Polystyrene Microsphere Optical Properties by...

9
Research Article Polystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation with a Single Integrating Sphere System: A Comparative Study Ali Shahin , 1 Wesam Bachir, 1,2 and Moustafa Sayem El-Daher 3,4 1 Biomedical Photonics Laboratory, Higher Institute for Laser Research and Applications, Damascus University, Damascus, Syria 2 Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria 3 Higher Institute for Laser Research and Applications, Damascus University, Damascus, Syria 4 Faculty 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 light spectrophotometric transmittance spectroscopy and a single integrating sphere system. To retrieve the optical characteristics, two analytical methods, namely, diffusion approximation and Kubelka–Munk were used, and then their results were compared with Mie theory calculations. e correspondence of the Kubelka–Munk scattering coefficient with Mie was obvious, and relative errors varied between 6.73% and 2.66% whereas errors varied between 6.87% and 3.62% for diffusion theory. Both analytical methods demonstrated 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 account absorption property of polystyrene. Complex refractive index of polystyrene based on these two methods was determined. Inverse Mie algorithm with scattering coefficient was also used to retrieve the real part of refractive index and absorption coefficient for calculating the imaginary part of refractive index. e relative errors of the real part did not exceed 2.6%, and the imaginary part was in consistence with the prior works. Finally, the presented results confirm the validity of diffusion theory with a single integrating sphere system. 1. Introduction Optical characterization techniques require both an exper- imental setup to measure the radiometric characteristics and a light propagation method to extract the macroscopic optical properties. Generally, these techniques are catego- rizedasdirectandindirectmethods[1,2].edirectmethod can be performed only ex vivo, and the samples used in this technique are thin enough so that the multiple scattering events can be negligible, but the advantage of this method depends on simple exponential equations to extract the optical properties [2]. In contrast, indirect methods can be implemented 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 mathematical principles and analytical and numerical solutions of the radiative transfer equation (RTE) [1–4]. Kubelka–Munk may be considered as the simplest analytical method that has been used for optical characterization, but the drawback of this 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 the jump in the refractive index between the sample and sur- rounding medium [6, 7]. Recently, this approach has been modified to overcome the refractive index mismatch be- tween the sample and holder, and the thickness does not exceed the transport length [7]. e present method has been investigated with a single integrating sphere system Hindawi Journal of Spectroscopy Volume 2019, Article ID 3406319, 8 pages https://doi.org/10.1155/2019/3406319

Transcript of Polystyrene Microsphere Optical Properties by...

Page 1: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

Research ArticlePolystyrene Microsphere Optical Properties by KubelkandashMunkand Diffusion Approximation with a Single Integrating SphereSystem A Comparative Study

Ali Shahin 1 Wesam Bachir12 and Moustafa Sayem El-Daher 34

1Biomedical Photonics Laboratory Higher Institute for Laser Research and Applications Damascus UniversityDamascus 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 alishahin88yahoocom

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

Academic Editor Daniel Cozzolino

Copyright copy 2019 Ali Shahin et al is is an open access article distributed under the Creative Commons Attribution Licensewhich 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 500ndash750 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 KubelkandashMunk were used and then their results were compared withMie theory calculationse correspondence of the KubelkandashMunk scattering coefficient withMie was obvious and relative errorsvaried between 673 and 266 whereas errors varied between 687 and 362 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 26 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 [2ndash5]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) [1ndash4] KubelkandashMunkmay 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 samplersquos 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 pageshttpsdoiorg10115520193406319

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 ie 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 approachesus albedo scattering coefficient extinction coefficientand complex refractive index of a 1 μm polystyrene mi-crosphere (07310-15 Polybead Polysciences USA) weredetermined by using diffusion approximation andKubelkandashMunk 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 modelsrsquo results which was considered as a standardmethod for a spherical particle like polystyrene Finallycomplex refractive index of a 1 μm polystyrene was de-termined in the range of wavelength 500ndash750 nm based onthese two modelsrsquo scattering coefficient and inverse Mietheory calculation

