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  • Research ArticlePolystyrene Microsphere Optical Properties by Kubelka–Munkand Diffusion Approximation with a Single Integrating SphereSystem: A Comparative Study

    Ali Shahin ,1 Wesam Bachir,1,2 and Moustafa Sayem El-Daher 3,4

    1Biomedical Photonics Laboratory, Higher Institute for Laser Research and Applications, Damascus University,Damascus, Syria2Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria3Higher Institute for Laser Research and Applications, Damascus University, Damascus, Syria4Faculty of Informatics and Communications, Arab International University, Daraa, Syria

    Correspondence should be addressed to Ali Shahin; [email protected]

    Received 25 September 2019; Revised 26 October 2019; Accepted 14 November 2019; Published 1 December 2019

    Academic Editor: Daniel Cozzolino

    Copyright © 2019 Ali Shahin et al. *is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

    *e optical properties of 1 μm polystyrene in the wavelength range of 500–750 nm were estimated by using a white lightspectrophotometric transmittance spectroscopy and a single integrating sphere system. To retrieve the optical characteristics, twoanalytical methods, namely, diffusion approximation and Kubelka–Munk were used, and then their results were compared withMie theory calculations.*e correspondence of the Kubelka–Munk scattering coefficient withMie was obvious, and relative errorsvaried between 6.73% and 2.66% whereas errors varied between 6.87% and 3.62% for diffusion theory. Both analytical methodsdemonstrated the absorption property of polystyrene over the abovementioned wavelength range. Although absorption co-efficient turned out to be much lower than scattering, constructing a realistic optical phantom requires taking into accountabsorption property of polystyrene. Complex refractive index of polystyrene based on these two methods was determined. InverseMie algorithm with scattering coefficient was also used to retrieve the real part of refractive index and absorption coefficient forcalculating the imaginary part of refractive index. *e relative errors of the real part did not exceed 2.6%, and the imaginary partwas in consistence with the prior works. Finally, the presented results confirm the validity of diffusion theory with a singleintegrating sphere system.

    1. Introduction

    Optical characterization techniques require both an exper-imental setup to measure the radiometric characteristics anda light propagation method to extract the macroscopicoptical properties. Generally, these techniques are catego-rized as direct and indirect methods [1, 2].*e direct methodcan be performed only ex vivo, and the samples used in thistechnique are thin enough so that the multiple scatteringevents can be negligible, but the advantage of this methoddepends on simple exponential equations to extract theoptical properties [2]. In contrast, indirect methods can beimplemented ex vivo and in vivo with thick samples [2–5].Unfortunately, the estimation of the optical properties via

    these methods is based on more complicated mathematicalprinciples and analytical and numerical solutions of theradiative transfer equation (RTE) [1–4]. Kubelka–Munkmay be considered as the simplest analytical method that hasbeen used for optical characterization, but the drawback ofthis method is limited to the case of highly scattering me-dium, and the sample’s thickness should exceed the trans-port length. Also, this model does not take into account thejump in the refractive index between the sample and sur-rounding medium [6, 7]. Recently, this approach has beenmodified to overcome the refractive index mismatch be-tween the sample and holder, and the thickness does notexceed the transport length [7]. *e present method hasbeen investigated with a single integrating sphere system

    HindawiJournal of SpectroscopyVolume 2019, Article ID 3406319, 8 pageshttps://doi.org/10.1155/2019/3406319

    mailto:[email protected]://orcid.org/0000-0001-9904-2662https://orcid.org/0000-0002-0236-0902https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2019/3406319

  • over visible and N-IR wavelength range on biological tissuesand optical phantoms [7, 8]. On the other hand, diffusionapproximation has been considered as an approximate so-lution of the radiative transfer equation for semi-infinite andhigh diffusive medium for collimated incident light [9, 10].*at has been used as a quantitative method to retrieve theoptical properties of several media using diffuse reflectancespectra which supplies a correlation of measurements withsome constraints, i.e., a highly diffusive medium with a largedistance between the semi-infinite sample and source. Ac-cordingly, diffusion approximation has been used in opticalcharacterization that has been in agreement to theoreticalmodels such as Mie theory and the Monte Carlo method[11, 12]. Also, this approach has been used with an in-tegrating sphere method in vivo with a large medium tosimulate the boundary conditions of this model [13, 14].

