Abstract

In this study, a flexible tool to simulate the bulk optical properties of polydisperse spherical particles in an absorbing host medium is described. The generalized Mie solution for Maxwell’s equations is consulted to simulate the optical properties for a spherical particle in an absorbing host, while polydispersity of the particle systems is supported by discretization of the provided particle size distributions. The number of intervals is optimized automatically in an efficient iterative procedure. The developed tool is validated by simulating the bulk optical properties for two aqueous nanoparticle systems and an oil-in-water emulsion in the visible and near-infrared wavelength range, taking into account the representative particle sizes and refractive indices. The simulated bulk optical properties matched closely (R2 ≥ 0.899) with those obtained by reference measurements.

© 2014 Optical Society of America

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2014

2013

2012

R. Watté, B. Aernouts, and W. Saeys, “A multilayer Monte Carlo method with free phase function choice,” Proc. SPIE 8429, 84290S (2012).
[CrossRef]

B. Aernouts, R. Watté, J. Lammertyn, and W. Saeys, “A flexible tool for simulating the bulk optical properties of polydisperse suspensions of spherical particles in an absorbing host medium,” Proc. SPIE 8429, 84290R (2012).
[CrossRef]

S. C. Kanick, V. Krishnaswamy, U. A. Gamm, H. J. Sterenborg, D. J. Robinson, A. Amelink, and B. W. Pogue, “Scattering phase function spectrum makes reflectance spectrum measured from Intralipid phantoms and tissue sensitive to the device detection geometry,” Biomed. Opt. Express 3(5), 1086–1100 (2012).
[CrossRef] [PubMed]

L. Wang, X. Sun, and F. Li, “Generalized eikonal approximation for fast retrieval of particle size distribution in spectral extinction technique,” Appl. Opt. 51(15), 2997–3005 (2012).
[CrossRef] [PubMed]

2011

2010

B. Cletus, R. Künnemeyer, P. Martinsen, and 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

B. Cletus, R. Künnemeyer, P. Martinsen, A. McGlone, and R. Jordan, “Characterizing liquid turbid media by frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 14(2), 024041 (2009).
[CrossRef] [PubMed]

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

2008

2007

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15(6), 2822–2836 (2007).
[CrossRef] [PubMed]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 13188–13202 (2007).
[CrossRef] [PubMed]

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz-Mie theory,” ACM SIGGRAPH 2007 Pap. - SIGGRAPH 26(3), 60 (2007).
[CrossRef]

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A, Pure Appl. Opt. 9(1), 49–55 (2007).
[CrossRef]

H. Berberoglu and L. Pilon, “Experimental measurements of the radiation characteristics of Anabaena variabilis ATCC 29413-U and Rhodobacter sphaeroides ATCC 49419,” Int. J. Hydrogen Energy 32(18), 4772–4785 (2007).
[CrossRef]

2006

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 137–142 (2006).
[CrossRef]

J. Yin and L. Pilon, “Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium,” J. Opt. Soc. Am. A 23(11), 2784–2796 (2006).
[CrossRef] [PubMed]

2005

S. K. Sharma and S. Banerjee, “Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model,” Med. Phys. 32(6), 1767–1774 (2005).
[CrossRef] [PubMed]

2004

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transf. 83(3-4), 483–492 (2004).
[CrossRef]

2003

S. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A, Pure Appl. Opt. 5(3), 294–302 (2003).
[CrossRef]

G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42(33), 6724–6727 (2003).
[CrossRef] [PubMed]

2002

2001

2000

R. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatterers,” J. Mod. Opt. 47(1), 103–120 (2000).
[CrossRef]

1999

A. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

M. Mishchenko, J. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, “Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 409–432 (1999).
[CrossRef]

1998

1996

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[CrossRef]

M. Quinten and J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[CrossRef]

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms : a fractal approach,” Pure Appl. Opt. 5(4), 377–388 (1996).
[CrossRef]

1991

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

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, and 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]

1988

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

1982

1980

F. Fritsch and R. Carlson, “Monotone piecewise cubic interpolation,” SIAM J. Numer. Anal. 17(2), 238–246 (1980).
[CrossRef]

1979

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[CrossRef]

1977

1974

1973

1965

Aernouts, B.

B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid phantoms in the 600-1850 nm range,” Opt. Express 22(5), 6086–6098 (2014).
[CrossRef] [PubMed]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marín, J. E. Guerrero-Ginel, and 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]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and 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, W. Saeys, D. Pérez-Marín, and J. E. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[CrossRef]

R. Watté, B. Aernouts, and W. Saeys, “A multilayer Monte Carlo method with free phase function choice,” Proc. SPIE 8429, 84290S (2012).
[CrossRef]

B. Aernouts, R. Watté, J. Lammertyn, and W. Saeys, “A flexible tool for simulating the bulk optical properties of polydisperse suspensions of spherical particles in an absorbing host medium,” Proc. SPIE 8429, 84290R (2012).
[CrossRef]

Amelink, A.

Avrillier, S.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms : a fractal approach,” Pure Appl. Opt. 5(4), 377–388 (1996).
[CrossRef]

Banerjee, S.

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A, Pure Appl. Opt. 9(1), 49–55 (2007).
[CrossRef]

S. K. Sharma and S. Banerjee, “Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model,” Med. Phys. 32(6), 1767–1774 (2005).
[CrossRef] [PubMed]

S. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A, Pure Appl. Opt. 5(3), 294–302 (2003).
[CrossRef]

Baum, B. A.

Berberoglu, H.

