ABSTRACT 1. INTRODUCTION. phone ; fax

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1 Spectroscopic measurements an characterization of soft tissue phantoms frain Solarte * an rick pus Quantum ptics Group, Dept. of Physics, niversia el Valle, A.A , Cali, Colombia ABSTRACT Tissue phantoms are important tools to calibrate an valiate light propagation effects, measurements an iagnostic test in real biological soft tissue. We prouce low cost phantoms using stanar commercial jelly, istillate water, glycerol an a 20% lipi emulsion (liclinomel N ) was use in place of the usual ntralipi. n a previous work we esigne a protocol to elaborate high purity phantoms which can be use over months. We prouce three ifferent types of phantoms regaring the lipi emulsion glycerol - gelatin water composition: Pure gelatin phantoms, lipi in glycerol, an lipi in gelatin phantoms were prouce an ifferent concentrations of the lipi emulsion were use to stuy optical propagation properties of iffusive mixtures. Besies, 1.09 µm poly latex spheres in istille water were use to prouce reference phantoms. n orer to use all the phantom sies, the phantoms were prouce in isposable spectrometer cuvettes, esigne for fluorescence stuies. Measurements were performe using an ceanptics 4000 channels spectrophotometer an integrating spheres. For the scattering measurements a homemae goniometer with a high resolution angular scale was use an the scattering etector was a linear array of optical fibers, with an angular collimator, connecte to the spectrophotometer. White LD was use as light source, an the nm HeNe Laser was use for calibration. n this work we present characterization measurements for gelatin an microspheres phantoms using spectral reflectance, iffuse an irect spectral transmittance, an angle scattering measurements. The results of these measurements an their comparison are presente. Keywors: Soft tissue Phantoms, Light Scattering, Reflectance, Transmittance, Tissue ptics 1. NTRDCTN The physical moeling of soft tissue an the unerstaning of their optical properties are important issues for numerous applications in Biophotonics an meical imaging, as it requires reliable reference stanars, simple to use, economical an reproucible 1, 2, 3. Recently, several stuies have been conucte in this area an ifferent types of materials have been esigne an teste 3, 4, 5. Lately, these works have been eicate specifically to "phantoms" organic lipi moels, base on soy oil issolve in glycerol or embee in gelatin. ntralipi is generally use as a source of ispersers. Specially, the behavior of Phantoms in the near infrare region (NR) has been stuie 6, 7 ue its importance in clinical imaging applications, an for monitoring physiological processes an for high resolution microscopy 8, 9, 10. ne avantage of choosing the ntralipi is the uniformity of the substance, which must meet clinical stanars. A further problem is presente by the kin an osage of the few absorption centers that are ae to the mixture, which usually come from a kin of ink (nia ink) or also Nigrosin. Due to the nee of a traceable stanar, significant efforts have been mae to efine an ensure the traceability of tissue phantoms; in this way, systems, evices an measurement an calibration protocols have been esigne an teste 6, 10, 11, 12. However it is not always possible to have ntralipi as scatter source or iffuse reflectance spectroscopy systems to esign an characterize biological tissue moels. We evelope a protocol for characterization an sterile prouction of gelatin phantoms 13, aime to be use as matrix for moels of soft tissue. n this work we use this protocol to prouce the gelatin matrix an aing scattering centers, using a lipi emulsion, which replaces the ntralipi, to manufacture a turbi meium, an we make the etermination of the optical constants for ifferent concentrations of lipis. Likewise, we evelope moels of Poly Latex microspheres suspene in istille water. *efrain.solarte@correounivalle.eu.co; phone ; fax Design an Performance Valiation of Phantoms se in Conjunction with ptical Measurement of Tissue V, eite by Robert J. Norstrom, Proc. of SP Vol. 8583, 85830D 2013 SP CCC coe: /13/$18 oi: / Proc. of SP Vol D-1