    On the other hand, polystyrene microsphere has beenwidely used as a tissue-simulating phantom component tomimic scattering property of a certain tissue. *e ability toestimate its optical characteristics accurately via Mie theorycalculation that provides a level of validation does not existin any other optical phantom component. However, mostprior research groups deal with this material as a purescattering without taking into account absorption propertyand retrieved scattering coefficient by using Mie theory[15, 16]. *us, precise optical characterization of thesematerials has an enormous effect on constructing idealphantoms [15].

    *e aim of this research is to investigate the validity ofdiffusion approximation with a single integrating spheresystem compared with analytical and theoretical approaches.*us, albedo, scattering coefficient, extinction coefficient,and complex refractive index of a 1 μm polystyrene mi-crosphere (07310-15, Polybead, Polysciences, USA) weredetermined by using diffusion approximation andKubelka–Munk based on radiometric measurements using asingle integrating sphere system and collimated trans-mission spectroscopy. *en, Mie theory calculation wasimplemented to compare its scattering coefficient with thetwo models’ results which was considered as a standardmethod for a spherical particle like polystyrene. Finally,complex refractive index of a 1 μm polystyrene was de-termined in the range of wavelength 500–750 nm based onthese two models’ scattering coefficient and inverse Mietheory calculation.

    2. Materials and Methods

    2.1. Diffusion Approximation Method. Diffusion equation isa differential equation for fluence rate which can be derivedfrom a radiative transfer equation depending on some as-sumptions as a highly homogenous scattering property for asemi-infinite medium. For a collimated beam incidentnormally on a surface and taking into account the refractiveindex mismatch, the diffuse reflectance Rd from a semi-infinite medium can be expressed as a function of a reducedalbedo a′ and an internal diffuse reflectance r, as follows[10, 13]:

    Rd �a′

    1 + 2 · K 1 − a′( +(1 +(2 · K/3)) ·��������

    3. 1 − a′( , (1)

    where a′ � μs′/(μs′ + μa) is the reduced albedo and k� (1 + r)/(1 − r) is a factor related to internal diffuse reflectance rwhich is given by [10, 13]

    r � − 1.44n− 2rel + 0.71n− 1rel + 0.668 + 0.0636nrel,

    nrel �nsample

    nsurroundingmeduim,

    (2)

    where nrel is the relative refractive index, nsample is thepolystyrene refractive index, and nsurroundingmeduim is thequartz cuvette refractive index [10, 13].

    2.2. Kubelka–Munk Model. Kubelka–Munk theory is ananalytical solution of a radiative transfer equation (RTE)based on some presumptions. *e simplicity of theKubelka–Munk method has been the main reason for itswidespread uses [6, 7]. *is theory introduced special co-efficients: K is a Kubelka–Munk absorption coefficient and Sis a Kubelka–Munk scattering coefficient, which are relatedto macroscopic optical coefficients as follows [1, 6]:

    K

    S�

    1 − R∞( 2

    2 · R∞,

    K � 2 · μa,

    S �34

    · μs′ −14

    · μa.

    (3)

    *is model has been studied and tested extensively byseveral research groups on chemical substances as well asbiological tissues. Recently, a modified approach has beendeveloped and implemented on tissues and optical phantomcomponents with a single integrating sphere system [7]. *emodified method takes into account the mismatch in therefractive index between sample and holder by using aFresnel transmission coefficient expressed as follows [7]:

    Tf �4 · n

    (n + 1)2, (4)

    where n is the refractive index of the sample. Scattering andabsorption coefficients can be retrieved by measuring diffusetransmission and reflection spectra which are given by thesecorrelations [7]:

    μa �1dlog

    T2fTd

    −2 · Rd · T2f · log T

    2f /Td(

    d · T4f − T2d(

    , (5)

    μs �1dlog

    Td

    Tc+2 · Rd · T2f · log T

    2f /Td(

    d · T4f − T2d(

    , (6)

    where Td is the diffuse transmittance, Rd is the diffuse re-flectance, Tc is the collimated transmittance, and d is thesample thickness. Since a small concentration of polystyrene

    2 Journal of Spectroscopy

  • was used, the refractive index can be considered as a re-fractive index of the solvent.