H. Berberoglu and L. Pilon, “Experimental measurements of the radiation characteristics of Anabaena variabilis ATCC 29413-U and Rhodobacter sphaeroides ATCC 49419,” Int. J. Hydrogen Energy 32(18), 4772–4785 (2007).
[CrossRef]

Berg, M.

R. Ceolato, N. Riviere, M. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings,Taipei (2013), pp. 717–721.

Berger, N. E.

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

Bhandari, A.

Biscans, B.

R. Ceolato, N. Riviere, M. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings,Taipei (2013), pp. 717–721.

Bohren, C. F.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[CrossRef]

Cairns, B.

Carlson, R.

F. Fritsch and R. Carlson, “Monotone piecewise cubic interpolation,” SIAM J. Numer. Anal. 17(2), 238–246 (1980).
[CrossRef]

Ceolato, R.

R. Ceolato, N. Riviere, M. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings,Taipei (2013), pp. 717–721.

Chowdhary, J.

Christensen, N. J.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz-Mie theory,” ACM SIGGRAPH 2007 Pap. - SIGGRAPH 26(3), 60 (2007).
[CrossRef]

Chylek, P.

Chýlek, P.

Cletus, B.

B. Cletus, R. Künnemeyer, P. Martinsen, and 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]

B. Cletus, R. Künnemeyer, P. Martinsen, A. McGlone, and R. Jordan, “Characterizing liquid turbid media by frequency-domain photon-migration spectroscopy,” J. Biomed. Opt. 14(2), 024041 (2009).
[CrossRef] [PubMed]

Dlugach, J.

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Innov. Food Sci. Emerg. Technol.

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marín, and J. E. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
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J. Acoust. Soc. Am.

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Supplementary Material (1)

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Figures (5)

Fig. 1
Fig. 1

Single-frame from a video (Media 1) that shows the discretization process for 2% (v/v) silica particles in water at 633 nm: (a) Discretization into discrete intervals of a normal (µ = 1.5, σ = 0.3) probability density function for the volume-frequency particle size distribution (radius); (b) Reduction of the normalized error εi for the bulk optical properties (BOP) with increasing number of considered intervals. The red circles indicate the first cycle for which the normalized error is below the threshold; (c) Convergence towards a stable value for the BOP ( μ a p , µs and g) with increasing number of considered intervals; (d) Convergence towards a stable angular distribution of the scattering phase function p(θ) with increasing number of considered intervals.

Fig. 2
Fig. 2

(b)-(f) Reduction of the normalized error εi for the bulk optical properties with increasing number of considered intervals in the discretization process of four normal (µ, σ) probability density functions for the volume-frequency particle size distribution (radius) of 2% (v/v) soybean oil emulsified in water at a wavelength of 633 nm (a). The red circles indicate the first cycle for which the normalized error is below the threshold.

Fig. 3
Fig. 3

Simulated apparent optical properties for a spherical silica particle in ‘water’ at 633 nm for 4 different values for the imaginary part of the medium’s refractive index (nm): (a) Ratio of absorption (σa) and geometrical cross-section (σg = πr2) of the particle; (b) Ratio of scattering (σs) and geometrical cross-section of the particle; (c) Anisotropy factor (g) of the particle.

Fig. 4
Fig. 4

(a) Cumulative volume-frequency particle size distributions (radius) for the 300 nm (red) and 800 nm (cyan) suspensions of silica particles in water, measured with dynamic light scattering; (b)-(d) Average (dots) plus and minus one standard deviation (error bars) of the measured bulk optical properties (respectively µs, g and µs’) for the two suspensions together with the simulated values (solid black lines) calculated from the particle size distributions in (a).

Fig. 5
Fig. 5

(a) The cumulative volume-frequency particle size distribution (radius) for Intralipid 20% measured with laser light scattering (cyan) and compared with results from literature [18,40,52]; (b)-(d) The average (red dots) and the standard deviation (red error bars) of the measured bulk optical properties (respectively µs, g and µs’) for diluted Intralipid 20% and compared with the simulated values (lines) using the particle size distributions in (a).

Tables (1)

Tables Icon

Table 1 Coefficients of determination (R2), indicating the agreement between measured and simulated bulk optical properties for the silica particle suspensions illustrated in Fig. 4.

Equations (7)

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μ s = j=1 J σ s ( r j )F( r j ) μ a =α j=1 J [ σ a m ( r j ) σ a ( r j ) ]F( r j )       with  α= 4πIm( n m ) λ 0 μ a p = j=1 J σ a ( r j )F( r j ) p( θ )= j=1 J σ s ( r j )p( θ, r j )F( r j ) μ s g= j=1 J σ s ( r j )g( r j )F( r j ) μ s
ε i ( x )=abs( x i+1 x i x i+1 )
J i = { 1 2 i1 +1        if  i=1 if  i>1  
r i,j = { ( r max + r min )/2 r min + ( r max r min ) 4( J i 1) r min + [ ( r max r min )( j1 ) ] ( J i 1) r max ( r max r min ) 4( J i 1)        if  i=1                            if  { i>1 j=1     if  { i>1                         with  2j( J i 1)     if  { i>1   j= J i    
bounds i ={ [ r min r max ] [ r min r min + [ ( r max r min )( 2j1 ) ] 2( J i 1) r max ]        if  i=1                     if  i>1                     with  1j( J i 1)
F( r i,j )=CND( bounds i (j+1))CND( bounds i (j))
r ( i+1 ),( 2j1 ) = r i,j       with  2j( J i 1)

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