Abstract

The effect of dependent scattering on the bulk scattering properties of intralipid phantoms in the 600-1850 nm wavelength range has been investigated. A set of 57 liquid optical phantoms, covering a wide range of intralipid concentrations (1-100% v/v), was prepared and the bulk optical properties were accurately determined. The bulk scattering coefficient as a function of the particle density could be well described with Twersky’s packing factor (R2 > 0.990). A general model was elaborated taking into account the wavelength dependency and the effect of the concentration of scattering particles (R2 = 0.999). Additionally, an empirical approach was followed to characterize the effect of dense packing of scattering particles on the anisotropy factor (R2 = 0.992) and the reduced scattering coefficient (R2 = 0.999) of the phantoms. The derived equations can be consulted in future research for the calculation of the bulk scattering properties of intralipid dilutions in the 600-1850 nm range, or for the validation of theories that describe the effects of dependent scattering on the scattering properties of intralipid-like systems.

© 2014 Optical Society of America

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2013

2011

M. I. Mishchenko, “Directional radiometry and radiative transfer: A new paradigm,” J. Quantum Spectrosc. Radiat. Transfer 112(13), 2079–2094 (2011).
[CrossRef]

P. D. Ninni, F. Martelli, G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. 56(2), N21–N28 (2011).
[CrossRef] [PubMed]

P. Di Ninni, F. Martelli, G. Zaccanti, “Effect of dependent scattering on the optical properties of Intralipid tissue phantoms,” Biomed. Opt. Express 2(8), 2265–2278 (2011).
[CrossRef] [PubMed]

2010

B. Cletus, R. Künnemeyer, P. Martinsen, V. A. McGlone, “Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 15(1), 017003 (2010).
[CrossRef] [PubMed]

2009

X. Wen, V. V. Tuchin, Q. Luo, D. Zhu, “Controling the scattering of intralipid by using optical clearing agents,” Phys. Med. Biol. 54(22), 6917–6930 (2009).
[CrossRef] [PubMed]

2008

2007

2006

S. N. Thennadil, H. Martens, A. Kohler, “Physics-based multiplicative scatter correction approaches for improving the performance of calibration models,” Appl. Spectrosc. 60(3), 315–321 (2006).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[CrossRef] [PubMed]

2003

2000

A. Bashkatov, E. Genina, V. I. Kochubey, V. Tuchin, “Effects of scattering particles concentration on light propagation through turbid media,” Proc. SPIE 3917, 256–263 (2000).
[CrossRef]

1998

1996

1995

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Media 5(4), 413–426 (1995).
[CrossRef]

P. A. Bascom, R. S. Cobbold, “On a fractal packing approach for understanding ultrasonic backscattering from blood,” J. Acoust. Soc. Am. 98(6), 3040–3049 (1995).
[CrossRef] [PubMed]

1994

M. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quantum Spectrosc. Radiat. Transfer 52(1), 95–110 (1994).
[CrossRef]

R. West, D. Gibbs, L. Tsang, K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11(6), 1854–1858 (1994).
[CrossRef]

1992

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

1991

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. 30(31), 4507–4514 (1991).
[CrossRef] [PubMed]

N. E. Berger, R. J. Lucas, V. Twersky, “Polydisperse scattering theory and comparisons with data for red blood cells,” J. Acoust. Soc. Am. 89(3), 1394–1401 (1991).
[CrossRef] [PubMed]

1988

V. Twersky, “Low-frequency scattering by mixtures of correlated nonspherical particles,” J. Acoust. Soc. Am. 84(1), 409–415 (1988).
[CrossRef]

1987

V. Twersky, “Low-frequency scattering by correlated distributions of randomly oriented particles,” J. Acoust. Soc. Am. 81(5), 1609–1618 (1987).
[CrossRef]

1982

L. Tsang, J. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71(3), 552–558 (1982).
[CrossRef]

A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72(10), 1317–1320 (1982).
[CrossRef]

1978

V. Twersky, “Acoustic bulk parameters in distributions of pair-correlated scatterers,” J. Acoust. Soc. Am. 64(6), 1710–1719 (1978).
[CrossRef]

1973

1952

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85(4), 621–629 (1952).
[CrossRef]

Aernouts, B.