    2.3. Mie 0eory Calculation. Mie theory is an analyticalsolution of Maxwell’s equations for the scattering of elec-tromagnetic radiation by a single spherical particle. Itprovides an exact solution for the scattering and the an-isotropy coefficients of perfect spheres [17]. Matzler com-puter program was used to calculate Mie scatteringparameters, i.e., scattering efficiency Q(ri, λ) and anisotropycoefficient g(ri, λ) that were used to extract the scatteringcoefficient μs(λ) and anisotropy factor g(λ) [18, 19]. *ismethod requires particle diameter, fraction, and wavelengthof radiation in the vacuum besides refractive index of theparticle and refractive index of the solvent [18, 19]. A purepolystyrene sample was an aqueous suspension (07310-15,Polybead, Polysciences, USA), and the fraction of 1 μmpolystyrene particles was 2.5% (w/v). In addition, refractiveindices of polystyrene as a scattering and water as a hostmaterial were found from previous work [20].

    2.4. Spectrophotometric Transmission Spectroscopy. Abroadband, fiber-based spectrophotometric transmissionsetup was arranged. *at consists of a broadband halogen-tungsten light source (HL-2000-HP-FHSA, Ocean OpticsInc., FL), a fiber-coupled cuvette holder with two collimatinglenses (CUV-ATT-DA, Avantes Inc., Netherlands), and aUSB portable spectrometer (USB4000 FL, Ocean OpticsInc.). *e extinction coefficient of polystyrene samples canbe measured within a broad wavelength range from 500–750 nm.*e sample was illuminated with a collimated whitelight beam. *us, the transmission intensity may be ap-proximated by the Beer–Lambert Law [8, 9]:

    Iz(λ) � I0(λ) · e− μt(λ)·z·c, (7)

    Iz(λ)I0(λ)

    � Tc, (8)

    where μt(λ) is the extinction coefficient, Iz(λ) is the intensityof light passed through the studied sample, I0(λ) is thereference intensity, z is the optical path length (thickness ofcuvette), c is the concentration, and Tc is the collimatedtransmittance [8, 9].

    2.5. Integrating Sphere System. A broadband single in-tegrating sphere (819C-IS-5.3, Newport, USA) system wasused. A schematic drawing of diffuse reflection measure-ment using a single integrating sphere system is shown inFigure 1(a). Diffuse transmittance measurement via an in-tegrating sphere can be seen from Figure 1(b). Light from atungsten-halogen lamp (HL-2000-HP-FHSA, Ocean OpticsInc., FL) was delivered to the sample of interest through aconvex lens with a 10 cm focal length and a 1.5mm pinhole,and the diffuse light emanated from the sample is guidedthrough an optical fiber to the spectrometer (USB4000 FL,Ocean Optics, USA).

    *e fiber optic spectrometer is connected to a computerfor data acquisition and further analysis. *e spectrum wasacquired in the range between 500 to 750 nmwith the help ofthe SpectraSuite software (version 2011, Ocean Optics,USA). Dark current and background measurements weretaken at the same setting before each recording [21, 22].

    3. Results

    Based on collimated transmission spectra extracted byspectrophotometric transmission spectroscopy and theBeer–Lamber law, equation (7), the extinction coefficient of1 μm polystyrene microsphere can be calculated over thewavelength range of 500–750 nm, as shown in Figure 2.Obviously, the extinction coefficient was found to be in-versely proportional to the increased wavelength over thestudied range of wavelength, Figure 2. Using the curvefitting procedure in Matlab 2014, the correlation of PSextinction coefficient and wavelength could be found andgiven by

    µt � 1.7∗ 106

    · λ− 1.498. (9)

    3.1. Mie 0eory. Mie theory is considered as an exact so-lution of the Maxwell equations for the scattering of elec-tromagnetic radiation by spherical particles such aspolystyrene microsphere (07310-15, Polybead, Polysciences,USA). Refractive index of PS was found from the prior work,and for water (host material), it was about 1.33 [20].Depending on a polystyrene datasheet from a manufacturerand Matzler computer program, scattering coefficient andanisotropy factor could be predicted [18, 19]. Mie scatteringcoefficient was found to be inversely proportional to in-creased wavelength, as shown in Figure 3(a). Using an-isotropy factor g and Mie scattering coefficient, reducedscattering coefficient could be found. *ese relations werepower equations estimated via the curve fitting procedure inMatlab and given by

    µs Mie � 1.7∗ 106

    · λ− 1.513,

    µs Mie′ � 3689 · λ− 0.9462

    .(10)