2 Collimate transmittance an iffuse transmittance an reflectance were measure to etermine the optical constants. The first one realizes the total processes responsible for the light beam intensity ecrement along the initial irection of propagation, the following two measurements permit etermining the optical constants of the processes allow the beam to be iffuse an absorbe into the meium. n a first approach, the turbi meium can be suppose as a substrate meium with an average refractive inex, higher than that of air, with in homogeneities, scattering an absorption centers uniformly istribute in it 1. These meium ispersion properties are responsible for the interface transmission an partial reflection of light, but the beam broaening an the light power absorption are ue to the scattering an absorption properties of the in homogeneities containe in it. So, a collimate (monochromatic) beam is attenuate as it travels a istance insie a meium of extinction coefficient μ t following the Beer-Lambert law, in the form: ( ) = 0(1 Ri )exp( μt) (1) Where 0 is the incient intensity [W.cm -2 ], () is the transmitte light intensity after passing a meium slab of thickness, the reflection coefficient at the meium/air bounary is given by R i, which for normal incience can be calculate as: R ( n 1) = i ( 1) n + (2) n is the relative refractive inex between tissue an the neighboring meium. The factor (1-R i ) takes into account the ( ) reflection losses at the entrance interface. The fraction = exp( μt), gives the correcte collimate 0(1 Ri ) transmittance of the meium slab, an allows calculating the extinction coefficient, which is also given by absorption μ ) an scattering ( μ ) coefficients as: ( a s μ = μ + μ t a To etermine the absorption an scattering constants a moel for the interaction between light an the meium is require. This must not only taking into account the photon losses along the beam path, but also consier the scattering effects, eflections that make that, in a certain volume within the meium, photons leave the initial irection of propagation an be lose, an also other photons reach this volume, in a given irection, coming from other sites into the meium, scattere from these, an moving initially in other irections. The stationary raiative transfer theory 14 [RTT] is habitually applie to etermine the photon ensity variation in an elemental volume. n this moel, the time iminution of the photon ensity in the volume is given by the raiation flux on the surface surrouning this volume, the absorption an the scattering remove photons from this volume, an consiers its increasing because of the photons arriving to the volume ue scattering, from irection s into the irection s, in all other points of the meium. The stationary conition is achieve setting the photon ensity as a constant, so that its time erivative is null, which gives the RRT equation. A usual form of this equation is written for the raiance [W.cm -2.sr -1 ], as follows 1, 15 : r r (, s) r r μs r r r r = μt (, s) + (, ') (, ') Ω' 4 s p s s s π 4π (4) r r p( s, s') is the phase function, which can be regare as the probability of photon scattering from irection s 2 (3) s v ' into irection s r ; s is the infinitesimal path length, an Ω the soli angle element. n this approach, the raiance can be separate into two terms: the coherent collimate raiance which follows the Beer-Lambert law, an will thus be characterize by an exponential ecay in a efinite irection (given by eq. 1 an the first term in 4), an the iffuse raiance coming from multiple scattering, consiering photons which o not follow a straight etermine path. Proc. of SP Vol D-2

