## Optical properties of fat emulsions

Optics Express, Vol. 16, Issue 8, pp. 5907-5925 (2008)

http://dx.doi.org/10.1364/OE.16.005907

Acrobat PDF (801 KB)

### Abstract

We present measurements of the optical properties of six different fat emulsions from three different brands, Clinoleic, Lipovenoes and Intralipid, with fat concentrations from 10% to 30%. The scattering coefficient, the reduced scattering coefficent, and the phase function of each sample are measured for wavelengths between 350nm and 900 nm. A method for the calculation of the particle size distribution of these fat emulsions is introduced. With the particle size distribution the optical properties of the fat emulsions are obtained with Mie theory. Simple equations for the calculation of the absorption coefficient, the scattering coefficient, the reduced scattering coefficient, the g factor, and the phase function of all measured samples are presented.

© 2008 Optical Society of America

## 1. Introduction

1. A. Kienle, F. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. **26**, 1571–1573 (2001). [CrossRef]

2. F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express **15**, 486–500 (2007). [CrossRef] [PubMed]

3. J. Allardice, A. M. Abulafi, D. Webb, and N. Willimas, “Standardization of intralipid for light scattering in clinical photodynamic therapy,” Lasers Med. Sci. **7**, 461–465 (1992). [CrossRef]

4. S. Flock, S. Jacques, B. Wilson, W. Star, and M. vanGemert, “The optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. **12**, 510–509 (1992). [CrossRef] [PubMed]

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

6. J. Choukeife and J. L’Huillier, “Measurements of scattering effects within tissue-like media at two wavelengths of 632.8 nm and 680 nm,” Lasers Med. Sci. **14**, 286–296 (1999). [CrossRef]

7. E. Drakaki, S. Psycharakis, M. Makropoulou, and A. Serafetinides, “Optical properties and chromophore concentration measurements in tissue-like phantoms,” Opt. Commun. **254**, 40–51 (2005). [CrossRef]

8. I. Driver, J. Feather, P. King, and J. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. **34**, 1927–1930 (1989). [CrossRef]

9. S. Flock and B. W. M. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. **14**, 835–841 (1987). [CrossRef] [PubMed]

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

11. T. Pham, F. Bevilacqua, T. Spott, J. Dam, and B. T. S. Andersson-Engels, “Quantifying the absorption and reduced scattering coefficients of tissuelike turbid media over a broad spectral range with noncontact fouriertransform hyperspectral imaging,” Appl. Opt. **39**, 6487–6497 (2000). [CrossRef]

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

*µ*, the reduced scattering coefficient

_{s}*µ*′

_{s}, the absorption coefficient

*µ*and the anisotropy factor

_{a}*g*, also the particle size distribution of Intralipid [5

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

6. J. Choukeife and J. L’Huillier, “Measurements of scattering effects within tissue-like media at two wavelengths of 632.8 nm and 680 nm,” Lasers Med. Sci. **14**, 286–296 (1999). [CrossRef]

6. J. Choukeife and J. L’Huillier, “Measurements of scattering effects within tissue-like media at two wavelengths of 632.8 nm and 680 nm,” Lasers Med. Sci. **14**, 286–296 (1999). [CrossRef]

**14**, 286–296 (1999). [CrossRef]

9. S. Flock and B. W. M. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. **14**, 835–841 (1987). [CrossRef] [PubMed]

*g*factor was measured mostly indirectly by calculating it from the measurement of

*µ*and

_{s}*µ*′

_{s}. In addition, the recipe and the manufacturing of Intralipid10% have changed since the study of van Staveren et al. [5

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

*µ*,

_{s}*µ*′

_{s},

*g*, and the phase function

*p*(

*θ*), of Intralipid, Lipovenoes and ClinOleic, with fat concentrations from 10% to 30% for wavelengths between 350nm and 900nm. The size distribution of each fat emulsion was calculated and is presented here. With the given size distribution the optical properties can be computed with Mie theory. Due to the complexity of the Mie theory simple analytic equations are presented to calculate the optical properties,

*µ*,

_{a}*µ*,

_{s}*µ*′

*,*

_{s}*g*, as well as the phase function

*p*(

*θ*), for wavelengths from 400nm to 1000nm for each sample.