    3.2. Kubelka–Munk. *e modified Kubelka–Munk ap-proach estimates scattering coefficient based on collimatedtransmittance Tc, diffuse reflectance Rd, and diffuse trans-mittance Td, as shown in equation (6). Using spectropho-tometric transmission spectroscopy and a single integratingsphere system, PS radiometric characteristics could bemeasured. *en, Kubelka–Munk scattering coefficient couldbe evaluated, as shown in Figure 4(a). Accordingly, K–Mscattering coefficient was plotted with wavelength, and thatwas found to be inversely proportional to increased wave-length. *e correlations of K–M scattering and reducedscattering coefficients and wavelength were found using thecurve fitting procedure which were compatible with Mierelations, as follows:

    Journal of Spectroscopy 3

  • µs KM � 1.7∗ 106

    · λ− 1.507,

    µs KM′ � 3689 · λ− 0.9405

    .(11)

    Based on extinction coefficient of PS and K–M scatteringresults, K–M albedo (blue dotted line) might be calculated,Figure 5(b). *en, using inverse Mie calculation and

    Kubelka–Munk scattering coefficient, the real part of re-fractive index could be estimated over the present wave-length range, Figure 5(c). *en, the wavelength dependenceof the real part of refractive index for Kubelka–Munk (bluedotted line) was fitted to the Cauchy relation:

    nr(λ) � 1.61 −0.02742

    λ2+0.008074

    λ4, (12)

    where λ is estimated in micrometer. *en, K–M absorptioncoefficient might be utilized to predict an imaginary part ofrefractive index using the following equation, Figure 5(d):

    ni �µa · λ4π

    . (13)

    3.3. Diffusion 0eory. Diffusion approximation introducesdiffuse reflectance Rd as a function of reduced albedo a′ andrelative refractive index nrel, equation (1). Based on diffusereflectance measured via a single integrating sphere systemand relative refractive index, reduced albedo could be

    (HL2000-HP-FH5A)

    Tungsten-halogen light source

    Convex lens(f = 10cm)Pinhole

    (ϕ = 1.5mm)

    Sam

    ple

    Spectrometer(USB4000-FL)

    Integrating sphere(819C-IS-5.3)

    Rd

    (a)

    Sample

    (HL2000-HP-FH5A)

    Tungsten-halogen light source

    Spectrometer(USB4000-FL)

    Integrating sphere(819C-IS-5.3)

    Tc

    Td

    Convex lens(f = 10cm)Pinhole

    (ϕ = 1.5mm)

    (b)

    Figure 1: (a) Schematic drawing of the diffuse reflection measurement setup and (b) schematic drawing of the diffuse transmissionmeasurement setup.

    500 550 600 650 700 7508090

    100110120130140150

    Wavelength (nm)

    Extin

    ctio

    n co

    effic

    ient

    (mm

    −1)

    Figure 2: Correlation of the extinction coefficient calculated bycollimated transmission spectroscopy and wavelength.

    4 Journal of Spectroscopy

  • evaluated. Using reduced albedo, extinction coefficient es-timated by collimated transmittance spectroscopy and an-isotropy factor predicted by Mie theory calculation, DAscattering coefficient (red dashed line) might be calculated,Figure 4(b). Also, DA scattering coefficient was found to beinversely proportional to increased wavelength, Figure 4(b).*at was obvious using the curve-fitting procedure inMatlab 2014 which was a power correlation given by

    µs DA � 1.7∗ 106

    · λ− 1.505,

    µs DA′ � 3689 · λ− 0.9386

    .(14)

    Depending on PS extinction and DA scattering co-efficients, DA albedo could be evaluated, Figure 5(b). It canbe seen from Figure 5(b) that DA albedo (red dashed line)was found to be unsystematically changed with wavelength.*en, the real part of refractive index might be calculatedbased on DA scattering coefficient and inverse Mie calcu-lation, Figure 5(c). Correlation of the DA real part of re-fractive index (red dashed line) and wavelength was fitted tothe Cauchy equation as follows:

    nr(λ) � 1.611 −0.02574

    λ2+0.007688

    λ4. (15)

    Using equation (13) and DA absorption coefficient, theimaginary part of refractive index could be estimated. *erelationship between DA imaginary part of refractive indexand wavelength could be seen in Figure 5(d).