Bascom, P. A.

P. A. Bascom, R. S. Cobbold, “On a fractal packing approach for understanding ultrasonic backscattering from blood,” J. Acoust. Soc. Am. 98(6), 3040–3049 (1995).
[CrossRef] [PubMed]

Bashkatov, A.

A. Bashkatov, E. Genina, V. I. Kochubey, V. Tuchin, “Effects of scattering particles concentration on light propagation through turbid media,” Proc. SPIE 3917, 256–263 (2000).
[CrossRef]

Berger, N. E.

N. E. Berger, R. J. Lucas, V. Twersky, “Polydisperse scattering theory and comparisons with data for red blood cells,” J. Acoust. Soc. Am. 89(3), 1394–1401 (1991).
[CrossRef] [PubMed]

Borghese, F.

Cairns, B.

Chowdhary, J.

Cletus, B.

B. Cletus, R. Künnemeyer, P. Martinsen, V. A. McGlone, “Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 15(1), 017003 (2010).
[CrossRef] [PubMed]

Cobbold, R. S.

P. A. Bascom, R. S. Cobbold, “On a fractal packing approach for understanding ultrasonic backscattering from blood,” J. Acoust. Soc. Am. 98(6), 3040–3049 (1995).
[CrossRef] [PubMed]

De Baerdemaeker, J.

Del Bianco, S.

Denti, P.

Di Ninni, P.

Dick, V. P.

Do Trong, N. N.

Erkinbaev, C.

Flock, S. T.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

Foschum, F.

Fricke, J.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Media 5(4), 413–426 (1995).
[CrossRef]

Fung, K.

Garrido-Varo, A.

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marín, J. E. Guerrero-Ginel, W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[CrossRef]

Genina, E.

A. Bashkatov, E. Genina, V. I. Kochubey, V. Tuchin, “Effects of scattering particles concentration on light propagation through turbid media,” Proc. SPIE 3917, 256–263 (2000).
[CrossRef]

Gibbs, D.

Giusto, A.

Göbel, G.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Media 5(4), 413–426 (1995).
[CrossRef]

Goldstein, D. H.

Guerrero-Ginel, J. E.

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marín, J. E. Guerrero-Ginel, W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[CrossRef]

Habashy, T.

L. Tsang, J. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71(3), 552–558 (1982).
[CrossRef]

Hale, G. M.

Iatì, M. A.

Ishimaru, A.

Jacques, S. L.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

Kienle, A.

Kochubey, V. I.

A. Bashkatov, E. Genina, V. I. Kochubey, V. Tuchin, “Effects of scattering particles concentration on light propagation through turbid media,” Proc. SPIE 3917, 256–263 (2000).
[CrossRef]

Kohler, A.

Kong, J.

L. Tsang, J. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71(3), 552–558 (1982).
[CrossRef]

Kuga, Y.

Kuhn, J.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Media 5(4), 413–426 (1995).
[CrossRef]

Kumar, G.

Künnemeyer, R.

P. I. Rowe, R. Künnemeyer, A. McGlone, S. Talele, P. Martinsen, R. Oliver, “Thermal stability of intralipid optical phantoms,” Appl. Spectrosc. 67(8), 993–996 (2013).
[CrossRef] [PubMed]

B. Cletus, R. Künnemeyer, P. Martinsen, V. A. McGlone, “Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 15(1), 017003 (2010).
[CrossRef] [PubMed]

Lammertyn, J.

Lax, M.

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85(4), 621–629 (1952).
[CrossRef]

Liu, L.

Lompado, A.

Lucas, R. J.

N. E. Berger, R. J. Lucas, V. Twersky, “Polydisperse scattering theory and comparisons with data for red blood cells,” J. Acoust. Soc. Am. 89(3), 1394–1401 (1991).
[CrossRef] [PubMed]

Luo, Q.

X. Wen, V. V. Tuchin, Q. Luo, D. Zhu, “Controling the scattering of intralipid by using optical clearing agents,” Phys. Med. Biol. 54(22), 6917–6930 (2009).
[CrossRef] [PubMed]

Mackowski, D. W.