*µ*and

_{s}*µ*is explained in section 2.1, the measurement of

_{a}*µ*′

*is stated in section 2.2 and the measurement of the phase function and the anisotropy factor is introduced in section 2.3. A brief introduction to the correction of the phase function measurement is given in section 2.4. The consistence and physical properties of the fat emulsions are explained in section 2.5. Mie theory is briefly introduced in section 2.6. The calculation of the size distribution is explained in section 2.7. In the result section we finally present the comparison of our measurement results with Mie theory. In section 3.1 two examples of the phase function measurements are discussed. The measurements of the anisotropy factor (section 3.2), of the scattering coefficient (section 3.3), of the reduced scattering coefficient (section 3.4) and of the absorption coefficient (section 3.5) follow. In section 3.6 analytical formulations for the calculation of*

_{s}*µ*,

_{a}*µ*,

_{s}*µ*′

*,*

_{s}*g*and

*p*(

*θ*) are given.

## 2. Methods and materials

### 2.1. Collimated transmission setup

*µ*(λ)=

_{t}*µ*(λ)+

_{a}*µ*(λ), of a sample is measured. In our setup the sample is illuminated with a collimated white light source. The measured intensity

_{s}*I*(λ) is described by the Lambert-Beer law:

*c*is the concentration,

*d*is the path length trough the sample, and

*I*

*is the incident intensity. The distance between sample and detector has to be large enough to detect only unscattered photons. Then, the measured attenuation coefficient of solely scattering samples,*

_{o}*µ*≫

_{s}*µ*, equals the scattering coefficient,

_{a}*µ*=

_{t}*µ*, like it is the case for fat emulsions. For solely absorbing samples,

_{s}*µ*≫

_{a}*µ*, the measured attenuation coefficient equals the absorption coefficient,

_{s}*µ*=

_{t}*µ*.

_{a}### 2.2. Spatially resolved reflectance setup

*R*(

*r*) emitted by a semi-infinite sample which is illuminated perpendicular with a collimated point source. In this work it was employed to measure the reduced scattering coefficient of diluted fat emulsion samples. The spatial resolved reflectance

*R*(

*r*) of homogeneous, semi infinite media can be calculated with the diffusion Eqs. [13

13. A. Kienle and M. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium.” J. Opt. Soc. Am. **14**, 246–254 (1997). [CrossRef]

14. A. Kienle, L. Lilge, M. Patterson, R. Hibst, R. Steiner, and B. Wilson, “Spatially-resolved absolute diffuse reflectance measurements for non-invasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. **35**, 2304–2314 (1996). [CrossRef] [PubMed]

*r*≫1/

*µ*′

*, and the medium has to be highly scattering,*

_{s}*µ*′

*≫*

_{s}*µ*. For unknown absorption and scattering properties of the media, an inverse calculation of the diffusion equation was employed to calculate the absorption and scattering coefficients of the sample. In general, the diffusion equation is fitted to the measured spatially resolved reflectance

_{a}*R*(

*r*) with variable

*µ*,

_{a}*µ*′

*and a multiplicative adjustment variable.*

_{s}*µ*′

*and the multiplicative factor, thus the reduced scattering coefficient can be calculated with high accuracy.*

_{s}*µ*′

*was analyzed with Monte Carlo simulations. The inverse calculation with known*

_{s}*µ*produced errors of less than 1%for Monte Carlo simulations using Henyey Greenstein phase function with

_{a}*µ*,

_{a}*µ*and

_{s}*g*similar to the optical properties of the measurements. Monte Carlo simulations which were performed with the measured phase function of Lipovenoes10%instead of the Henyey-Greenstein phase function produced higher errors which are still below 3%. An illustration to the difference of Henyey Greenstein and Lipovenoes phase functions with the same

*g*factor is given in Fig. 3(b).

*µ*or

_{a}*µ*′

*because the dynamic range of the spatially resolved reflectance function*

_{s}*R*(

*r*) will raise. The errors that are expected for a CCD based measurement setup were investigated with convoluted Monte Carlo simulations. The previous Monte Carlo simulation which utilizes the phase function of Lipovenoes10% was convoluted with the point spread function of the camera objective which was measured at 633nm. The inverse calculation of the convoluted simulation showed a deviation of up to 8%. Thus the inverse calculation of the measured spatially resolved reflectance is expected to have an uncertainty of about 8% for samples with similar optical properties.

