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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014
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Dependent scattering in Intralipid® phantoms in the 600-1850 nm range

Ben Aernouts, Robbe Van Beers, Rodrigo Watté, Jeroen Lammertyn, and Wouter Saeys  »View Author Affiliations


Optics Express, Vol. 22, Issue 5, pp. 6086-6098 (2014)
http://dx.doi.org/10.1364/OE.22.006086


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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

1. Introduction

Propagation of Visible (Vis) and Near Infrared (NIR) light through turbid media, like biological tissues, can be described by the radiative transfer theory (RTT), taking into account the medium’s bulk optical properties (BOP): bulk absorption coefficient µa, bulk scattering coefficient µs, reduced scattering coefficient µs, and scattering phase function p(θ) or derived anisotropy factor g. In biomedical optics and spectroscopic applications, knowledge about the product’s BOP is, therefore, essential for a correct understanding of measured optical signals [1

1. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE Press, 2007), p. 840.

,2

2. A. Ishimaru, Wave Propagation and Scattering in Random Media, Volume 1: Single Scattering and Transport Theory, 1st ed. (Academic Press, 1978), p. 250.

]. Accordingly, accurate calibration, validation and comparison of measurement setups with optical phantoms, for which the BOP’s are known accurately, is crucial. Optical phantoms with variable BOP’s can be constructed by mixing an absorbing dye, a scattering agent and a (neutral) matrix in different ratios. Intralipid® (IL) is a fat-in-water emulsion which is frequently used in biomedical optics as scattering component for the preparation of liquid optical phantoms [3

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

]. Since the majority of the fat globules in IL have a diameter smaller than 500 nm, scattering is high in the Vis and decreases with increasing wavelength [4

4. 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]

12

12. 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]

]. Recent studies demonstrated that the batch-to-batch variability in scattering properties of IL is very small and that IL is highly stable over a long time and at different temperatures [4

4. 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]

,5

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

,13

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

]. This confirms that IL is a very suitable scattering component for liquid optical phantoms.

Variability in scattering levels (µs and µs) of the optical phantoms can be created by diluting IL with water (scattering neutral matrix) [3

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

]. If the scattering events are independent and dilution with the matrix (and absorbing dye) does not influence the optical properties of the single scattering particles, µs and µs follow a linear decrease (through the origin) with reducing IL concentration [6

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

]. Moreover, under these conditions, the normalized scattering phase function and the anisotropy factor are independent of the dilution factor. If these conditions are met, the production process for optical phantoms is straightforward as the mixing ratios required to obtain the desired BOP’s can be easily calculated from the known optical properties of the individual components [8

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

,9

9. 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]

,12

12. 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]

]. Di Ninni et al. [6

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

] already reported that the microphysical properties of the single scattering particles in IL are not affected by dilution with water. Furthermore, the results of their experimental investigation showed that dilution only affects absorption according to the linear Beer-Lambert relation. However, if the concentration of scattering particles is high, individual scattering events can influence each other, especially at longer wavelengths [6

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

,11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

,12

12. 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]

,14

14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

]. This phenomenon is often referred to as dependent or correlated scattering, which can be explained by coherent addition of the radiation amplitudes of single scattering events (far-field interaction). For small volume fractions, the arrangement of the scattering particles can be assumed random and at sufficient distance, but this is no longer true at higher volume fractions [15

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

].

In the analytical or multiple scattering theory, which starts from Maxwell equations or wave equations, various multiple scattering processes in a medium can be described with inclusion of dependent scattering, diffraction and interference effects. Although these theories are considered the most rigorous, they are too complex for practical use. Therefore, theories like Twersky’s theory, Foldy-Lax formulation and T-matrix computations have been derived [16

16. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, 3rd ed. (Cambridge University, 2006).

21

21. 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]

]. However, the computations for these theories are still very intensive and knowledge of the dielectric properties at the microscale is required [2

2. A. Ishimaru, Wave Propagation and Scattering in Random Media, Volume 1: Single Scattering and Transport Theory, 1st ed. (Academic Press, 1978), p. 250.

,22

22. A. Ishimaru, Wave Propagation and Scattering in Random Media, Volume 2: Multiple Scattering, Turbulence, Rough Surfaces, and Remote Sensing, 1st ed. (Academic, 1978), p. 319.