    4. Discussion

    Spectrophotometric transmission spectroscopy was used tomeasure the collimated transmittance of a 1 μm polystyreneutilized to estimate the extinction coefficient, Figure 2. FromFigure 2 and equation (9), the power correlation of theextinction coefficient and wavelength over a studied rangewere obvious. Based on diffuse transmittance and reflectancethat weremeasured by a single integrating sphere system andcollimated transmittance, the scattering coefficient of 1 μmpolystyrene sphere could be predicted using Kubelka–Munkand diffusion approximationmethods, Figures 4(a) and 4(b),respectively. As can be seen from equations (11) and (14),

    500 550 600 650 700 750

    80

    90

    100

    110

    120

    130

    140

    Wavelength (nm)

    Mie

    scat

    terin

    g co

    effic

    ient

    (mm

    –1)

    (a)

    500 550 600 650 700 750

    0.87

    0.88

    0.89

    0.9

    0.91

    0.92

    0.93

    Wavelength (nm)

    Ani

    sotro

    py fa

    ctor

    (b)

    Figure 3: (a) Correlation of Mie scattering coefficient and wavelength and (b) anisotropy factor calculated using Mie theory withwavelength.

    500 550 600 650 700 750

    80

    90

    100

    110

    120

    130

    140

    150

    K–M

    scat

    terin

    g co

    effic

    ient

    (mm

    –1)

    Wavelength (nm)

    (a)

    500 550 600 650 700 750

    80

    90

    100

    110

    120

    130

    140

    Wavelength (nm)

    DA

    scat

    terin

    g co

    effic

    ient

    (mm

    –1)

    (b)

    Figure 4: (a) Correlation of Kubelka–Munk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength.

    Journal of Spectroscopy 5

  • Kubelka–Munk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation, and theirpower factor was about − 1.505 for diffusion theory, − 1.507for the K–Mmodel, and − 1.513 for Mie calculation.*is canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17]. In addition, K–M scatteringwas in agreement withMie calculation and the relative errorsvaried between 6.73% to 2.66%, but scattering coefficientestimated by diffusion approximation turned out to behigher, and low absorption property could be noticed thatwas obvious from albedo values, Figure 5(b). DA relativeerrors varied between 6.87% and 3.62%.*e small differencebetween two methods’ results could be explained by somereasons.*e first one is that the thickness of a sample used inthe experiment is about 1 cm which exceeds the transportlength of incident light, and using a convex lens makes adiameter of beam to not exceed the dimension of the sample;

    all these points make the tested sample simulate approxi-mately the semi-infinite medium which has been inagreement with using a diffusion approximation and notKubelka–Munk [7, 10, 13].*e second one is that a modifiedKubelka–Munk method has been introduced in a case of asingle scattering event, and the use of a polystyrene mi-crosphere sample and a 1 cm sample thickness withoutadding any absorption materials makes the restriction un-fulfilled, and multiple scattering event is dominant in themedium that is in agreement with diffusion approximationconditions [7, 10, 13]. Finally, the anisotropy factor has beenestimated by Mie calculation that was about 0.9 as shown inFigure 3(b), and using this sample with a high anisotropyfactor was in correspondance with a condition of deriving adiffusion approximation equation, equation (1), [10]. *efindings presented in the previous section explain the ap-plicability of diffusion approximation with an integratingsphere system and polystyrene sample. *ese methods,

    500 550 600 650 700 75070

    80

    90

    100

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    120

    130

    140

    150Sc

    atte

    ring

    coef

    ficie

    nt (m

    m–1

    )

    Wavelength (nm)

    Kubelka–Munk scattering coefficientMie theory scattering coefficient

    Diffusion approximation scattering coefficient

    (a)

    500 550 600 650 700 7500.8

    0.820.840.860.88

    0.90.920.940.960.98

    Wavelength (nm)

    Alb

    edo

    Kubelka–Munk albedoDiffusion approximation albedo

    (b)

    500 550 600 650 700 7501.57

    1.58

    1.59

    1.6

    1.61

    1.62

    1.63

    1.64

    Wavelength (nm)

    Real

    par

    t of r

    efra

    ctiv

    e ind

    ex

    Diffusion approximationKubelka–Munk method

    Sultanova et al.Ma et al.