### 2.3. Goniometer setup

*p*(

*s⃗*,

*s⃗*′) describes the probability that a photon having an incident direction

*s⃗*is scattered in direction

*s⃗*′, see Fig. 3(a). The phase functions of different scattering samples can vary strongly. Also phase functions with the same anisotropy factor can have big differences, see Fig. 3(b).

*p*(

*θ*,

*ϕ*) is measured for nearly the whole solid angle [16

16. F. Forster, A. Kienle, R. Michels, and R. Hibst, “Phase function measurements on nonspherical scatterers using a two-axis goniometer,” J. Biomed. Opt. **11**, 024,018 (2006). [CrossRef]

*p*(

*s⃗*,

*s⃗*′) for many incident directions

*s⃗*. However, for spherical scatterers like fat droplets the phase function is independent of the incident direction

*s⃗*and can be noted as

*p*(

*θ*,

*ϕ*). Furthermore the phase function is rotationally symmetric for unpolarized light. That means, the phase function

*p*(

*θ*) is constant for different

*ϕ*. With our setup the phase function

*p*(

*θ*) of spherical scatterers is always measured in the z-y plane. The polarization direction of an incident linear polarized light source is rotated using special optics. The phase function of the whole solid angle

*p*(

*θ*,

*ϕ*) can be calculated by the superposition of the phase function for perpendicular (in respect to the measurement plane) (

*p*) and parallel (

_{per}*p*) polarized light

_{par}*p*(

*θ*,

*ϕ*)=

*p*(

_{per}*θ*)·cos(

*ϕ*)+

*p*(

_{par}*θ*)·sin(

*ϕ*).

### 2.4. Phase function correction

**14**, 286–296 (1999). [CrossRef]

*p*(

*θ*) for all

*θ*-angles. Slab geometry cuvettes, like the ones used in this work, prohibit the measurement of the phase function in slab direction (usually the x-y plane). Since this goniometer is originally built to measure thin slices of biological samples, correction algorithms for samples in slab geometry have been developed. Hence, a slab geometry cuvette was used for the measurement of the fat emulsions as is shown in Fig. 4(a). We note that the distortion of the phase function measurement caused by a cylindrical cuvette is not that obvious, but it has to be corrected similar as it is done for slab geometry cuvettes. Furthermore, cylindrical cuvettes produce a strong distortion of the incident beam, thus they appeared unsuitable for phase function measurement with high angle resolution in our opinion.

*θ*toward 90°. As can be seen in Fig. 4(b), no light is exiting the cuvette at

*θ*=90° (dashed line). Furthermore, the incident beam is reflected at the rear glass which causes the phase function to be superposed by itself in backward direction. Also, the scattered light itself is reflected at the glass/fluid boundary when exiting the cuvette. An analytical solution for the correction of these distortions was developed. The forward calculation of the distortion and the backward correction are shown in Fig. 4(b) for a theoretical phase function of Intralipid. The geometrical errors can be corrected completely if single scattering is assumed.

*s⃗*is still in z direction, but the cuvette is rotated around the x axis and has an angle to the x-y plane. This is demonstrated in Fig. 5. Figure 5(a) shows the measurement of Lipovenoes20% in a cuvette having slab geometry with different angles of the cuvette to the x-y plane. It was illuminated with perpendicular (in respect to the measurement plane) polarized light at

*λ*=650nm. The measurement was performed for tilt angles of the cuvette of 0°, 9.3°, 16.8° and 33.3° (respective to the x-y plane). The distortion of the phase function depends on the tilt angle. The shading of the cuvette moves from 90° toward 56.7°. Additionally, the reflected peak of the incident beam moves from 180° toward 113.4°.

*g*-factor can be calculated as it is explained in section 2.6. With the known anisotropy factor it is possible to compare the measurement of the collimated transmission and the spatially resolved reflectance using

### 2.5. Fat emulsions

*µ*,

_{s}*µ*′

*,*

_{s}*g*and

*p*(

*θ*), of the fat emulsions can be calculated with Mie theory, as it is explained in section 2.6. For the calculation with Mie theory the knowledge of the size distribution of the fat droplets, the inner and outer refractive index of the fat droplets as well as the volume concentration of the droplets are needed.

