Opt. Soc. Am. B 7(6), 1077–1012 (2001).

E. L. Hull and T. H. Foster, “Steady-state reflectance spectroscopy in the P3 approximation,” J. Opt. Soc. Am. A 18(3), 584–599 (2001).
[Crossref]

M. Canpolat and J. R. Mourant, “Particle size analysis of turbid media with a single optical fiber in contact with the medium to deliver and detect white light,” Appl. Opt. 40(22), 3792–3799 (2001).
[Crossref]

A. Kienle, F. K. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26(20), 1571–1573 (2001).
[Crossref]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

1992 (1)

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(4), 879–888 (1992).
[Crossref] [PubMed]

1979 (1)

B. K. Horn and R. W. Sjoberg, “Calculating the reflectance map,” Appl. Opt. 18(11), 1770–1779 (1979).
[Crossref] [PubMed]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11(2), 431–441 (1963).
[Crossref]

A’Amar, O.

Aerts, J. G.

Akyuz, M.

Amelink, A.

Arhaliass, A.

P. Snabre and A. Arhaliass, “Anisotropic scattering of light in random media: incoherent backscattered spotlight,” Appl. Opt. 37(18), 4017–4026 (1998).
[Crossref]

Assanto, G.

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[Crossref]

Backman, V.

A. Wax and V. Backman, Biomedical Applications of Light Scattering (McGraw-Hill, 2010).

Bard, M. P.

Bargo, P. R.

P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Collection efficiency of a single optical fiber in turbid media,” Appl. Opt. 42(16), 3187–3197 (2003).
[Crossref] [PubMed]

Baumgartner, R.

Beck, T.

Bevilacqua, F.

Beyer, W.

Bigio, I. J.

Boiko, I.

Boyer, J.

Bremmer, R. H.

Brown, J. Q.

Burgers, S. A.

Burke, G.

B. W. Pogue and G. Burke, “Fiber-optic bundle design for quantitative fluorescence measurement from tissue,” Appl. Opt. 37(31), 7429–7436 (1998).
[Crossref]

Canpolat, M.

Collier, T.

Conde, O. M.

Dadani, F.

de Bruin, D. M.

de Kinkelder, R.

Depeursinge, C.

Diamond, K. R.

Djamin, R. S.

Drezek, R.

Ediger, M. N.

Faber, D. J.

Farrell, T. J.

Follen, M.

K. Sokolov, M. Follen, and R. Richards-Kortum, “Optical spectroscopy for detection of neoplasia,” Curr. Opin. Chem. Biol. 6(5), 651–658 (2002).
[Crossref] [PubMed]

Forster, F. K.

Foschum, F.

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008).
[Crossref] [PubMed]

Foster, T. H.

E. L. Hull and T. H. Foster, “Steady-state reflectance spectroscopy in the P3 approximation,” J. Opt. Soc. Am. A 18(3), 584–599 (2001).
[Crossref]

Gallo, K.

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[Crossref]

Garcia-Allende, P. B.

Georgakoudi, I.

German, D.

Giller, C.

Gokhan, G. A.

Gross, J. D.

Guillaud, M.

Gurer, E. I.

Hibst, R.

Hielscher, A. H.

Hoogsteden, H. C.

Hoopes, P. J.

Horn, B. K.

B. K. Horn and R. W. Sjoberg, “Calculating the reflectance map,” Appl. Opt. 18(11), 1770–1779 (1979).
[Crossref] [PubMed]

Hull, E. L.

E. L. Hull and T. H. Foster, “Steady-state reflectance spectroscopy in the P3 approximation,” J. Opt. Soc. Am. A 18(3), 584–599 (2001).
[Crossref]

Jacques, S. L.

P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Collection efficiency of a single optical fiber in turbid media,” Appl. Opt. 42(16), 3187–3197 (2003).
[Crossref] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Janssens, A. M.

Johns, M.

Kanick, S. C.

Kascakova, S.

Kepner, G. R.

G. R. Kepner, “Saturation behavior: a general relationship described by a simple second-order differential equation,” Theor. Biol. Med. Model 7, 11 (2010).
[Crossref] [PubMed]

Kienle, A.

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008).
[Crossref] [PubMed]

Kim, A.

Kodach, V. M.

Krishnaswamy, V.

Lee, C.

Liu, H.

Macaulay, C.

Malpica, A.

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11(2), 431–441 (1963).
[Crossref]

Marquet, P.

Menke-Pluymers, M.

Michels, R.

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008).
[Crossref] [PubMed]

Moffitt, T. P.