Martelli, F.

Martens, H.

Martinsen, P.

P. I. Rowe, R. Künnemeyer, A. McGlone, S. Talele, P. Martinsen, R. Oliver, “Thermal stability of intralipid optical phantoms,” Appl. Spectrosc. 67(8), 993–996 (2013).
[CrossRef] [PubMed]

B. Cletus, R. Künnemeyer, P. Martinsen, V. A. McGlone, “Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 15(1), 017003 (2010).
[CrossRef] [PubMed]

McGlone, A.

McGlone, V. A.

B. Cletus, R. Künnemeyer, P. Martinsen, V. A. McGlone, “Temperature-dependent optical properties of Intralipid measured with frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 15(1), 017003 (2010).
[CrossRef] [PubMed]

Michels, R.

Mishchenko, M.

M. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quantum Spectrosc. Radiat. Transfer 52(1), 95–110 (1994).
[CrossRef]

Mishchenko, M. I.

Moes, C. J.

Nicolaï, B. M.

Ninni, P. D.

P. D. Ninni, F. Martelli, G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. 56(2), N21–N28 (2011).
[CrossRef] [PubMed]

Oliver, R.

Patterson, M. S.

B. W. Pogue, M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[CrossRef] [PubMed]

Pérez-Marín, D.

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marín, J. E. Guerrero-Ginel, W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[CrossRef]

Pogue, B. W.

B. W. Pogue, M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[CrossRef] [PubMed]

Prahl, S. A.

Querry, M. R.

Rowe, P. I.

Saeys, W.

Saija, R.

Schmitt, J. M.

Sindoni, O. I.

Star, W. M.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

Talele, S.

Thennadil, S. N.

Tsang, L.

R. West, D. Gibbs, L. Tsang, K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11(6), 1854–1858 (1994).
[CrossRef]

L. Tsang, J. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71(3), 552–558 (1982).
[CrossRef]

Tsuta, M.

Tuchin, V.

A. Bashkatov, E. Genina, V. I. Kochubey, V. Tuchin, “Effects of scattering particles concentration on light propagation through turbid media,” Proc. SPIE 3917, 256–263 (2000).
[CrossRef]

Tuchin, V. V.

X. Wen, V. V. Tuchin, Q. Luo, D. Zhu, “Controling the scattering of intralipid by using optical clearing agents,” Phys. Med. Biol. 54(22), 6917–6930 (2009).
[CrossRef] [PubMed]

Twersky, V.

N. E. Berger, R. J. Lucas, V. Twersky, “Polydisperse scattering theory and comparisons with data for red blood cells,” J. Acoust. Soc. Am. 89(3), 1394–1401 (1991).
[CrossRef] [PubMed]

V. Twersky, “Low-frequency scattering by mixtures of correlated nonspherical particles,” J. Acoust. Soc. Am. 84(1), 409–415 (1988).
[CrossRef]

V. Twersky, “Low-frequency scattering by correlated distributions of randomly oriented particles,” J. Acoust. Soc. Am. 81(5), 1609–1618 (1987).
[CrossRef]

V. Twersky, “Acoustic bulk parameters in distributions of pair-correlated scatterers,” J. Acoust. Soc. Am. 64(6), 1710–1719 (1978).
[CrossRef]

Van Beers, R.

van Gemert, M. J.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. 30(31), 4507–4514 (1991).
[CrossRef] [PubMed]

van Marie, J.

van Staveren, H. J.

Videen, G.

Wang, L.

Watté, R.

Wen, X.

X. Wen, V. V. Tuchin, Q. Luo, D. Zhu, “Controling the scattering of intralipid by using optical clearing agents,” Phys. Med. Biol. 54(22), 6917–6930 (2009).
[CrossRef] [PubMed]

West, R.

Wilson, B. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992).
[CrossRef] [PubMed]

Zaccanti, G.

Zamora-Rojas, E.

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[CrossRef] [PubMed]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marín, J. E. Guerrero-Ginel, W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[CrossRef]

Zhu, D.