**30**, 4507–4514 (1991). [CrossRef] [PubMed]

*I*=1.311, J=1.15

_{water}^{4}×104 and K=-1.132×10

^{9}. The wavelength λ is given in nanometers. The wavelength dependent refractive index of soy bean oil is not well-investigated. Van Staveren, et al., [5

**30**, 4507–4514 (1991). [CrossRef] [PubMed]

*I*=1.451 and the same J and K coefficients that are used for water. Thus, soy bean oil is expected to show the same dispersion as water with a constant difference of Δ

_{soy}*n*=

*n*-

_{soy}*n*=

_{water}*I*-

_{soy}*I*=0.140. We performed refractometer measurements which did not show differences outside the measurement accuracy to

_{water}*n*(λ)

*calculated with Eq. 3 for wavelength higher than 400nm. For wavelengths below 400nm the results of Eq. 3 are invalid. Mie theory can be used slightly below 400nm because the refractive index difference between soy bean oil and water, Δ*

_{soy}*n*, is expected to be constant. The refractive index of egg lipid is not known and is assumed to be identical to the refractive index of soy bean oil. For ClinOleic the refractive index of olive oil is assumed to be identical with soy bean oil.

### 2.6. Mie theory

*µ*,

_{s}*µ*′

*,*

_{s}*g*and the phase function

*p*(

*θ*), of the fat emulsions using Mie theory. The Mie theory is the analytical solution of the Maxwell’s equations for the scattering of electromagnetic wave by a single spherical particle [21

21. G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Physik **330**, 377–445 (1908). [CrossRef]

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

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

*d*found in the solution. The scattering coefficient of the solution can be calculated with

*µ*equals the sum of the scattering cross sections

_{s}*C*, which is calculated with Mie theory, for every particle diameter weighted by the volume concentration σ

_{sca}*(volume of fat and egg lipid divided by the total volume) and particle volume*

_{sca}*d*a single phase function

*p*(

_{i}*θ*) can be calculated using Mie theory. The phase function of the whole solution

*p*(

_{tot}*θ*) is the sum of all, unnormalized,

*p*(

_{i}*θ*) weighted by the number of particles

*N*with the corresponding diameter

_{i}*N*=∑

_{tot}*N*. With the knowledge of the phase function the anisotropy factor

_{i}*g*is determined by

### 2.7. Size distribution calculation

*µ*and the phase function for all measured wavelengths. A Gaussian distribution of particle sizes did not fit the measurements. The attempt to fit a free size distribution did not succeed. The size distribution of Intralipid10% which was measured by van Staveren [5

_{s}**30**, 4507–4514 (1991). [CrossRef] [PubMed]

*N*(

*d*) of fat emulsions with only two parameters, the constant decay

*α*and the maximum particle size

*d*. The number of particles

_{max}*N*(

*d*) is calculated for every particle diameter

*d*from the minimum diameter

*d*to the maximum diameter

_{min}*d*. The smallest particles in fat emulsions are lipid micelles. A minimum micelles diameter of

_{max}*d*=25nm is assumed. The maximum diameter

_{min}*d*can differ in dependence of the manufacturing process, thus it was a free fitting parameter. For the Mie theory calculation 21 discrete values of

_{max}*d*between

*d*and

_{min}*d*are used.

_{max}*α*and

*d*, are listed in Tab. 2.

_{max}**30**, 4507–4514 (1991). [CrossRef] [PubMed]

## 3. Results

*µ*,

_{s}*µ*′

*,*

_{s}*g*and

*p*(

*θ*) of six different fat emulsions within a wavelength range from 400nm to 900nm are presented. Additionally, the optical properties are calculated with the Mie theory method which was explained in section 2.6 and the calculated size distribution of section 2.7. Finally simple equations are provided for the calculation of the optical properties of each measured fat emulsion for wavelengths from 400nm to 1000nm for unpolarized light.

### 3.1. Phase function

*g*factor. For 650nm the

*g*factor is not significantly affected, for 350nm, the measured

*g*factor is lowered by 3%. From 650nm to 350nm we expect, according to our experience, a linear increase of the error. The

*g*factor measurements presented in section 3.2 are corrected for these errors.

