Abstract

A method for determining a two-parametric Gegenbauer-kernel phase function that accurately describes the diffuse reflectance from a polydispersive scattering media at small source-detector separations (0.23 to 1.2 mm), is presented. The method involves spectral collimated transmission measurements, spatially resolved spectral diffuse reflectance (SRDR) measurements, and inverse Monte Carlo technique. Both absolute calibration (using a monodispersive polystyrene microsphere suspension) and relative calibration (eliminating differences between fibers) of SRDR spectra yielded comparable results. When applied to water dilutions of milk, simulated and measured spectra deviated less than 6.5% and 2.5% for the absolute and relative calibration case, respectively, even for the closest fiber separation. Corresponding values for milk including ink as an absorber, were 13.4% and 7.3%.

© 2009 Optical Society of America

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2008 (3)

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13, 041304-1 – 041304-10 (2008).
[Crossref] [PubMed]

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

2007 (1)

T. Lindbergh, M. Larsson, I. Fredriksson, and T. Strömberg, “Reduced scattering coefficient determination by non-contact oblique angle illumination: Methodological considerations,” in Progress in Biomedical Optics and Imaging - Proceedings of SPIE, 64350I-1 – 64350I-12 (2007).

2006 (2)

B.W. Pogue and M.S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102-1 – 041102-16 (2006).
[Crossref] [PubMed]

G.M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062“1071 (2006).
[Crossref] [PubMed]

2005 (1)

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

2004 (2)

J.C. Finlay and T.H. Foster, “Hemoglobin oxygen saturations in phantoms and in vivo from measurements of steady-state diffuse reflectance at a single, short source-detector separation,” Med. Phys. 31, 1949–1959 (2004).
[Crossref] [PubMed]

A. Amelink, H.J.C.M. Sterenborg, M.P.L. 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, 1087–1089 (2004).
[Crossref] [PubMed]

2003 (4)

G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42, 4023–4030 (2003).
[Crossref] [PubMed]

A. Giusto, R. Saija, M.A. Iati, P. Denti, F. Borghese, and O.I. Sindoni, “Optical properties of high-density dispersions of particles: Application to intralipid solutions,” Appl. Opt. 42, 4375–4380 (2003).
[Crossref] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

2000 (2)

S.A. Ramakrishna and K.D. Rao, “Estimation of light transport parameters in biological media using coherent backscattering,” Pramana J. Phys. 54, 255–267 (2000).
[Crossref]

I.D. Nikolov and I.D. Ivanov, “Optical plastic refractive measurements in the visible and the near-infrared regions,” Appl. Opt. 39, 2067–2070 (2000).
[Crossref]

1999 (2)

1996 (3)

1994 (3)

H. Buiteveld, J.M.H. Hakvoort, and M. Donze, “The optical properties of pure water,” in Ocean Optics XII -Proceedings of SPIE,174–183 (1994).

L. Wang and S.L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[Crossref] [PubMed]

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, and W. Zinth, “Time-gated transillumination of biological tissues and tissuelike phantoms,” Appl. Opt. 33, 6699–6710 (1994).
[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, 879–888 (1992).
[Crossref] [PubMed]

1985 (1)

M. C. Ambrose Griffin and W.G. Griffin, “A simple turbidimetric method for the determination of the refractive index of large colloidal particles applied to casein micelles,” J. Colloid Interface Sci. 104, 409–415 (1985).
[Crossref]

1980 (1)

1973 (1)

Alerstam, E.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13, 041304-1 – 041304-10 (2008).
[Crossref] [PubMed]

Amelink, A.

Andersson-Engels, S.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13, 041304-1 – 041304-10 (2008).
[Crossref] [PubMed]

Avrillier, S.

Backman, V.

Bard, M.P.L.

Bargo, P.R.

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

Bennett, C.L.

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

Bevilacqua, F.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

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, 2935–2945 (1999).
[Crossref]

Bianco, S. Del

Blair, G.

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

Borghese, F.

Buiteveld, H.

H. Buiteveld, J.M.H. Hakvoort, and M. Donze, “The optical properties of pure water,” in Ocean Optics XII -Proceedings of SPIE,174–183 (1994).