3 As the integral equation (4) is too complicate to solve in the actual circumstances of light propagation through normal turbi meia an biological tissues, some approximations an simplifications of the RTT equation have been consierate 1, 15 as the first orer scattering, the Kubelka- Munk Flux theories, the iffusion approximation, as well as numerical solutions of the RTT equation 16, statistical methos as the Monte Carlo simulations, an the nverse Aing- Doubling metho 17. All these methos have been use an teste in ifferent conitions taking into account the possible initial an bounary conitions; the accuracy is relate to the complexity of each approach. n this work we present the spectral measurements performe on sample phantoms with the ouble integrating sphere metho to etermine the optical parameters using sequential measurements of iffuse transmittance, T, iffuse reflectance, R an collimate transmittance, T c, to etermine the phantom absorption an the scattering coefficients, as well as the asymmetry parameter g, as functions of the light wavelength. Despite the controversies about the significance, accuracy an utility of the Kubelka-Munk moel (KM) 18, 19, 20, 21, 22, 23, we use the most elemental moel of light propagation 1, 15, 24 to calculate the optical coefficients, following the expressions for the Kubelka-Munk coefficients, S KM an A KM in the form: With: S KM 1 1 R ( a b) = ln b T AKM = SKM ( a 1) (6) 2 2 T + R a = ; b = a 2 R The optical parameters of the meium are correlate to the K-M coefficients as: 3 1 AKM = 2μa; SKM = μs( 1 g) μa (8) 4 4 n this way the measurement of the iffuse transmittance, T, iffuse reflectance, R, an collimate transmittance, T c, an the relationships given in equations 1, 3, an 8, allow the calculation of the turbi meium optical constants. We want to stuy the phantom optical properties in the VS region an by incoherent white light illumination. (5) (7) 2. XPRMNTAL MTHDS 2.1 Phantom Preparation The phantoms were prepare following the proceure escribe in a previous work 13. The matrix meium was commercial unflavore gelatin, selecte between the previous use classes, because of the observe scattering characteristics for laser beam illumination, as shown in Figure 1. We use gelatin type B to elaborate the phantom matrix. 16g of gelatin power were issolve in 150 ml of pre-heate istille water (3 min. 750 W MicroW); in these cases no physiological saline solution was ae. The mixture was stirre until there were no lumps an after cooling, poure into 3.5 ml acrylic fluorescence spectroscopic cuvettes, using a sterile calibrate syringe. The amounts of lipi emulsion were ae with a calibrate 1ml syringe. The cuvettes were close with special Teflon caps an the mixture was shaken, approximately 4 min. until obtain a uniform istribution. ach sample was mae to 3 ml volume. As lipi source we use LCLNML N7-1000, which is an emulsion of refine olive oil combine with refine soybean oil, in proportion 80/20, for a total of 20 g of fat in 100 ml of emulsion; moels were left to rest for 12 hours. For the Micro Spheres (MS) phantoms SP #2713, 1.09 microns Poly Latex microspheres, at 1% MS in 15ml concentration were use. The MS emulsion contains 0.1% NaN 3. These phantoms are liqui, an the MS were ae to corresponing volumes of 2ml istille water, in the spectroscopic cuvettes. Four samples are elaborate to stuy the Gelatin Lipi phantoms an three for the Microspheres phantoms, an extra cuvette was prepare with istille water as reference for the pure gelatin, an the microsphere phantoms. A base Proc. of SP Vol D-3

4 emulsion was prepare with 4ml lipi emulsion in 2 ml glycerol an samples of this were taken to prouce the turbi phantoms Raial Position [Pixel] Figure 1. Transverse intensity profile of HeNe laser light scattere by two ifferent gelatin phantom matrices. The scatter-concentrations use in the ifferent phantoms are given in the following Table 1. Table 1. Lipi composition of the ifferent phantoms. Scatters Concentration Lipis in Gelatin Phantoms Microspheres Phantoms 2 ml Lipi, 1 ml Gelatin: 0.4g 0.3 ml MS, cm -3 1 ml Lipi, 2 ml Gelatin 0.2g 0.2 ml MS cm ml Lipi, 2.5 Gelatin 0.1g 0.1 ml MS cm ml Lipi, 2.7 ml Gelatin 0.06g 2.2 xperimental proceure Collimate transmittance an iffuse reflectance an transmittance were measure using a white LD as light source, an an cean ptics SB4000 mini spectrometer was use as etection system. MS an Gelatin phantoms were place in a 4 way cuvette holer for T c measurements, incient an transmitte light was transporte