### 3.2. Anisotropy factor

*g*was calculated, see Fig. 9. The measured anisotropy factors were corrected for multiple scattering at small wavelengths as it is explained in the end of section 3.1. In Fig. 9 the measured anisotropy factor is plotted for the six different fat emulsions for non polarized light from 350nm to 650nm. The corresponding Mie theory calculations for the different size distribution of the according samples are shown. The measurements show a good correlation with the Mie theory calculations. The anisotropy factor is strongly dependent on the wavelength. Large differences between the different samples are found. The relative standard deviation of the measured

*g*is less than 1% and, thus, within the symbol sizes. It was calculated from multiple measurements using different bottles of the same brand. The measured anisotropy factors of the samples exhibit large deviations to the anisotropy factor reported by van Staveren [5

**30**, 4507–4514 (1991). [CrossRef] [PubMed]

### 3.3. Scattering coefficient

*µ*of the different fat emulsions measured with the collimated transmission setup are plotted from 400nm′900nm in Fig. 10. The results are given for the undiluted fat emulsions. The relative error of

_{s}*µ*is approximately 3% for all wavelengths. It was calculated from multiple measurements of nine different bottles of Lipovenoes 20%. The Mie theory calculations are plotted in the same color as the corresponding measurements. The relative difference between theory and measurement reaches its maximum of about 10% for small wavelengths. The differences of the various samples are large in comparison to the standard deviation of different measurements on the same sample.

_{s}### 3.4. Reduced Scattering Coefficient

*µ*and

_{s}*g*, with

*µ*′

*=(1-*

_{s}*g*)

*µ*. The differences of the measurements compared to the theory can be explained by the error analysis of this method which is explained in section 2.2. In contrast to the preceding measurements of

_{s}*µ*and

_{s}*g*the measured reduced scattering coefficient of Intralipid10% (and Lipovenoes10%) is close to the values measured by van Staveren [5

**30**, 4507–4514 (1991). [CrossRef] [PubMed]

*g*and

*µ*of Intralipid10% do accurately compensate one another [22

_{s}22. R. Graaff, J. Aarnoudse, J. Zijp, P. Sloot, F. de Mul, J Greve, and M. Koelink, “Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. **31**, 1370–1376 (1992). [CrossRef] [PubMed]

### 3.5. Absorption coefficient

23. R. Pope and E. Fry, “Absorption spectrum (380-700 nm) of pure water. II Integrating cavity measurements,” Appl. Opt. **36**, 8710–8723 (1997). [CrossRef]

*µ*(

_{a}*VIS*)≤0.001mm

^{-1}). The absorption is strongly increasing versus smaller wavelengths, as can be seen in Fig. 12.

*µ*

_{a}_{(ges)}, is the sum of the single absorbers multiplied with their volume concentration

### 3.6. Fitted equations

*g*(

*λ*) can be approximated by a linear function

*µ*(

_{s}*λ*) by a power function

*µ*′

*(*

_{s}*λ*) by a polynomial of second order

*λ*=650 for red light), then

*µ*and

_{s}*µ*′

*of the undiluted fat emulsions are obtained in [mm*

_{s}^{-1}].

*µ*(

_{a}*λ*) of pure water and soy bean oil are listed in Tab. 6 in the appendix. The absorption coefficient is obtained in [mm

^{-1}] for the pure substance with

23. R. Pope and E. Fry, “Absorption spectrum (380-700 nm) of pure water. II Integrating cavity measurements,” Appl. Opt. **36**, 8710–8723 (1997). [CrossRef]

*r*

^{2}is defined by

*r*

^{2}=1-

*S*/

_{err}*S*with

_{mean}*S*, the sum of squares error and

_{err}*S*the sum of squares about the mean. A perfect fit is characterized by a residual of one, in practice a good fit is characterized by a residual very close to one (e.g. 0.99 or 0.999).

_{mean}*p*(

*θ*,

*λ*) over the whole solid angle for wavelengths from 400nm to 1000nm the phase functions are normalized to a maximum of one. The logarithm of the intensity log(

*I*(

*λ*)) is plotted against the negative cosine -cos(

*θ*) of the angle

*θ*and the wavelength, see Fig. 13(a). We found that a rational equation fits the data

## 4. Conclusion

*µ*,

_{a}*µ*,

_{s}*µ*′

*,*

_{s}*g*and

*p*(

*θ*), of six different fat emulsions were performed. The absorption coefficient of the fat emulsions was calculated from the water and soy bean absorption as was explained in section 3.5. The optical properties of the six fat emulsions were completely defined for VIS and NIR wavelengths.