Burgers, S.A.

Casimir-Ahn, H.

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

Charvet, I.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

Crofcheck, C.L.

Dam, J. Van

Denti, P.

Depeursinge, C.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

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, 2935–2945 (1999).
[Crossref]

Donze, M.

H. Buiteveld, J.M.H. Hakvoort, and M. Donze, “The optical properties of pure water,” in Ocean Optics XII -Proceedings of SPIE,174–183 (1994).

Durkin, A.J.

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

Ediger, M.N.

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

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 in vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Feld, M.S.

Finlay, J.C.

J.C. Finlay and T.H. Foster, “Hemoglobin oxygen saturations in phantoms and in vivo from measurements of steady-state diffuse reflectance at a single, short source-detector separation,” Med. Phys. 31, 1949–1959 (2004).
[Crossref] [PubMed]

Fitzmaurice, M.

Forster, F.K.

Foschum, F.

Foster, T.H.

J.C. Finlay and T.H. Foster, “Hemoglobin oxygen saturations in phantoms and in vivo from measurements of steady-state diffuse reflectance at a single, short source-detector separation,” Med. Phys. 31, 1949–1959 (2004).
[Crossref] [PubMed]

Fredriksson, I.

T. Lindbergh, M. Larsson, I. Fredriksson, and T. Strömberg, “Reduced scattering coefficient determination by non-contact oblique angle illumination: Methodological considerations,” in Progress in Biomedical Optics and Imaging - Proceedings of SPIE, 64350I-1 – 64350I-12 (2007).

Gall, J.A.

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

Ghislain, M.S.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

Giusto, A.

Goldbach, T.

Goodell, T.T.

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

Griffin, M. C. Ambrose

M. C. Ambrose Griffin and W.G. Griffin, “A simple turbidimetric method for the determination of the refractive index of large colloidal particles applied to casein micelles,” J. Colloid Interface Sci. 104, 409–415 (1985).
[Crossref]

Griffin, W.G.

M. C. Ambrose Griffin and W.G. Griffin, “A simple turbidimetric method for the determination of the refractive index of large colloidal particles applied to casein micelles,” J. Colloid Interface Sci. 104, 409–415 (1985).
[Crossref]

Häggblad, E.

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

Hakvoort, J.M.H.

H. Buiteveld, J.M.H. Hakvoort, and M. Donze, “The optical properties of pure water,” in Ocean Optics XII -Proceedings of SPIE,174–183 (1994).

Hale, G.M.

Hibst, R.

Iati, M.A.

Ivanov, I.D.

Jacques, S.L.

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

L. Wang and S.L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[Crossref] [PubMed]

S.L. Jacques, Optical fiber reflectance spectroscopy, http://omlc.ogi.edu/news/oct03/saratov/index.htm.

Jenness, R.

P. Walstra and R. Jenness, Dairy Chemistry and Physics (Wiley, New York,1984).

Karlsson, M.G.D.

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

Kienle, A.

Kolzer, J.

Koval, G.

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
[Crossref] [PubMed]

Larsson, M.

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

T. Lindbergh, M. Larsson, I. Fredriksson, and T. Strömberg, “Reduced scattering coefficient determination by non-contact oblique angle illumination: Methodological considerations,” in Progress in Biomedical Optics and Imaging - Proceedings of SPIE, 64350I-1 – 64350I-12 (2007).

Lilge, L.

Lindbergh, T.

E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G. Salerud, and T. Strömberg, “Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting,” J. Biomed. Opt. 13, 054030-1 ” 054030-9 (2008).
[Crossref] [PubMed]

T. Lindbergh, M. Larsson, I. Fredriksson, and T. Strömberg, “Reduced scattering coefficient determination by non-contact oblique angle illumination: Methodological considerations,” in Progress in Biomedical Optics and Imaging - Proceedings of SPIE, 64350I-1 – 64350I-12 (2007).

Manoharan, R.

Marquet, P.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

Martelli, F.

Matchette, L.S.