T. P. Moffitt and S. A. Prahl, “Sized-fiber reflectometry for measuring local optical properties,” IEEE J. Sel. Top. Quantum Electron. 7, 952–958 (2001).
[Crossref]

T. P. Moffitt and S. A. Prahl, “The specular reflection problem with a single fiber for emission and collection,” SPIE Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, 5068, (2003).

Mourant, J. R.

Nishioka, N. S.

Palmer, G. M.

Patterson, M. S.

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Fig. 1 Schematic of single fiber reflectance probe machinery.

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Fig. 2 Angular distribution of scattering events for selected scattering phase functions.

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Fig. 3 Single fiber reflectance vs dimensionless scattering for HG phase function (g=[0.5,0.7,0.8,0.9] and MHG phase function (g=[0.9]).

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Fig. 4 (A) Single fiber reflectance and mathematical model fit for HG phase function (g=0.8). Model estimates of incident photons contacting fiber face (B) and collection efficiency of fiber (C).

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Fig. 5 MC simulated single fiber reflectance vs. model estimate.

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Fig. 6 Single fiber reflectance measured on TiO₂ phantoms and simulated by MC model (HG phase function with g=0.8).

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Fig. 7 Single fiber reflectance measured (A) and simulated (B) from Intralipid optical phantoms at multiple wavelengths λ = [400, 500, 600, 800, 900] nm; other wavelengths measured in this range not shown to improve clarity.

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Fig. 8 Comparison of (A) single fiber reflectance intensity from MC simulations with experimental measurements from Intralipid phantoms λ = [400 – 900] nm; (B)

μ_{s}^{'}

estimated from

R_{SF}^{meas - abs}

vs. known value.

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Tables (1)

Table 1 Estimated Parameter Values Resulting from Fits of Single Fiber Reflectance Model (Eqs. (2)–(4)) to R_SF Simulated by Monte Carlo Models for HG and MHG Phase Function (top) and Wavelength-Dependent Phase Functions [36] in Intralipid (bottom)

View Table

Equations (6)

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

R_{SF}^{MC} = \frac{TPC}{TPL}

R_{SF}^{Model} = \frac{TPC}{TPL} = η_{c} Φ

Φ = \frac{TPH}{TPL} = [\frac{{(μ_{s}^{'} d_{fib})}^{ρ_{2}}}{ρ_{1} + {(μ_{s}^{'} d_{fib})}^{ρ_{2}}}]

η_{c} = \frac{TPC}{TPH} = η_{limit} (1 + ρ_{3} e^{- ρ_{1} (μ_{s}^{'} d_{fib})})

R_{SF}^{meas - rel} = [\frac{I - I_{water}}{I_{white} - I_{black}}]

R_{SF}^{meas - abs} (IL) = R_{SF}^{meas - rel} (IL) [\frac{R_{SF}^{meas - abs} (phantom)}{R_{SF}^{meas - rel} (phantom)}]

Phase Function	g	ρ ₁		ρ ₂		ρ ₃		r

		Value	CI	Value	CI	Value	CI

HG	0.9	9.374	0.406	1.152	0.027	2.338	0.851	0.9994
HG	0.8	8.866	0.321	1.120	0.022	2.295	0.667	0.9995
HG	0.7	8.315	0.270	1.086	0.020	2.267	0.561	0.9996
HG	0.5	7.251	0.199	1.018	0.017	2.108	0.405	0.9998
MHG	0.9	5.676	0.383	1.034	0.046	3.125	1.131	0.9987

Phase Function	g	ρ ₁		ρ ₂		ρ ₃		r

		Value	CI	Value	CI	Value	CI

Intralipid (400nm)	0.818	9.496	0.103	1.245	0.011	2.995	0.362	0.9998
Intralipid (450nm)	0.783	10.001	0.093	1.208	0.010	3.144	0.313	0.9999
Intralipid (500nm)	0.749	9.927	0.124	1.170	0.014	3.072	0.401	0.9997
Intralipid (550nm)	0.715	9.512	0.124	1.127	0.015	2.745	0.375	0.9996
Intralipid (600nm)	0.681	9.014	0.119	1.090	0.017	2.533	0.350	0.9995
Intralipid (650nm)	0.647	8.389	0.091	1.054	0.015	2.170	0.255	0.9996
Intralipid (700nm)	0.613	7.816	0.077	1.021	0.014	2.010	0.218	0.9996
Intralipid (750nm)	0.579	7.361	0.077	0.983	0.016	1.723	0.209	0.9995
Intralipid (800nm)	0.545	6.899	0.077	0.947	0.018	1.437	0.204	0.9994
Intralipid (850nm)	0.511	6.592	0.060	0.935	0.016	1.461	0.168	0.9997
Intralipid (900nm)	0.477	6.323	0.054	0.911	0.016	1.390	0.156	0.9997

Abstract

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