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 (1)

2006 (1)

2004 (2)

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]

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]

2003 (4)

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]

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]

2002 (1)

2001 (1)

2000 (2)

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

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]

1999 (2)

1996 (3)

1994 (2)

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]

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]

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)

Ambrose Griffin, M. C.

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]

Amelink, A.

Avrillier, S.

Backman, V.

Bard, M. P. L.

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]

Borghese, F.

Burgers, S. A.

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.

Del Bianco, S.

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]

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]

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.

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]

Hale, G. M.

Hibst, R.

Iati, M. A.

Ivanov, C. D.

Jacques, S. L.

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]

Kienle, A.

Kolzer, J.

Lilge, L.

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.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[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]

Payne, F. A.

Perelman, L. T.

Pfefer, T. 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]

Plies, E.

Querry, M. R.

Ramakrishna, S. A.

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]

Ramanujam, N.

Rao, K. D.

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]

Reynolds, L. O.

Saija, R.

Schwarzmaier, H.-J.

Sindoni, O. I.

Solkner, G.

Steiner, R.

Sterenborg, H. J. C. M.

Thueler, 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]

Tinet, E.

Tualle, J. M.

Van Dam, J.

Vermeulen, B.

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]

Wang, L.

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]

Wilke, J. 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]

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

Wilson, B. C.

Yaroslavsky, A. N.

Yaroslavsky, I. V.

Zaccanti, G.

Zinth, W.

Zonios, G.

Appl. Opt. (10)

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]

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

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[CrossRef] [PubMed]

I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements," Appl. Opt. 35, 6797-6809 (1996).
[CrossRef] [PubMed]

G. M. Hale and M. R. Querry, "Optical constants of water in the 200-nm to 200-µm wavelength region," Appl. Opt. 12, 555-563 (1973).
[CrossRef] [PubMed]

G. Zonios, L. T. Perelman, V. 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]

C. L. Crofcheck, F. A. Payne, and M. P. Mengüc, "Characterization of milk properties with a radiative transfer model," Appl. Opt. 41, 2028-2037 (2002).
[CrossRef] [PubMed]

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]

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]

J. Biomed. Opt. (2)

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]

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]

J. Colloid Interface Sci. (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]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Med. Phys. (2)

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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)

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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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