T.J. Pfefer, L.S. Matchette, C.L. Bennett, J.A. Gall, J.N. Wilke, A.J. Durkin, and M.N. Ediger, “Reflectance-based determination of optical properties in highly attenuating tissue,” J. Biomed. Opt. 8, 206–215 (2003).
[Crossref] [PubMed]

McCormick, N.J.

Meda, P.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

Mengüc, M.P.

Michels, R.

Mitic, G.

Nikolov, I.D.

Ory, G.

P. Thueler, I. Charvet, F. Bevilacqua, M.S. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[Crossref] [PubMed]

Otto, J.

Palmer, G.M.

Patterson, M.S.

B.W. Pogue and M.S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102-1 – 041102-16 (2006).
[Crossref] [PubMed]

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[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13, 041304-1 – 041304-10 (2008).
[Crossref] [PubMed]

P.R. Bargo, S.A. Prahl, T.T. Goodell, R.A. Sleven, G. Koval, G. Blair, and S.L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy.,” J. Biomed. Opt. 10, 034018-1 034018-15 (2005).
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[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Left Panel: The SCT setup. Right Panel: The tip of the probe used for SRDR measurements, with source fiber (S) and detector fibers (D 1–4). Note: The SRDR probe is not drawn to scale, except for fiber separations. The distance from the edge of the probe to the edge of the closest fiber (S) was 2 mm.

Fig. 2.
Fig. 2.

Left Panel: Calibration measurements using a polystyrene microsphere suspension. Measured (black) and simulated (gray) spectra for the source-detector separations D 1–4. Measured spectra are normalized by A abs (see Eq. 2). Note: The intensities are unitless, since the simulated spectra are normalized with the incident light intensity. Right Panel: A abs for D 1–4 from the microsphere suspension measurement (*) and A rel from the uniform illumination measurement (Δ). Both series are normalized by their mean value.

Fig. 3.
Fig. 3.

Left Panel: μ s for OP 1–4 as a function of wavelength. Right Panel: μs,OPi /μs,OP1 , i = 2,3,4 . Dotted lines: Expected quotients assuming linear response between μ s and concentration. Solid lines: experimental quotients.

Fig. 4.
Fig. 4.

The wavelength-resolved parameters for the two-parametric phase function. Left Panel: α Gk,abs *, (oe-17-03-1610-i001) and α Gk,rel * (oe-17-03-1610-i002). Right Panel: g * abs (oe-17-03-1610-i003), g * rel(oe-17-03-1610-i004) and g HG,abs (O).

Fig. 5:
Fig. 5:

Measured (black) and simulated (solid gray : I MC,abs *, dashed black : I MC,rel *) intensities, with phase function approximation based on [OP 1–3, D 1–3]. Left Panel: D 1, Right Panel: D 3.

Fig. 6:
Fig. 6:

Left Panel: μ a for diluted blue ink (1/500) as function of wavelength. Right Panel: Measured (black) and simulated (solid gray : I MC,abs *, dashed black : I MC,rel *) intensities for D 3.

Tables (1)

Tables Icon

Table 1: Deviations (E rms abs and E rms rel) between simulated and measured spectra evaluated over OP 1–3, D 1–3, using different data-sets a) in the phase function estimation. Deviations are given as mean and min-max range.

Equations (5)

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

P Gk ( θ ) = α Gk g Gk ( 1 g Gk 2 ) 2 α Gk π [ ( 1 + g Gk ) 2 α Gk ( 1 g Gk ) 2 α Gk ] [ 1 + g Gk 2 2 g Gk cos ( θ ) ] α Gk + 1 .
E abs ( α Gk , g ) = I MC ( α Gk , g , λ , OP , D ) I mean ( λ , OP , D ) / A abs ( D ) 1
E rel ( α Gk , g ) = I MC ( α Gk , g , λ , OP , D ) I meas ( λ , OP , D ) / A rel ( D ) ( I MC ( α Gk , g , λ , OP , D ) I meas ( λ , OP , D ) / A rel ( D ) λ , OP , D ) 1 1 .
E abs rms = ( E abs 2 ( α Gk , abs * , g abs * ) λ ) 1 / 2
E rel rms = ( E rel 2 ( α Gk , rel * , g rel * ) λ ) 1 / 2 .

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