]. This information is often not available and difficult to determine.

RTT, on the other hand, deals directly with the transport of energy [23

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

]. It is a conceptually simpler approach, approximating the tissue as a homogeneous layer defined by its BOP’s. Nevertheless, it has been found to accurately describe light propagation in turbid media [1

1. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE Press, 2007), p. 840.

]. Since no correlation between fields is assumed in RTT, dependent scattering is not directly accounted for [24

24. M. I. Mishchenko, D. H. Goldstein, J. Chowdhary, and A. Lompado, “Radiative transfer theory verified by controlled laboratory experiments,” Opt. Lett. 38(18), 3522–3525 (2013). [CrossRef] [PubMed]

]. Therefore, the effect of dependent scattering is included in the bulk scattering properties (µs, µs, g and p(θ)). For this reason, µs and µs deviate from the linear relation with the volume concentration of scattering particles Φp for a specific scattering agent. This deviation typically increases with increasing Φp. Additionally, the normalized p(θ) and g become dependent on Φp [11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

].

Several approximations have been derived to demonstrate the effect of dependent scattering on the bulk scattering coefficient [14

14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

,15

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

,20

20. V. P. Dick, “Applicability limits of Beer’s law for dispersion media with a high concentration of particles,” Appl. Opt. 37(21), 4998–5004 (1998). [CrossRef] [PubMed]

,25

25. R. West, D. Gibbs, L. Tsang, and 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]

27

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

]. However, a closed form solution was only derived by Twersky for small particles compared to the considered wavelength [28

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

]. A correlation-packing factor Wp was determined by reducing the integral of the statistical pair correlation function for impenetrable particles. The pair correlation function characterizes the radial distribution of particles in a three-dimensional space. Hence, the derived packing factor is a simple rational function of the fraction of space occupied by the correlated statistical mechanics particles (volume concentration Φp):

Wp(ϕp)=(1ϕp)p+1[1+ϕp(p1)]p1
(1)

This packing factor Wp decreases monotonously from unity to zero as Φp increases from zero to unity, representing the deviation from the linear relation between µs and Φp [29

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

]. Apart from Φp, Twersky’s packing factor only depends on the packing dimension p [29

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

31

31. J. M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt. 37(13), 2788–2797 (1998). [CrossRef] [PubMed]

]. The packing dimension describes the rate at which the empty space between the scatterers reduces as the total number density increases [31

31. J. M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt. 37(13), 2788–2797 (1998). [CrossRef] [PubMed]

].

The effect of dependent scattering on the scattering phase function and the anisotropy factor has, however, not been studied intensively. Mishchenko used the Percus-Yevick approximation [35

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

], while Mackowski and Mishchenko consulted their T-matrix computations to investigate the effect of the compaction state of monodisperse scattering spheres on the anisotropy factor g [18

18. D. W. Mackowski and M. I. Mishchenko, “Direct simulation of extinction in a slab of spherical particles,” J. Quantum Spectrosc. Radiat. Transfer 123, 103–112 (2013). [CrossRef]

]. Both studies showed a reduction in g with an increase of Φp, especially if the particle radii were in the range of the wavelength.

Dependent scattering in IL dilutions has been studied at a few discrete wavelengths in the Visible and short-wave NIR [6

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

,11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

,14

14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

]. Di Ninni et al. measured the reduced scattering coefficient (µs) at 751 and 833 nm for IL dilutions with a Φp up to 0.032 ml/ml. The relation between Φp and µs could be well explained by second-order polynomials (through the origin) and showed a deviation within 2% from the linear relation (through the origin) for Φp < 0.023 ml/ml [6

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

]. Zaccanti et al. and Giusto et al. studied the bulk scattering properties (µs, µs and g) at 633 nm for IL dilutions with a Φp up to 0.227 ml/ml (pure IL) [11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

,14

14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

]. Both µs and µs followed a second-order polynomial (through the origin) as a function of Φp, while g followed a nearly linear decrease. Unfortunately, no information is available about the effect of dependent scattering on the scattering properties of IL dilutions for wavelengths above 850 nm. However, for spectroscopic applications, the longer wavelength range is more valuable because of the presence of many important molecular overtones and combination vibrations in the NIR [36