2 Materials and Methods

21 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 aprime and an internal diffuse reflectance r as follows[10 13]

Rd aprime

1 + 2 middot K 1 minus aprime( 1113857 +(1 +(2 middot K3)) middot

3 1 minus aprime( 1113857

1113969 (1)

where aprime μsprime(μsprime + μa) is the reduced albedo and k (1 + r)

(1 minus r) is a factor related to internal diffuse reflectance rwhich is given by [10 13]

r minus 144nminus 2rel + 071n

minus 1rel + 0668 + 00636nrel

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]

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

K

S

1 minus Rinfin( 11138572

2 middot Rinfin

K 2 middot μa

S 34

middot μsprime minus

14

middot 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 middot 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

T2f

Tdminus2 middot Rd middot T2

f middot log T2f Td( 1113857

d middot T4f minus T2

d( 1113857 (5)

μs 1dlog

Td

Tc+2 middot Rd middot T2

f middot log T2f Td( 1113857

d middot T4f minus T2

d( 1113857 (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

23 Mie 0eory Calculation Mie theory is an analyticalsolution of Maxwellrsquos 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 ie 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 (07310-15Polybead Polysciences USA) and the fraction of 1 μmpolystyrene particles was 25 (wv) In addition refractiveindices of polystyrene as a scattering and water as a hostmaterial were found from previous work [20]

24 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 500ndash750 nme sample was illuminated with a collimated whitelight beam us the transmission intensity may be ap-proximated by the BeerndashLambert Law [8 9]

Iz(λ) I0(λ) middot eminus μt(λ)middotzmiddotc

(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]

25 Integrating Sphere System A broadband single in-tegrating sphere (819C-IS-53 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 15mm pinholeand the diffuse light emanated from the sample is guidedthrough an optical fiber to the spectrometer (USB4000 FLOcean 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 OpticsUSA) 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 theBeerndashLamber law equation (7) the extinction coefficient of1 μm polystyrene microsphere can be calculated over thewavelength range of 500ndash750 nm as shown in Figure 2Obviously 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

microt 17lowast 106 middot λminus 1498 (9)

31 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 PolysciencesUSA) Refractive index of PS was found from the prior workand for water (host material) it was about 133 [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

micros Mie 17lowast 106 middot λminus 1513

micros Mieprime 3689 middot λminus 09462

(10)

32 KubelkandashMunk e modified KubelkandashMunk 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 KubelkandashMunk scattering coefficient couldbe evaluated as shown in Figure 4(a) Accordingly KndashMscattering coefficient was plotted with wavelength and thatwas found to be inversely proportional to increased wave-length e correlations of KndashM scattering and reducedscattering coefficients and wavelength were found using thecurve fitting procedure which were compatible with Mierelations as follows

Journal of Spectroscopy 3

micros KM 17lowast 106 middot λminus 1507

micros KMprime 3689 middot λminus 09405

(11)

Based on extinction coefficient of PS and KndashM scatteringresults KndashM albedo (blue dotted line) might be calculatedFigure 5(b) en using inverse Mie calculation and

KubelkandashMunk 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 KubelkandashMunk (bluedotted line) was fitted to the Cauchy relation

nr(λ) 161 minus002742

λ2+0008074

λ4 (12)

where λ is estimated in micrometer en KndashM absorptioncoefficient might be utilized to predict an imaginary part ofrefractive index using the following equation Figure 5(d)

ni microa middot λ4π

(13)

33 Diffusion 0eory Diffusion approximation introducesdiffuse reflectance Rd as a function of reduced albedo aprime 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 = 15mm)

Sam

ple

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Rd

(a)

Sample

(HL2000-HP-FH5A)

Tungsten-halogen light source

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Tc

Td

Convex lens(f = 10cm)Pinhole

(ϕ = 15mm)

(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

minus1)

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 calculatedFigure 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

micros DA 17lowast 106 middot λminus 1505

micros DAprime 3689 middot λminus 09386

(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 wavelengthen 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) 1611 minus002574