*µ*,

_{s}*g*and

*p*(

*θ*) of the different brands are significant and bigger than the standard deviations measured for different bottles of the same brand and concentration. Interestingly, also the same brands with different fat concentrations have significant differences in

*µ*,

_{s}*g*and

*p*(

*θ*) when diluted to the same fat concentration. Our measurements of

*µ*,

_{s}*g*and

*p*(

*θ*) of Intralipid10% shows large deviations to the measurements of van Staveren in 1991 [5

**30**, 4507–4514 (1991). [CrossRef] [PubMed]

*µ*and

_{s}*g*do just compensate each other when calculating the reduced scattering coefficient with

*µ*′

*=(1-*

_{s}*g*)

*µ*. Also all other fat emulsions show a similar reduced scattering coefficient when diluted to the scatterer concentration of Intralipid 10%.

_{s}*µ*,

_{s}*µ*′

*,*

_{s}*g*and the phase function, were calculated with Mie theory. The calculations match the measurements reasonable well in the range of the measurement accuracy. With this method it was possible to calculate the optical properties also for wavelengths, at which no measurements have been performed. In comparison to standard methods for the particle size distribution measurement we got a more realistic result for the particle size distribution which could explain the optical properties well. Since the calculation with Mie theory is complicated, we introduced simple equations for the calculation of

*µ*,

_{a}*µ*,

_{s}*µ*′

*,*

_{s}*g*and

*p*(

*θ*) for unpolarized light. We presented parameters for six different fat emulsions for calculating the optical properties and the phase function with these equations for wavelengths from 400nm–900nm in the appendix.

## 5. Appendix

*µ*,

_{s}*µ*′

*,*

_{s}*µ*, the phase function and the anisotropy coefficient are given in tables 3, 4, 5, 6 and 7 for unpolarized light respectively. The scattering and reduced scattering coefficient are calculated for the undiluted sample. For example, Intralipid10% which consists of 100g/l soy bean oil with a density of 0.927g/ml and 12g/l egg lipid is given for 12.0% scatterer concentration and Intralipid 20% is given for 22.8% scatterer concentration.

_{a}## Acknowledgment

## References

1. | A. Kienle, F. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. |

2. | F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express |

3. | J. Allardice, A. M. Abulafi, D. Webb, and N. Willimas, “Standardization of intralipid for light scattering in clinical photodynamic therapy,” Lasers Med. Sci. |

4. | S. Flock, S. Jacques, B. Wilson, W. Star, and M. vanGemert, “The optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. |

5. | H. van Staveren, C. Moes, J. van Marle, S. Prahl, and M. Gemert, “Light scattering in Intralipid-10 in the wavelength range of 400-1100 nm,” Appl. Opt. |

6. | J. Choukeife and J. L’Huillier, “Measurements of scattering effects within tissue-like media at two wavelengths of 632.8 nm and 680 nm,” Lasers Med. Sci. |

7. | E. Drakaki, S. Psycharakis, M. Makropoulou, and A. Serafetinides, “Optical properties and chromophore concentration measurements in tissue-like phantoms,” Opt. Commun. |

8. | I. Driver, J. Feather, P. King, and J. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. |

9. | S. Flock and B. W. M. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. |

10. | A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, and O. Sindoni, “Optical properties of high-density dispersions of particles: application to intralipid solutions,” Appl. Opt. |

11. | T. Pham, F. Bevilacqua, T. Spott, J. Dam, and B. T. S. Andersson-Engels, “Quantifying the absorption and reduced scattering coefficients of tissuelike turbid media over a broad spectral range with noncontact fouriertransform hyperspectral imaging,” Appl. Opt. |

12. | G. Zaccanti, S. Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. |

13. | A. Kienle and M. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium.” J. Opt. Soc. Am. |

14. | A. Kienle, L. Lilge, M. Patterson, R. Hibst, R. Steiner, and B. Wilson, “Spatially-resolved absolute diffuse reflectance measurements for non-invasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. |