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

,37

37. 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]

]. Since scattering by IL in the NIR is relatively low, high concentrations are needed in the optical phantoms to mimic the relatively high µs and/or µs of biological tissues or other turbid samples. Additionally, the effect of dependent scattering is even more dominant for longer wavelengths [6

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

,11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

,12

12. 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]

,14

14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

,27

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

,31

31. J. M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt. 37(13), 2788–2797 (1998). [CrossRef] [PubMed]

]. For these reasons, dependent scattering is expected to be more significant in IL phantoms in the NIR range and has to be taken into account in the calculation of the BOP for a specific mixing ratio of the different phantom components [38

38. R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. M. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013). [CrossRef] [PubMed]

].

The main objective of this research was to study and describe the effect of dependent scattering on the bulk scattering properties of IL phantoms in the 600-1850 nm wavelength range. Semi-empirical equations were derived, describing the bulk scattering properties (µs, µs and g) as a function of the wavelength λ and the volume concentration of scattering IL particles Φp.

2. Materials and methods

2.1 Liquid optical phantoms

The set of 57 liquid optical phantoms consulted in this study is the same set as used in [12

12. 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]

], covering a wide range of IL concentrations (1-100% v/v). Methylene Blue (M9140, Sigma-Aldrich, Missouri, USA), Intralipid® 20% (batch 10FH1726, expiring date 07/2014, Fresenius Kabi, Germany) and deionized water were respectively used as absorbing, scattering and dilution agent and mixed in different ratios. Methylene Blue (MB) was chosen as absorber since it has a sharp absorption peak in the 550-750 nm range where absorption by water and IL is minimal (both µa < 0.03 cm−1) [8

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

]. Taking into account the density of the different IL components, pure IL contains 22.7% (v/v) scattering particles (soybean oil + egg lecithin) [8

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

11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

]. 56 phantoms were created by combining 8 absorption levels, corresponding to MB concentrations of 0, 4, 8, 16, 32, 64, 128 and 136 µM, and 7 scattering levels, corresponding to IL concentrations of 1, 2, 4, 8, 16, 32 and 64% (v/v) or a Φp of respectively 0.00227, 0.00454, 0.00908, 0.01816, 0.03632, 0.07264 and 0.14528 ml/ml. Additionally, pure IL (Φp = 0.227 ml/ml) was also measured.

2.2 Optical characterization of phantoms

The diffuse reflectance and total transmittance for all phantoms was measured in a DIS setup, while the unscattered transmittance was measured in a separate measurement path. The measurement setup was especially designed to obtain high signal-to-noise spectra in the 500 – 2250 nm wavelength range for very turbid media. An extensive description about the measurement setup and calibration and measurement procedure can be found in [12

12. 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]

].

The inverse adding doubling (IAD) program developed and optimized by Prahl [39

39. S. A. Prahl, “Everything I think you should know about Inverse Adding-Doubling,” http://omlc.ogi.edu/software/iad/iad-3-9-10.zip.

] was consulted for the estimation of the BOP values from the diffuse reflectance and total and unscattered transmittance measurements. Apart from the three measurements, also the real refractive index (n) of the sample has to be provided to the algorithm and was therefore calculated based on the volume concentration of scattering particles (Φp) in the sample: nsample = nwater + 0.14Φp [8

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

,9

9. 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]

]. The wavelength-dependent real refractive index of water at room temperature was adopted from Hale and Querry [40

40. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12(3), 555–563 (1973). [CrossRef] [PubMed]

]. The effect of MB on the refractive index of the sample was neglected because of the very low concentrations.