λ2+0007688

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 KubelkandashMunkand 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

ndash1)

(a)

500 550 600 650 700 750

087

088

089

09

091

092

093

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

KndashM

scat

terin

g co

effic

ient

(mm

ndash1)

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

ndash1)

(b)

Figure 4 (a) Correlation of KubelkandashMunk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength

Journal of Spectroscopy 5

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

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Page 2: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

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 ie 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 approachesus albedo scattering coefficient extinction coefficientand complex refractive index of a 1 μm polystyrene mi-crosphere (07310-15 Polybead Polysciences USA) weredetermined by using diffusion approximation andKubelkandashMunk 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 modelsrsquo results which was considered as a standardmethod for a spherical particle like polystyrene Finallycomplex refractive index of a 1 μm polystyrene was de-termined in the range of wavelength 500ndash750 nm based onthese two modelsrsquo scattering coefficient and inverse Mietheory calculation

2 Materials and Methods

21 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 aprime and an internal diffuse reflectance r as follows[10 13]

Rd aprime

1 + 2 middot K 1 minus aprime( 1113857 +(1 +(2 middot K3)) middot

3 1 minus aprime( 1113857

1113969 (1)

where aprime μsprime(μsprime + μa) is the reduced albedo and k (1 + r)

(1 minus r) is a factor related to internal diffuse reflectance rwhich is given by [10 13]

r minus 144nminus 2rel + 071n

minus 1rel + 0668 + 00636nrel

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]

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

K

S

1 minus Rinfin( 11138572

2 middot Rinfin

K 2 middot μa

S 34

middot μsprime minus

14

middot 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 middot 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

T2f

Tdminus2 middot Rd middot T2

f middot log T2f Td( 1113857

d middot T4f minus T2

d( 1113857 (5)

μs 1dlog

Td

Tc+2 middot Rd middot T2

f middot log T2f Td( 1113857

d middot T4f minus T2

d( 1113857 (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

23 Mie 0eory Calculation Mie theory is an analyticalsolution of Maxwellrsquos 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 ie 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 (07310-15Polybead Polysciences USA) and the fraction of 1 μmpolystyrene particles was 25 (wv) In addition refractiveindices of polystyrene as a scattering and water as a hostmaterial were found from previous work [20]

24 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 500ndash750 nme sample was illuminated with a collimated whitelight beam us the transmission intensity may be ap-proximated by the BeerndashLambert Law [8 9]

Iz(λ) I0(λ) middot eminus μt(λ)middotzmiddotc

(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]

25 Integrating Sphere System A broadband single in-tegrating sphere (819C-IS-53 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 15mm pinholeand the diffuse light emanated from the sample is guidedthrough an optical fiber to the spectrometer (USB4000 FLOcean 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 OpticsUSA) 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 theBeerndashLamber law equation (7) the extinction coefficient of1 μm polystyrene microsphere can be calculated over thewavelength range of 500ndash750 nm as shown in Figure 2Obviously 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

microt 17lowast 106 middot λminus 1498 (9)

31 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 PolysciencesUSA) Refractive index of PS was found from the prior workand for water (host material) it was about 133 [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

micros Mie 17lowast 106 middot λminus 1513

micros Mieprime 3689 middot λminus 09462

(10)

32 KubelkandashMunk e modified KubelkandashMunk 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 KubelkandashMunk scattering coefficient couldbe evaluated as shown in Figure 4(a) Accordingly KndashMscattering coefficient was plotted with wavelength and thatwas found to be inversely proportional to increased wave-length e correlations of KndashM scattering and reducedscattering coefficients and wavelength were found using thecurve fitting procedure which were compatible with Mierelations as follows

Journal of Spectroscopy 3

micros KM 17lowast 106 middot λminus 1507

micros KMprime 3689 middot λminus 09405

(11)

Based on extinction coefficient of PS and KndashM scatteringresults KndashM albedo (blue dotted line) might be calculatedFigure 5(b) en using inverse Mie calculation and