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Figures (8)

Fig. 1
Fig. 1

Effect of dependent scattering with increasing volume concentration of scattering particles Φp on the bulk scattering coefficient at 6 wavelengths. The average (cyan dots) and standard deviation (cyan error bars) of the µs measurements are plotted at the considered volume concentrations of the scattering particles. The Twersky equation with variable packing dimension p is fitted to the data for the different wavelengths (solid lines). The equation proposed in [11] at 633 nm is illustrated by the dashed line.

Fig. 2
Fig. 2

(a) The variable packing dimension p of the Twersky equation fitted to the bulk scattering coefficient as a function of volume concentration of scattering particles for the 600-1850 nm range. (b) Determination coefficient R2 of the fit for the 600-1850 nm wavelength range. The solid line represents the linear fit to the packing dimension p as a function of the wavelength.

Fig. 3
Fig. 3

The measured bulk scattering coefficient as a function of the wavelength and the volume concentration of scattering particles (grey dots), together with the fitted surface function given by the substitution of Eq. (2) and the equation for the wavelength-dependent packing dimension p [Fig. 2(a)] in Eq. (3).

Fig. 4
Fig. 4

Effect of dependent scattering with increasing volume concentration of scattering particles Φp on the anisotropy factor g. The average (cyan dots) and standard deviation (cyan error bars) of the g measurements are plotted at the considered volume concentrations of the scattering particles. A linear polynomial is fitted to the data for the different wavelengths (solid lines). The equation proposed in [11] at 633 nm is illustrated by the dashed line.

Fig. 5
Fig. 5

(a) The slope parameter of the linear polynomial fitted to the anisotropy factor as a function of volume concentration of scattering particles for the 600-1850 nm wavelength range. (b) Determination coefficient R2 of the linear fit for the 600-1850 nm wavelength range. The solid line represents a high-order polynomial fit to the slope parameter as a function of the wavelength.

Fig. 6
Fig. 6

The measured anisotropy factor as a function of the wavelength (600-1850 nm) and the volume concentration of scattering particles (grey dots), together with the fitted surface function obtained by substitution of Eq. (4) and the equation for the wavelength-dependent slope k [Fig. 5(a)] in Eq. (6).

Fig. 7
Fig. 7

Effect of dependent scattering with increasing volume concentration of scattering particles Φp on the reduced scattering coefficient. The average (cyan dots) and standard deviation (cyan error bars) of the µs measurements are plotted at the considered volume concentrations of the scattering particles. The solid lines correspond to the general model derived in Eq. (5). The equation proposed in [11] at 633 nm is illustrated by the dashed line, while the equations proposed in [6] at 751 and 833 nm are shown by the dash-dotted lines.

Fig. 8
Fig. 8

The measured reduced scattering coefficient as a function of the wavelength (600-1850 nm) and the volume concentration of scattering particles (grey dots), together with the fitted surface function obtained by substitution of Eqs. (3) and (5) in Eq. (6).

Equations (6)

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W p ( ϕ p ) = ( 1 ϕ p ) p + 1 [ 1 + ϕ p ( p 1 ) ] p 1
μ s i n d e p ( λ ) = 1.868 * 10 10 λ 2.59
μ s ( λ , ϕ p ) = μ s i n d e p ( λ ) 0.227 ϕ p { ( 1 ϕ p ) p ( λ ) + 1 [ 1 + ϕ p ( p ( λ ) 1 ) ] p ( λ ) 1 }
g i n d e p ( λ ) = a ( 1 f 1 + e c ( λ + d ) + f ) + b ( 1 h 1 + e c ( λ + d ) + h ) λ a = 1.094 ; b = 5.653 * 10 4 ; c = 5.3 * 10 3 ; d = a ( f 1 ) b ( h 1 ) ; f = 0.3516 ; h = 0.1933
μ s ( λ , ϕ p ) = μ s ( λ , ϕ p ) [ 1 g ( λ , ϕ p ) ]
g ( λ , ϕ p ) = g i n d e p ( λ ) + k ( λ ) ϕ p

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