The bulk absorption (µa) and reduced scattering coefficient (µs) could be estimated for the entire range. However, separation between µs and g could not be established when the scattering depth (µs*d) was very high. The reason for this was the presence of a significant amount of scattered photons in the measurement of the unscattered transmittance [12

12. 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]

]. In general, good estimations for µs and g were obtained for λ ≥ 560 + 2200Φp in the case of 0.55 mm sample thickness and λ ≥ 600 + 3000Φp for 1.1 mm sample thickness (λ in nm and Φp in ml/ml). Moreover, because of low signal levels in the diffuse reflectance measurements for wavelengths above 1200 nm (high absorption by water) for phantoms with very low scattering levels (Φp ≤ 0.02 ml/ml), no accurate estimates for the anisotropy factor could be established for that specific range [12

12. 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]

]. As for the remaining range, the estimated BOP’s for the phantoms measured at two different sample thicknesses were nearly the same, it was concluded that the measurement and BOP estimation procedure were accurate [12

12. 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]

]. Hence, the BOP’s of the same phantom for both thicknesses were treated here as replicates. Moreover, as the separation between scattering and absorption was very successful, with nearly no cross-talk, the phantoms with different absorption levels for a fixed scattering level were also treated as replicates for the bulk scattering properties (µs, g and µs).

2.3 Equation fitting to the bulk scattering properties

For fitting the equations, only the wavelength range 600-1850 nm was considered. Below 600 nm, no estimates for µs and g were available for phantoms with Φp ≥ 0.018 ml/ml since the unscattered transmittance measurements were incorrect. Above 1850 nm, the estimated BOP’s for low scattering levels (Φp ≤ 0.03 ml/ml) showed large variability. This can be explained by the low signal levels in the diffuse reflectance measurements, due to combination of the high absorption by water and the low scattering for low IL concentrations [12

12. 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]

].

The Twersky equation [Eq. (1)] describes the deviation from the linear ‘independent scattering’ relation between µs and Φp. In order to describe the direct relation between µs and Φp, including dependent scattering, the Twersky equation needs to be multiplied with this linear relation. An accurate equation for the µs spectrum of pure IL in the 500-2250 nm range, in absence of dependent scattering, was derived in [12

12. 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]

], with µs in cm−1 and λ in nm:

μsindep(λ)=1.868*1010λ2.59
(2)

The linear relation between µs and Φp for independent scattering can be obtained by correcting Eq. (2) with 0.227 ml/ml (Φp for pure IL) and multiplying with the actual Φp. The final equation, describing µs as a function of λ and Φp, taking into account dependent scattering by including the packing factor, can be written as follows:

μs(λ,ϕp)=μsindep(λ)0.227ϕp{(1ϕp)p(λ)+1[1+ϕp(p(λ)1)]p(λ)1}
(3)

As p is unknown for IL in the Vis-NIR range, Eq. (3) was evaluated by fitting a p-parameter at each wavelength. The fitted p-parameters were then used in the further analysis.

Since no closed form solution describing the effect of dependent scattering on the anisotropy factor for densely packed scattering media was found in literature, an empirical approach was followed. For very low IL concentrations (Φp → 0 ml/ml), independent scattering is valid and the g-value only depends on the wavelength (λ). In [12

12. 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]

], the following equation was derived for this relation in the 500-2250 nm range, with λ in nm:

gindep(λ)=a(1f1+ec(λ+d)+f)+b(1h1+ec(λ+d)+h)λa=1.094;b=5.653*104;c=5.3*103;d=a(f1)b(h1);f=0.3516;h=0.1933
(4)

A more general equation for the anisotropy factor g(λ, Φp) in the 600-1850 nm range, also valid for the case of dependent scattering (Φp > 0.02 ml/ml), will be determined empirically after visual inspection of the data, starting from the formula for gindep(λ) [Eq. (4)].

The derived equations were fitted to the measured BOP spectra in Matlab (version 7.10, The Mathworks Inc., Massachusetts, USA) with the curve fitting tool (cftool) for the case of 1 independent variable or the surface fitting tool (sftool) for 2 independent variables.

To describe the effect of dependent scattering on µs, the derived general equations for µs [Eq. (3)] and g were substituted in the similarity relation [41

41. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley, 1957), p. 470.

]:

μs(λ,ϕp)=μs(λ,ϕp)[1g(λ,ϕp)]
(5)

3. Results and discussion

This manuscript presents a more thorough analysis of the effect of dependent scattering on the estimated BOPs of IL phantoms presented in [12

12. 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]

]. For the measured diffuse reflectance and total and unscattered transmittance spectra, as well as an overview and detailed description on the estimated BOP’s, the reader is referred to that publication. Moreover, in the results presented in [12

12. 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]

] no effect of dependent scattering on the bulk absorption coefficient (µa) can be observed, which confirms the conclusion presented in [6

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

].