KubelkandashMunk 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 KubelkandashMunk (bluedotted line) was fitted to the Cauchy relation

nr(λ) 161 minus002742

λ2+0008074

λ4 (12)

where λ is estimated in micrometer en KndashM absorptioncoefficient might be utilized to predict an imaginary part ofrefractive index using the following equation Figure 5(d)

ni microa middot λ4π

(13)

33 Diffusion 0eory Diffusion approximation introducesdiffuse reflectance Rd as a function of reduced albedo aprime 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 = 15mm)

Sam

ple

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Rd

(a)

Sample

(HL2000-HP-FH5A)

Tungsten-halogen light source

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Tc

Td

Convex lens(f = 10cm)Pinhole

(ϕ = 15mm)

(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

minus1)

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 calculatedFigure 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

micros DA 17lowast 106 middot λminus 1505

micros DAprime 3689 middot λminus 09386

(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 wavelengthen 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) 1611 minus002574

λ2+0007688

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 KubelkandashMunkand 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

ndash1)

(a)

500 550 600 650 700 750

087

088

089

09

091

092

093

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

KndashM

scat

terin

g co

effic

ient

(mm

ndash1)

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

ndash1)

(b)

Figure 4 (a) Correlation of KubelkandashMunk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength

Journal of Spectroscopy 5

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 3: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

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

23 Mie 0eory Calculation Mie theory is an analyticalsolution of Maxwellrsquos 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 ie 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 (07310-15Polybead Polysciences USA) and the fraction of 1 μmpolystyrene particles was 25 (wv) In addition refractiveindices of polystyrene as a scattering and water as a hostmaterial were found from previous work [20]

24 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 500ndash750 nme sample was illuminated with a collimated whitelight beam us the transmission intensity may be ap-proximated by the BeerndashLambert Law [8 9]

Iz(λ) I0(λ) middot eminus μt(λ)middotzmiddotc

(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]

25 Integrating Sphere System A broadband single in-tegrating sphere (819C-IS-53 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 15mm pinholeand the diffuse light emanated from the sample is guidedthrough an optical fiber to the spectrometer (USB4000 FLOcean 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 OpticsUSA) 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 theBeerndashLamber law equation (7) the extinction coefficient of1 μm polystyrene microsphere can be calculated over thewavelength range of 500ndash750 nm as shown in Figure 2Obviously 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

microt 17lowast 106 middot λminus 1498 (9)

31 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 PolysciencesUSA) Refractive index of PS was found from the prior workand for water (host material) it was about 133 [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

micros Mie 17lowast 106 middot λminus 1513

micros Mieprime 3689 middot λminus 09462

(10)

32 KubelkandashMunk e modified KubelkandashMunk 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 KubelkandashMunk scattering coefficient couldbe evaluated as shown in Figure 4(a) Accordingly KndashMscattering coefficient was plotted with wavelength and thatwas found to be inversely proportional to increased wave-length e correlations of KndashM scattering and reducedscattering coefficients and wavelength were found using thecurve fitting procedure which were compatible with Mierelations as follows

Journal of Spectroscopy 3

micros KM 17lowast 106 middot λminus 1507

micros KMprime 3689 middot λminus 09405

(11)

Based on extinction coefficient of PS and KndashM scatteringresults KndashM albedo (blue dotted line) might be calculatedFigure 5(b) en using inverse Mie calculation and

KubelkandashMunk 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 KubelkandashMunk (bluedotted line) was fitted to the Cauchy relation

nr(λ) 161 minus002742

λ2+0008074

λ4 (12)

where λ is estimated in micrometer en KndashM absorptioncoefficient might be utilized to predict an imaginary part ofrefractive index using the following equation Figure 5(d)

ni microa middot λ4π

(13)

33 Diffusion 0eory Diffusion approximation introducesdiffuse reflectance Rd as a function of reduced albedo aprime 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 = 15mm)

Sam

ple

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Rd

(a)