15. | M. Pilz and A. Kienle, “Determination of the optical properties of turbid media by measurement of the spatially resolved reflectance,” in |

16. | F. Forster, A. Kienle, R. Michels, and R. Hibst, “Phase function measurements on nonspherical scatterers using a two-axis goniometer,” J. Biomed. Opt. |

17. | R. Michels, S. Boll, and A. Kienle, “Measurement of the phase function of phantom medias with a two axis goniometer,” in |

18. | D. Lide, |

19. | C. Wabel, “Influence of lecithin on structure and stability of parental fat emulsions,” Ph.D. thesis, University Erlangen, Germany (1998). |

20. | The International Association for the Properties of Water and Steam, “Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” (1997). |

21. | G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Physik |

22. | R. Graaff, J. Aarnoudse, J. Zijp, P. Sloot, F. de Mul, J Greve, and M. Koelink, “Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. |

23. | R. Pope and E. Fry, “Absorption spectrum (380-700 nm) of pure water. II Integrating cavity measurements,” Appl. Opt. |

**OCIS Codes**

(290.3030) Scattering : Index measurements

(290.7050) Scattering : Turbid media

**ToC Category:**

Scattering

**History**

Original Manuscript: February 1, 2008

Revised Manuscript: March 18, 2008

Manuscript Accepted: April 4, 2008

Published: April 11, 2008

**Virtual Issues**

Vol. 3, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Rene Michels, Florian Foschum, and Alwin Kienle, "Optical properties of fat emulsions," Opt. Express **16**, 5907-5925 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5907

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### References

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- I. Driver, J. Feather, P. King, and J. Dawson, "The optical properties of aqueous suspensions of Intralipid, a fat emulsion," Phys. Med. Biol. 34, 1927-1930 (1989). [CrossRef]
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- A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, and O. Sindoni, "Optical properties of high-density dispersions of particles: application to intralipid solutions," Appl. Opt. 42, 4375-4380 (2003). [CrossRef] [PubMed]
- T. Pham, F. Bevilacqua, T. Spott, J. Dam, and B. T. S. Andersson-Engels, "Quantifying the absorption and reduced scattering coefficients of tissuelike turbid media over a broad spectral range with noncontact fouriertransform hyperspectral imaging," Appl. Opt. 39, 6487-6497 (2000). [CrossRef]
- G. Zaccanti, S. Bianco, and F. Martelli, "Measurements of optical properties of high-density media," Appl. Opt. 42, 4023-4030 (2003). [CrossRef] [PubMed]
- A. Kienle and M. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium." J. Opt. Soc. Am. 14, 246-254 (1997). [CrossRef]
- A. Kienle, L. Lilge, M. Patterson, R. Hibst, R. Steiner, and B. Wilson, "Spatially-resolved absolute diffuse reflectance measurements for non-invasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996). [CrossRef] [PubMed]
- M. Pilz and A. Kienle, "Determination of the optical properties of turbid media by measurement of the spatially resolved reflectance," in Proc. SPIE Int. Soc. Opt. Eng. (2007).
- F. Forster, A. Kienle, R. Michels, and R. Hibst, "Phase function measurements on nonspherical scatterers using a two-axis goniometer," J. Biomed. Opt. 11, 024,018 (2006). [CrossRef]
- R. Michels, S. Boll, and A. Kienle, "Measurement of the phase function of phantom medias with a two axis goniometer," in Photon Migration and Diffuse-Light Imaging (SPIE, 2007).
- D. Lide, Handbook of chemistry and physics (CRC, 2008).
- C. Wabel, "Influence of lecithin on structure and stability of parental fat emulsions," Ph.D. thesis, University Erlangen, Germany (1998).
- The International Association for the Properties ofWater and Steam, "Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure," (1997).
- G. Mie, "Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen," Ann. Physik 330, 377-445 (1908). [CrossRef]
- R. Graaff, J. Aarnoudse, J. Zijp, P. Sloot, F. de Mul, J. Greve, and M. Koelink, "Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations," Appl. Opt. 31, 1370- 1376 (1992). [CrossRef] [PubMed]
- R. Pope and E. Fry, "Absorption spectrum (380-700 nm) of pure water. II Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997). [CrossRef]

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