3.1 Bulk scattering coefficient

In Figs. 1(a)
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.
and 1(b), the estimated bulk scattering coefficient (µs) values are presented as a function of the volume concentration of scattering particles Φp for respectively 3 wavelengths below and 3 wavelengths above 1000 nm.

The average of 16 replicates (2 sample thicknesses x 8 absorption levels) for each scattering level is plotted as a cyan dot surrounded by error bars, indicating the standard deviation. The error bars are, however, rather small, indicating the high repeatability of the measurements and BOP estimation procedure. For phantoms with high IL concentrations, the scattering (depth) was very high, especially for short wavelengths (Vis). As a result, scattered photons were captured during the unscattered transmittance measurements and no correct separation between µs and g could be established. Therefore, µs data for short wavelengths were only available for low IL concentrations [Fig. 1(a)]. Equation (3), with a variable packing dimension p, was fitted successfully (all R2 > 0.996) to the µs data for all 6 wavelengths [Figs. 1(a) and 1(b), solid lines]. In Fig. 1(a), the second-order polynomial derived for IL at 633 nm by Zaccanti et al. [11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

] has also been plotted. A very good agreement between this model, the data and the fitted Twersky model can be noticed.

3.2 Anisotropy factor

g(λ,ϕp)=gindep(λ)+k(λ)ϕp
(6)

For each individual wavelength, the linear function [Eq. (6)] with predetermined intercept and variable slope k was fitted to g as a function of Φp. The results for 3 wavelengths below and 3 wavelengths above 1000 nm are presented in respectively Figs. 4(a) and 4(b). It can be concluded that the fitted linear equations describe the effect of dependent scattering on g well. Comparison of our results at 635 nm with the results reported by Zaccanti et al. [11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

] for g as a function of Φp at 633 nm shows a good agreement. Nevertheless, one might argue that for Φp going to zero, a convergence to a stable value would be more appropriate. Moreover, following these linear equations for Φp above 0.227 ml/ml (pure IL), g would become negative which is very rare for biological tissues or fluids [35

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

]. So, the underlying relation is probably more complex, but not enough data were available to fit a more complex function.

In Fig. 5(a)
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.
the fitted slope parameters at each wavelength are presented, while the R2 for each fit is illustrated in Fig. 5(b). The R2 values corresponding to the linear equations for wavelengths outside the 800-1400 nm range indicate a rather poor fit. This can be explained by the relatively large variation in g for a specific Φp compared to the variability of the average g between different levels of Φp, characterized by a slope close to 0. However, the linear function tends to describe the slightly decreasing trend fairly good. The slope, and with that the effect of dependent scattering on g, is more negative for wavelengths in the 800-1400 nm window with a minimum around 1000 nm. It was noticed by Mishchenko [35

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

] that the effect of dependent scattering on g is maximum if the wavelength is between 0.5 and 20 times larger than the radii of the scattering particles. As most of the fat globules in IL have a diameter smaller than 500 nm, with a mean particle radius around 50 nm [9

9. 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]

], our results confirm these observations.

In order to define a general model for g as a function of both λ and Φp, an equation for the slope parameter k had to be derived, while the wavelength dependency of k cannot be described by a simple function. From Fig. 5(a), it can be observed that the k-parameter decreases with increasing wavelength until it reaches a minimum around 1000 nm. For longer wavelengths it increases again until it tends to converge to a constant value. A fifth order polynomial was fitted (R2 = 0.934) to the k-data and plotted as a solid line in Fig. 5(a). The combination of the equation for k and Eqs. (4) and (6) provides a general equation for g as a function of both λ and Φp. This general model is presented as a surface in 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).
and compared (R2 = 0.992) with the measured g-data (grey dots). It should, however, be emphasized that the general equations for µs and g were only validated against data for which λ ≥ 560 + 2200Φp, λ ≤ 1850 nm and Φp ≤ 0.227 ml/ml, and that extrapolation of the models is not advised.