Sample

(HL2000-HP-FH5A)

Tungsten-halogen light source

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Tc

Td

Convex lens(f = 10cm)Pinhole

(ϕ = 15mm)

(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

minus1)

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 calculatedFigure 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

micros DA 17lowast 106 middot λminus 1505

micros DAprime 3689 middot λminus 09386

(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 wavelengthen 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) 1611 minus002574

λ2+0007688

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 KubelkandashMunkand 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

ndash1)

(a)

500 550 600 650 700 750

087

088

089

09

091

092

093

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

KndashM

scat

terin

g co

effic

ient

(mm

ndash1)

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

ndash1)

(b)

Figure 4 (a) Correlation of KubelkandashMunk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength

Journal of Spectroscopy 5

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 4: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

micros KM 17lowast 106 middot λminus 1507

micros KMprime 3689 middot λminus 09405

(11)

Based on extinction coefficient of PS and KndashM scatteringresults KndashM albedo (blue dotted line) might be calculatedFigure 5(b) en using inverse Mie calculation and

KubelkandashMunk 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 KubelkandashMunk (bluedotted line) was fitted to the Cauchy relation

nr(λ) 161 minus002742

λ2+0008074

λ4 (12)

where λ is estimated in micrometer en KndashM absorptioncoefficient might be utilized to predict an imaginary part ofrefractive index using the following equation Figure 5(d)

ni microa middot λ4π

(13)

33 Diffusion 0eory Diffusion approximation introducesdiffuse reflectance Rd as a function of reduced albedo aprime 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 = 15mm)

Sam

ple

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Rd

(a)

Sample

(HL2000-HP-FH5A)

Tungsten-halogen light source

Spectrometer(USB4000-FL)

Integrating sphere(819C-IS-53)

Tc

Td

Convex lens(f = 10cm)Pinhole

(ϕ = 15mm)

(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

minus1)

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 calculatedFigure 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

micros DA 17lowast 106 middot λminus 1505

micros DAprime 3689 middot λminus 09386

(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 wavelengthen 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) 1611 minus002574

λ2+0007688

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 KubelkandashMunkand 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

ndash1)

(a)

500 550 600 650 700 750

087

088

089

09

091

092

093

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

KndashM

scat

terin

g co

effic

ient

(mm

ndash1)

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

ndash1)

(b)

Figure 4 (a) Correlation of KubelkandashMunk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength

Journal of Spectroscopy 5

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 5: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

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 calculatedFigure 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

micros DA 17lowast 106 middot λminus 1505

micros DAprime 3689 middot λminus 09386

(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 wavelengthen 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) 1611 minus002574

λ2+0007688

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 KubelkandashMunkand 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

ndash1)

(a)

500 550 600 650 700 750

087

088

089

09

091

092

093

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

KndashM

scat

terin

g co

effic

ient

(mm

ndash1)

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

ndash1)

(b)

Figure 4 (a) Correlation of KubelkandashMunk scattering coefficient and wavelength and (b) relation between diffusion approximationscattering coefficient with wavelength

Journal of Spectroscopy 5

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 6: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

KubelkandashMunk and diffusion approximation scatteringwere found to be inversely proportional to the wavelengththat were in consistence with Mie calculation and theirpower factor was about minus 1505 for diffusion theory minus 1507for the KndashMmodel and minus 1513 for Mie calculationis canbe explained by the small incident wavelength in comparisonwith polystyrene diameter [17] In addition KndashM scatteringwas in agreement withMie calculation and the relative errorsvaried between 673 to 266 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 687 and 362e small differencebetween two methodsrsquo results could be explained by somereasonse 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 notKubelkandashMunk [7 10 13]e second one is that a modifiedKubelkandashMunk 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 09 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

110

120

130

140

150Sc

atte

ring

coef

ficie

nt (m

mndash1

)

Wavelength (nm)

KubelkandashMunk scattering coefficientMie theory scattering coefficient

Diffusion approximation scattering coefficient

(a)