    (c)

    500 550 600 650 700 7501

    2

    3

    4

    5

    6

    ×10–4

    Wavelength (nm)

    Imag

    inar

    y pa

    rt o

    f ref

    ract

    ive i

    ndex

    Diffusion approximationKubelka-Munk methodMa et al.

    (d)

    Figure 5: (a) Comparison between KM, DA, andMie scattering over the wavelength. (b) Correlation of DA (red) and KM (blue) albedo withwavelength. (c) Correlation of the real part of refractive index estimated by diffusion approximation (red) and Kubelka–Munk (blue) withwavelength. (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and Kubelka–Munk(blue) with wavelength.

    6 Journal of Spectroscopy

  • which were used in this paper, make it possible to re-construct the absorption coefficient of a given sample,Figure 5(b). It should be noted that K–M absorptionproperty was higher compared to diffusion results. Bycomparison with absorption coefficient of water, 1 μmpolystyrene absorption property could not be neglected[23, 24]. It can be seen from Figure 5(b) that the variation ofalbedo with wavelength was about 0.95 for the K–Mmethodand higher for diffusion. *us, polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property. In addition,the ratio between scattering and absorption over the presentwavelength range varied from 30.69 at 505 nm to 13.52 at665 nm based on Kubelka–Munk and from 32.03 at 505 nmto 19.71 at 665 nm for the diffusion method. *erefore, theabsorption property of 1 μm polystyrene microsphere couldnot be neglected when the ratio of scattering and absorptioncoefficient of a certain tissue is comparable with the latervalues. Furthermore, when the ratio of scattering and ab-sorption coefficients equals the later ratios, the polystyrenecan mimic optical properties of the given tissue only withoutadding any absorbing material.

    Based on scattering and absorption coefficients of thesemethods and inverse Mie algorithm, the complex refractiveindex of 1 μm polystyrene microsphere could be evaluated,Figures 5(c) and 5(d). As can be seen from Figure 5(c), thecorrelation of the real part of refractive index for these twomethods with wavelength has similar trends that could beseen in equations (12) and (15). Also, K–M real refractiveindex seems to be lower whereas its imaginary part is higher.*at difference could be explained by the mismatch betweentwo models’ optical properties. Based on a deviation anglemethod for refractive index measurement of polystyrene, thesystematic errors of real refractive index calculations usingK–M and diffusion theory were estimated to be comparedwith prior research studies [20, 25, 26]. For Kubelka–Munkvalues, the relative reconstructed error varies between 1.8%to 0.2% and from 1.9% to 0.38% for diffusion theory results[20, 25, 26]. Inverse Mie calculation based on Monte Carloalgorithm was used to reconstruct the real refractive index ofpolystyrene, and the relative error of the Kubelka–Munkmethod varies between 2.52% and 0.43% and between 2.57%and 0.55% for diffusion theory results [24]. Furthermore,two approaches’ calculations show a relatively high error inthe lower wavelength, and the small errors could be seen at600 nm [20, 24–26]. For the imaginary part of polystyrenerefractive index, a similar behavior of ni variation withwavelength could be seen as shown in Figure 5(d), butdiffusion theory ni turned out to be lower due to the smallabsorption property than K–M ni values. However, therelative error for the imaginary part of refractive index variesbetween 3% and 30% for Kubelka–Munk and between 10%and 35% for diffusion theory [24].

    5. Conclusions

    In summary, the results given in this paper were an attemptto investigate the optical properties of 1 μm polystyrenemicrosphere as a scattering material in solid and liquid

    optical phantoms. For this purpose, Kubelka–Munk anddiffusion approximation methods were used to calculate theoptical properties of polystyrene. *en, results confirm theaccuracy of the results and applicability of diffusion theorywith the present experimental limitations.

    On the one hand, the applicability of using diffusiontheory has been constrained by many factors. *is theorycould be used with a semi-infinite diffusive medium andcollimated beam simulated by a thick scattering sample.Moreover, anisotropy factor of the sample should not exceed0.95 whereas Kubelka–Munk could be applied for any givenmedium.

    On the other hand, it can be seen that polystyreneshowed an absorption effect that was small in comparisonwith the scattering effect and varied over the spectral range.*e decisive factor for neglecting polystyrene absorptiondepends on the ratio of scattering and absorption of a givenmedium.

    Data Availability

    *e data used to support the findings of this study areavailable from the corresponding author upon request.

    Conflicts of Interest

    *e authors declare that they have no conflicts of interest.

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