3.3 Reduced scattering coefficient

If the general equations for µs and g are combined with Eq. (5), a general model is obtained describing the reduced scattering coefficient (µs) as a function of λ and Φp. In Figs. 7(a)
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.
and 7(b), the effect of dependent scattering on the measured µs values (cyan markers) for respectively 3 wavelengths below and 3 wavelengths above 1000 nm is presented. Moreover, the results of the general equation for µs at the 6 discrete wavelengths are plotted as solid lines. A very good agreement was found between the measured values and the model (all R2 > 0.993). At 635 nm, the model was in better agreement with the measured data than the results at 633 nm presented in [11

11. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

] [Fig. 7(a)]. Moreover, a very good agreement was found with the empirical equations derived by Di Ninni et al. [6

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

] at 751 and 833 nm [Fig. 7(a) detail].

In 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).
, the general model for µs (surface) is plotted together with the measured µs data (grey dots). A very good correspondence (R2 = 0.999) can be observed. The model even performs well in the region for which no µs and g data could be extracted from µs because of erroneous unscattered transmittance measurements (λ < 560 + 2200Φp, λ ≥ 600 nm and Φp ≤ 0.227 ml/ml). This result strengthens the general models for µs and g, even in the regions where only limited data was available.

4. Conclusion

A set of 57 liquid optical phantoms was designed, prepared and optically characterized in order to study the effect of a dense distribution of scatterers on the scattering properties. Under the assumption of independent scattering, the bulk and reduced scattering coefficients follow a linear relation with the volume concentration for a specific type of scattering particles, while the anisotropy factor remains constant. However, for densely packed particles, the scattering events are correlated and the scattering properties deviate from those simple relations. From our study, it can be concluded that the bulk scattering coefficient as a function of the particle concentration for IL dilutions corresponds well with the packing factor proposed by Twersky in combination with a variable packing dimension. It was observed that in the case of constant particle sizes, the effect of dependent scattering is more significant for longer wavelengths. The developed general model for the bulk scattering coefficient describes the relation with wavelength and particle concentration very well (R2 = 0.999). From observations of anisotropy factors of IL dilutions, both in literature and measured, it was noticed that they follow a nearly linear decrease with increasing particle density. Moreover, the slope of the linear decrease was more steep for wavelengths around 1000 nm. This information was combined in a general model which describes the anisotropy factor as a function of the wavelength and particle concentration very well (R2 = 0.992). Additionally, by merging the models for the bulk scattering coefficient and the anisotropy factor, very accurate predictions of the reduced scattering coefficient values were obtained (R2 = 0.999). The equations or models given in this manuscript were derived following a semi-empirical approach and do not rely on a rigorous theory. Nevertheless, very good agreement was found with measured data and models derived by other researchers. Therefore, they provide a valuable tool for the calculation of the bulk scattering properties of IL dilutions, and the validation of theories that describe dependent scattering for IL-like systems.

Acknowledgments

Ben Aernouts is funded as aspirant of the Research Foundation-Flanders (FWO-Flanders, grant 11A4813N). Rodrigo Watté and Robbe Van Beers are funded by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Flanders, respectively grants 101552 and 131777). The authors gratefully acknowledge IWT-Flanders for the financial support through the GlucoSens project (SB-090053).

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

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S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and 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]

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

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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]

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G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]

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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]

13.

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

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A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, and O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]

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OCIS Codes
(290.5820) Scattering : Scattering measurements
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:
Scattering

History
Original Manuscript: January 31, 2014
Revised Manuscript: February 20, 2014
Manuscript Accepted: February 21, 2014
Published: March 6, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Ben Aernouts, Robbe Van Beers, Rodrigo Watté, Jeroen Lammertyn, and Wouter Saeys, "Dependent scattering in Intralipid® phantoms in the 600-1850 nm range," Opt. Express 22, 6086-6098 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-6086


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References

  1. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE Press, 2007), p. 840.
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media, Volume 1: Single Scattering and Transport Theory, 1st ed. (Academic Press, 1978), p. 250.
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. R. Michels, F. Foschum, A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16(8), 5907–5925 (2008). [CrossRef] [PubMed]
  9. 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]
  10. 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]
  11. G. Zaccanti, S. Del Bianco, F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42(19), 4023–4030 (2003). [CrossRef] [PubMed]
  12. 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]
  13. 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]
  14. A. Giusto, R. Saija, M. A. Iatì, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. 42(21), 4375–4380 (2003). [CrossRef] [PubMed]
  15. 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]
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