500 550 600 650 700 75008

082084086088

09092094096098

Wavelength (nm)

Alb

edo

KubelkandashMunk albedoDiffusion approximation albedo

(b)

500 550 600 650 700 750157

158

159

16

161

162

163

164

Wavelength (nm)

Real

par

t of r

efra

ctiv

e ind

ex

Diffusion approximationKubelkandashMunk method

Sultanova et alMa et al

(c)

500 550 600 650 700 7501

2

3

4

5

6

times10ndash4

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 KubelkandashMunk (blue) withwavelength (d) Relation between the imaginary part of refractive index calculated by diffusion approximation (red) and KubelkandashMunk(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 sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 7: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

which were used in this paper make it possible to re-construct the absorption coefficient of a given sampleFigure 5(b) It should be noted that KndashM 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 095 for the KndashMmethodand higher for diffusion us polystyrene microsphere canbe considered as a turbid medium with highly scatteringevents in comparison with absorption property In additionthe ratio between scattering and absorption over the presentwavelength range varied from 3069 at 505 nm to 1352 at665 nm based on KubelkandashMunk and from 3203 at 505 nmto 1971 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 evaluatedFigures 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 KndashM real refractiveindex seems to be lower whereas its imaginary part is higherat difference could be explained by the mismatch betweentwo modelsrsquo optical properties Based on a deviation anglemethod for refractive index measurement of polystyrene thesystematic errors of real refractive index calculations usingKndashM and diffusion theory were estimated to be comparedwith prior research studies [20 25 26] For KubelkandashMunkvalues the relative reconstructed error varies between 18to 02 and from 19 to 038 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 KubelkandashMunkmethod varies between 252 and 043 and between 257and 055 for diffusion theory results [24] Furthermoretwo approachesrsquo calculations show a relatively high error inthe lower wavelength and the small errors could be seen at600 nm [20 24ndash26] 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 KndashM ni values However therelative error for the imaginary part of refractive index variesbetween 3 and 30 for KubelkandashMunk and between 10and 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 KubelkandashMunk 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 sampleMoreover anisotropy factor of the sample should not exceed095 whereas KubelkandashMunk 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 rangee 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

References

[1] B C Wilson M S Patterson and S T Flock ldquoIndirect versusdirect techniques for the measurement of the optical prop-erties of tissuesrdquo Photochemistry and Photobiology vol 46no 5 pp 601ndash608 1987

[2] A N Bashkatov E A Genina and V V Tuchin ldquoOpticalproperties of skin subcutaneous and muscle tissues a re-viewrdquo Journal of Innovative Optical Health Sciences vol 4no 1 pp 9ndash38 2011

[3] J L Sandell and T C Zhu ldquoA review of in-vivo opticalproperties of human tissues and its impact on PDTrdquo Journalof Biophotonics vol 4 no 11-12 pp 773ndash787 2011

[4] A N Yaroslavsky P C Schulze I V Yaroslavsky R SchoberF Ulrich and H-J Schwarzmaier ldquoOptical properties ofselected native and coagulated human brain tissues in vitro inthe visible and near infrared spectral rangerdquo Physics inMedicine and Biology vol 47 no 12 pp 2059ndash2073 2002

[5] H Soleimanzad H Gurden and F Pain ldquoOptical propertiesof mice skull bone in the 455-to 705-nm rangerdquo Journal ofBiomedical Optics vol 22 no 1 Article ID 010503 2017

[6] S N ennadil ldquoRelationship between the Kubelka-Munkscattering and radiative transfer coefficientsrdquo Journal of theOptical Society of America A vol 25 no 7 pp 1480ndash14852008

[7] A D Krainov A M Mokeeva E A Sergeeva P D AgrbaandM Y Kirillin ldquoOptical properties of mouse biotissues andtheir optical phantomsrdquo Optics and Spectroscopy vol 115no 2 pp 227ndash234 2013