with 50, 200 or µm optical fibers, epening on the use light intensity. Reference spectra, as well as ark corrections were taken for every measurement proceure, an the incient an transmitte light spectra were processe consiering the corresponing spectra ata an the respective integration times, to calculate the corresponing transmittance using the stanar calculation formulae. For the iffuse reflectance an transmittance measurements, a set of two ientical ThorLabs 2 ϕ integrating spheres in a tanem array was use. The cuvette phantom was place between them. At the first sphere the light source was attache using a focusing lens to prouce an almost parallel light beam which goes across the spheres, passing through the sample. The first sphere collects the iffusely reflecte light, an the secon the transmitte, the light was sample through a very small hole in a irection perpenicular to e incient light beam. As in the previous case, reference spectra, as well as ark corrections were taken for every measurement proceure, an the incient, reflecte an transmitte light spectra were processe as above. All ata were processe using rigin Lab Software, to perform the calculations an the corresponing graphics. The spectral transmittance an reflectance values were use to calculate the K-M coefficients accoring to the above presente equations, an from these the attenuation, absorption an scattering coefficients, as well as the g factor are calculate. Proc. of SP Vol D-4

5 o o 3. XPRMNTAL RSLTS 3.1 Microspheres Phantom The measure collimate transmittance for microsphere phantoms is presente in Figure 2. ca t, 0,4 0,3 0,2 cvi 0,1 2 0,03 ú 0,02 p 0,01 Microspheres Phantom Composition ml ( cm -3) ml ( cm -3) 0.3 ml (2407 cm -3) 0, ,0 8,5-71 Microspheres Phantom Composition ml ( cm -3) 7, ml ( cm -3) 7,0-0.3 ml (2407 cm-3) Ç 6,5-6,0 5,5 - p 5,0 4,5 =G 4,0 Ti 3,5 3,0 Q 2,5 ß 2,0 1,5 1,0 Figure 2. Collimate Transmittance (L) an the corresponing Total Attenuation Coefficient for microsphere phantoms. The results for the iffuse measurements are showing in the next Figure Phantom Composition ml Microspheres ( cm-3) 0.2 ml Microspheres ( cm-3) ml Microspheres (24 07 cm-3) ó Microspheres Phantom Composition ml Microspheres ( cm-3) 0.2 ml Microspheres ( cm-3) 0.3 ml Microspheres (2407 cm-3) Q cc 25 ca Ce 20 a> N 15 o, i, i, i, i, i, i, i, i, i, Figure 3. Diffuse Transmittance an Reflectance for microsphere phantoms. The calculate absorption an scattering coefficients for the microspheres phantoms are given in the following Figure 4. 1,5 1,4 -' 1,3 1,2 y 1,1 i.2 1,0 c 0,9 a 0,8 0,7 0,4 - Microspheres Phantom Composition ml ( cm-3) ml ( cm-3) ml (2407 cm-3) Microspheres Phantom Composition ml ( cm-3) ( cm-3) ml (2407 cm-3) u w - 3 _ - 0,3 Figure 4. Absorption an Scattering Coefficients for microsphere phantoms. Proc. of SP Vol D-5

6 The results of the calculations of the anisotropy factor g, an the phase function for the microspheres phantoms are presente below, in the Figure 5. The scattering measurement was performe only for the microspheres phantoms, an only for nm HeNe laser line. 1,0 5,0 0,9 0,8 0,7 4,5 4,0 3,5 - -AngularScattering Measurement (Normalize Phase Function) -- Normalize Henyey- Greenstein -Yoon Phase Function (g =0.43; u =0.03) 0,6 :53, 0,5 0,4 Li..' 0,3 0,2 0,1 0,0 Microspheres Phantom Composition ml ( cm -3) ml ( cm -3) ml (2407 cm -3) 1,5 Z 1,0 0,5 0,1. i. i. i. i. i. i. i. i. i. 0,0-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 Scattering Angle [ra] Figure 5. Anisotropy factor an phase function calculate from e spectroscopy an the scattering measurements. 3.2 Gelatin -Lipi phantoms The aition of relative small amounts of lipis moifies changes appreciably the transmittance of the phantom, proucing a remarkable iminution of the transmitte intensity. Figure 6 shows the effect. Gelatin alone has a relative high transmittance, about 40% at the VS spectrum center. The lipis contribute to a high change in the intensity of transmitte light leaing transmittances up to the 0.01% an below H ç ,07 2 0,06 - v 0,05 0,04 cri 0,03 Z. 0,02 0,01 0,00 -- Pure Gelatin -- A ml Lipi: 0.03 g.cm tc 0,07 0,06 0,05 0,04 N :.i 0,03 0,02 0, ml Lipi: 0.03 g.cm ml Lipi: 0.05 g.cm -3 1 ml Lipi: 0.1 g.cm ml Lipi: 0.2 g.cm -3 Reference: Pure Gelatin 0,00 Figure 6. ffect of the lipi aition in the transmittance of gelatin phantoms (Left) an comparison between ifferent lipi content, taking the pure gelatin spectrum as reference (Right). The transmittance measurements of the gelatin samples were performe using istille water as reference; by the more ense phantoms long integration times were necessary, increasing the noise an therefore the ifficulties to achieve the calculations. n this case, the gelatin presents scattering an absorption, which is ifferent as the preceent case of MS phantom that use istille water as matrix. The low intensities an the large noise can prouce false results i.e. negative values. Proc. of SP Vol D-6

7 The measure collimate transmittance for Gelatin-Lipi phantoms an the calculate total attenuation coefficient are presente in the Figure 7. 0,12 12,0 0,10 0,08 H c, a 0.3 ml Lipi: 0.03 g.cm ml Lipi: 0.05 g.cm -3 1 ml Lipi: 0.1 g.cm -3 2 ml Lipi: 0.2 g.cm ml Lipi: 0.03 g.cm o ml Lipi: 0.05 g.cm -3 1 ml Lipi: 0.1 g.cm ml Lipi: 0.2 g.cm -3 Reference: Destille Water 10,0 0,06 0,04 a ca 0, ,00-0,02 Q 8,0 7,5 i i i i i 675 Figure 7. Measure collimate transmittance of gelatin lipi phantoms (Left), an the calculate total attenuation coefficients for Gelatin Lipi phantoms (Right). The results of the iffuse reflectance an transmittance are presente in the next Figure ml Lipi (0.03 g.cm -3) ó a, ml Lipi (0.03 g.cm -3) 0.5 ml Lipi (0.05 g.cm -3) 1 ml Lipi (0.1 g.cm -3) 2 ml Lipi (0.2 g.m -3) -\ p 30 4 ca ml Lipi (0.05 g.cm -3) 1 ml Lipi (0.1 g.cm -3) 2 ml Lipi (0.2 g.cm -3) C N aß Ce w Figure 8. Diffuse Reflectance (L) an Transmittance for the Gelatin-Lipi phantoms. The results of the KM coefficients calculation are presente in the Figure 9, as note the noisily measurement, ue the high integration times prouces spurious points. 4,2 4,0 3,5 4,0 - - Akm (Pure Gelatin) 3,8 Akm (0.3 ml Lipi) Akm (0.5 ml Lipi) --v- -Akm (1 ml Lipi) Akm (2 ml Lipi) 3,0 c Gelentin Phantom Coefficient --Skm (0.3 ml Lipi) 3,6 3,4 2,5 2,0 ' "" 3,2 ú 3,0 +. 2,8 2,6 Skm (0.5 ml Lipi) Skm (1 ml Lipi) Skm (2 ml Lipi) 2,4 2,2 0,6 0,4 0,2 2,0 Ñ 1,8 1,6 1,4 0,0 1,2 1,0-0, Figure 9. The calculate Kubelka Munk coefficients for the Gelatin Lipi phantoms are shown. n the left sie, the pure gelatin AKM coefficient is presente for comparison. Proc. of SP Vol D-7

8 u 2,0 1,8 1,6 1,4 1,2 1,0 V 0,30 G 0,25 Q 0,20 Ñ 0,15 Q 0,10 0,05 - Pure Gelatin (Mua) ml Lipi: 0.03 g.cm -3 (Mua) ml Lipi: 0.05 g.cm -3 (Mua)- Y 1 ml Lipi: 0.1 g.cm -3 (Mua) - 2 ml Lipi: 0.2 g.cm -3 (Mua) - 0,00 -- t t' 1,75 V 1,50 L 1,25 1,00 tv) 0,75 0, Pure Gelatin (Mus) 0.3 ml Lipi: 0.03 g.cm -3 (Mus) 0.5 ml Lipi: 0.05 g.cm -3 (Mus) -- 1 ml Lipi: 0.1 g.cm -3 (Mus) 2 ml Lipi: 0.2 g.cm -3 (Mus) Figure 10. Calculate Absorption an Scattering coefficients for Gelatin-Lipi phantoms. The respective coefficients for pure gelatin are shown for comparison. Finally, the anisotropy factor for pure gelatin an for the gelatin-lipi phantoms are calculate an shown in Figure 11. The incorporation of lipis moifies the g factor values proucing lower g values. 0,90 0,85 0,80 0,75 0,70 0,65 0,60 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0,20, i, -- Pure Gelatin ml Lipi: 0.03 g.cm -3 (g) 0.5 ml Lipi: 0.05 g.cm -3 (g) -- 1 ml Lipi: 0.1 g.cm -3 (g) 2 ml Lipi: 0.2 g.cm -3 (g) 675 Figure 11. Calculate anisotropy factor values for the prouce Gelatin-Lipi phantoms. 4. CNCLSNS Gelatin Lipi phantoms were prouce, using a commercial jelly bran an an ntralipi substitute; calibrate microsphere (1.09 µm) emulsions were elaborate as comparison an reference. The optical properties were stuie by experimental measurements of spectral reflectance an transmittance, both in collimate an iffuse configurations, using a white LD as broaban, incoherent illuminator, an the meium optical constants were etermine by Kubelka- Munk calculations, proucing the epenence of these constants on the light wavelength. The effect of forwar scattering is appreciable by low scatters concentrations an is especially present in the MS phantoms, going to isotropic scattering by long wavelengths. The gelatin phantoms, exhibit a more uniform value of the g factor over almost the Proc. of SP Vol D-8

9 whole VS spectrum, but the more ense the lipi phantom, the more isotropic the scattering, with g factors varying from 0.8 (pure gelatin) up to 0.45 for the more ense prouce phantom. ACKNWLDGMNTS Authors woul like to thank the niversia el Valle for the technical an financial support. RFRNCS [1] Tuchin, V.V. [Tissue optics: Light scattering methos an instruments for meical iagnosis, 2n..], SP Press, Bellingham WA SA, 3-17 (2007) [2] Hwang, J., Ramella-Roman, J. C., Norstrom, R., ntrouction: feature issue on phantoms for the performance evaluation an valiation of optical meical imaging evices, Biome pt xpress. 3(6), (2012) [3] Pogue, B. W., Patterson, M. S., Review of tissue simulating phantoms for optical spectroscopy, imaging an osimetry, J Biome pt. 11(4), (2006) [4] Cubeu, R., Pifferi, A., Taroni, P., Torricelli, A., Valentini, G.A., A soli tissue phantom for photon migration stuies, Phys Me Biol. 42(10), (1997) [5] Moffitt, T., Chen, Y. C., Prahl, S. A., Preparation an characterization of polyurethane optical phantoms, J Biome pt. 11(4), (2006) [6] F. Martelli an G. Zaccanti, Calibration of scattering an absorption properties of a liqui iffusive meium at NR wavelengths. CW metho, pt. xpress 15(2), 486 (2007). [7] Di Ninni, P., Martelli, F. an Zaccanti, G., ffect of epenent scattering on the properties of ntralipi tissue phantoms, Biome pt xpress 2(8), (2011) [8] Dururan, T., Choe, T. R., Baker, W. B. an Yoh, A. G., Diffuse optics for tissue monitoring an Tomography, Rep. Prog. Phys. 73, (2010) [9] Rao, K. P., Rahakrishnan, S., Rey, M. R., Brain tissue phantoms for optical near infrare imaging, xp. Brain Res. 170(4) (2006) [10] Wang, D., Chen, Y., Liu, J. T., A liqui optical phantom with tissue-like heterogeneities for confocal microscopy, Biome pt xpress 3(12), (2012) [11] Steven L. Jacques, Bo Wang, an Ravikant Samatham, R., Reflectance confocal microscopy of optical phantoms, Biome pt xpress 3(6) (2012) [12] Pfefer, T. J., Matchette, L. S., Bennett, C. L., Gall, J. A., Wilke, J. N., Durkin, A.J., iger, M. N., Reflectancebase etermination of optical properties in highly attenuating tissue, J. Biome. pt. 8(2), (2003) [13] Vales, C. P. an Solarte. "Lateral scattere light use to stuy laser light propagation in turbi meia phantoms", Proc. SP 7567, Design an Performance Valiation of Phantoms se in Conjunction with ptical Measurement of Tissue, 75670C (2010) [14] Chanrasekhar, S., [Raiative Transfer], Dover Publications nc., New York, 393 (1960) [15] Niemz, M.H. [Laser-Tissue nteractions: Funamentals an Applications, 3r..], Springer Verlag, Berlin Heielberg Germany, (2007) [16] Ren, K., Bal, G., an Hielscher, A. H., Transport- an iffusion-base optical tomography in small omains: a comparative stuy, Applie ptics 46(27), (2007) [17] Prahl, S. A. van Gemert, M. J. C., Welch, A. J., Determining the optical properties of turbi meia by using the aing-oubling metho Applie ptics 32(4), (1993) [18] Yang, L. an Kruse, B. Revise Kubelka Munk theory.. Theory an application, J. pt. Soc. Am. A 21(10) (2004) [19] Yang, L., Kruse, B., Miklavcic, S. J., Revise Kubelka Munk theory.. nifie framework for homogeneous an inhomogeneous optical meia, J. pt. Soc. Am. 21(10) (2004) [20] Yang, L., Miklavcic, S. J., Revise Kubelka Munk theory.. A general theory of light propagation in scattering an absorptive meia, J. pt. Soc. Am. 22(9) (2005) [21] ström, P., xamination of the revise Kubelka Munk theory: consierations of moeling strategies, J. pt. Soc. Am. 24(2) (2007) Proc. of SP Vol D-9

10 [22] Neuman, M., ström, P., Anisotropic reflectance from turbi meia.. Theory, J. pt. Soc. Am. 27(5) (2010) [23] Neuman, M., ström, P., Anisotropic reflectance from turbi meia.. Measurements, J. pt. Soc. Am. 27(5) (2010) [24] Thennail, S. N., Relationship between the Kubelka Munk scattering an raiative transfer coefficients, J. pt. Soc. Am. 25(7) (2008) Proc. of SP Vol D-10