[8] A Shahin M Sayem El-Daher and W Bachir ldquoDe-termination of the optical properties of Intralipid 20 over abroadband spectrumrdquo Photonics Letters of Poland vol 10no 4 pp 124ndash126 2018

Journal of Spectroscopy 7

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 8: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

[9] A Shahin and W Bachir ldquoBroadband spectroscopy forcharacterization of tissue-like phantom optical propertiesrdquoPolish Journal of Medical Physics and Engineering vol 23no 4 pp 121ndash126 2017

[10] S T Flock M S Patterson B C Wilson and D R WymanldquoMonte Carlo modeling of light propagation in highly scat-tering tissues I model predictions and comparison withdiffusion theoryrdquo IEEE Transactions on Biomedical Engi-neering vol 36 no 12 pp 1162ndash1168 1989

[11] A T Lovell J C Hebden J C Goldstone and M CopeldquoDetermination of the transport scattering coefficient of redblood cellsrdquo in Proceedings of the SPIE vol 3597 San JoseCA USA July 1999

[12] R Michels F Foschum and A Kienle ldquoOptical properties offat emulsionsrdquo Optics Express vol 16 no 8 pp 5907ndash59252008

[13] A J Welch and M J C van Gemert Optical-0ermal Re-sponse of Laser-Irradiated Tissue Springer New York NYUSA 2011

[14] P R Bargo S A Prahl T T Goodell et al ldquoIn vivo de-termination of optical properties of normal and tumor tissuewith white light reflectance and an empirical light transportmodel during endoscopyrdquo Journal of Biomedical Opticsvol 10 no 3 Article ID 034018 2005

[15] B W Pouge and M S Patterson ldquoReview of tissue simulatingphantoms for optical spectroscopy imaging and dosimetryrdquoJournal of Biomedical Optics vol 11 no 4 Article ID 0411022006

[16] Y Liu Y L Kim and V Backman ldquoDevelopment of abioengineered tissue model and its application in the in-vestigation of the depth selectivity of polarization gatingrdquoApplied Optics vol 44 no 12 pp 2288ndash2299 2005

[17] H C van de Hulst Light Scattering by Small Particles DoverPublication New York NY USA 1981

[18] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Bern University Bern Germany 2002

[19] C Matzler Matlab Functions for Mie Scattering and Ab-sorption Version 2 Bern University Bern Germany 2002

[20] N Sultanova S Kasarova and I Nikolov ldquoDispersionproperties of optical polymersrdquo Acta Physica Polonica Avol 116 no 4 pp 585ndash587 2009

[21] N Salas Development of a Delivery System and Optical-0ermal Model for Laser Interstitial 0ermotherapy of BreastTumors dissertation University of Miami Florida FL USA2007

[22] M Almadi Optical Properties Measurements of Rat Muscleand Myocardium at 980 and 1860 NmUsing Single IntegratingSphere Technique Master thesis University of Miami FloridaFL USA 2014

[23] G Segelstein 0e Complex Refractive Index of Water PhDdissertation University ofMissouri-Kansas City Kansas MOUSA 1981

[24] X Ma J Q Lu R S Brock K M Jacobs P Yang andX-H Hu ldquoDetermination of complex refractive index ofpolystyrene microspheres from 370 to 1610 nmrdquo Physics inMedicine and Biology vol 48 no 24 pp 4165ndash4172 2003

[25] I D Nikolov and C D Ivanov ldquoOptical plastic refractivemeasurements in the visible and the near-infrared regionsrdquoApplied Optics vol 39 no 13 pp 2067ndash2070 2000

[26] N G Sultanova S N Kasarova and I D Nikolov ldquoChar-acterization of optical properties of optical polymersrdquo Opticaland Quantum Electronics vol 45 no 3 pp 221ndash232 2013

8 Journal of Spectroscopy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Page 9: Polystyrene Microsphere Optical Properties by …downloads.hindawi.com/journals/jspec/2019/3406319.pdfPolystyrene Microsphere Optical Properties by Kubelka–Munk and Diffusion Approximation

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom