Research Article Combined Experimental and Monte-Carlo Ray …downloads.hindawi.com/archive/2013/385345.pdf · 2019. 7. 31. · ISRN Optics 0 10 20 0 10203040506070 Gain of light

Hindawi Publishing CorporationISRN OpticsVolume 2013 Article ID 385345 5 pageshttpdxdoiorg1011552013385345

Research ArticleCombined Experimental and Monte-Carlo Ray-TracingApproach for Optimizing Light Extraction in LED COB Modules

Marianne Consonni Julien Routin Anthony Piveteau and Adrien Gasse

CEA-Leti Minatec Campus 17 rue des Martyrs 38054 Grenoble Cedex 9 France

Correspondence should be addressed to Marianne Consonni marianneconsonniceafr

Received 6 May 2013 Accepted 26 June 2013

Academic Editors L R P Kassab and Y S Kivshar

Copyright copy 2013 Marianne Consonni et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

High-power light-emitting diodes (LEDs) for lighting applications require a high-efficient packaging to optimize their per-formances Due to its high thermal dissipation potential the chip-on-board (COB) technology is widely used for developinghigh-power lighting sources In order to optimize the optical properties of such sources and to propose high optically efficientencapsulation geometry ray-tracing simulations have been performed The impact of the shape and volume of the siliconeencapsulation on the light extraction and on the intensity distribution of the module was derived Then simulation resultswere correlated with experimental measurements on blue light-emitting COB sources It is shown that a nearly hemisphericalencapsulation with a minimal volume of 5 to 10mm3 for a 1 mm2 LED die is the optimal configuration regarding both the lightextraction and the intensity distribution

1 Introduction

High-power light-emitting diodes (LEDs) have attracted alot of interest in the recent years due to their low-powerconsumption and long lifetime However the integrationof these light sources for general lighting applications willrequire high-efficient packaging with low thermal resistanceand compact size [1] Thus due to its compactness and itshigh thermal dissipation potential the chip-on-board (COB)technology is one of the favourite candidates for developingcustomized and thermal-efficient LEDs [2]

Beyond the thermal efficiency one of the key perfor-mance criteria of a LED light source is its optical efficiencyThis efficiency comprises several components [3] The firstone is the ldquointernal quantum efficiencyrdquo It is defined asthe ratio between the number of photons emitted from theactive region per second and the number of electrons injectedinto the LED per second It describes the LED junctionperformance

In this paper we focus on the second component of thisefficiency the ldquolight extraction efficiencyrdquo It is defined asthe ratio between the number of photons emitted into freespace per second and the number of photons emitted from

the active region per second At the die level this efficiencyis limited by the total internal reflexions which appear at theinterface between the semiconductormaterial and the air dueto their refractive index mismatch It may be improved eitherby structuring the die surface [4 5] andor by packaging thedie with dome-shaped encapsulants with a high refractiveindex [6] At the package level the extraction is limited by thelosses which may occur during light propagation within thepackage A lot of work has been done to reduce these lossesand to optimize the light extraction of a packaged LED Thisincluded adjusting the encapsulation refractive index [7]inserting a reflective part around the light-emitting element[8 9] or optimizing the exit surface shape of the package[9 10]

However in a COB module an important point is tokeep a simple realization process which allows both costreduction and performance In order to reach this targetand to optimize the module performances the parameterswhich are easier to modify are the encapsulation shape andthe volume Several studies have already been performedto evaluate the impact of the encapsulation on the lightextraction [11 12] Nevertheless to our knowledge these

2 ISRN Optics

PCB

HR = 03

(a)

PCB

HR = 1

2R

H

(b)

PCB

HR = 17

(c)

Figure 1 Cross-sections of the geometries which have been modelled for evaluating the impact of the encapsulation shape and size on a LEDCOB performance (a) Nearly flat encapsulation with an aspect ratio HR of 03 (b) hemispherical encapsulation (c) oblong encapsulationwith an aspect ratio HR = 17

works stayed at the theoretical stage and they were notdemonstrated experimentally

That is why we propose in this paper to combine botha ray-tracing and an experimental approach for optimizingthe light extraction and intensity distribution of a LED COBmodule Thanks to the Monte-Carlo ray-tracing simulationswe have determined the encapsulation shape and the volumeallowing to maximize light extraction Then the originalityof this study is that these results have been correlated withexperimental measurements done on COB samples whichwere made from a 1mm2 LED die encapsulated with siliconeThe experimental results are found to be in good agreementwith the simulations

2 Simulations

In order to determine the parameters which are critical forthe LEDCOBencapsulation performance we have developeda simulation model which calculates the amount of lightextracted from a blue light-emitting die depending on theshape and on the size of its encapsulation

We have used the Zemax software which is based ontheMonte-Carlo ray-tracingThe typical LEDCOB geometryincludes a 1times1mm2 GaNLEDdie (refractive index 119899 = 242for a 450 nm incident wavelength) on a large board Thenthe die emission has been modelled as a lambertian intensitydistribution The light-emitting wavelength has been fixedequal to 450 nm which is close to the typical wavelengthof Royal Blue LEDs For simplicity reasons we have alsochosen not to take into account the die roughness in thesesimulations As will be detailed later this does not impactthe trend of the results but it implies to carefully analysethem Then the board has been considered as a reflectiveelement In order to reproduce the behaviour of the printedcircuit board (PCB) which will be used for the comparativeexperimental tests and which comprises a white solder maskwe have fixed its reflectivity to 70 with a surface lambertiandiffusion Finally this module has been covered with asilicone encapsulation (119899 = 14 for a 450 nm incidentwavelength) whose shape and size have been modified asdepicted in Figure 1 119867 is the height and 119877 is the radius ofthe encapsulation

The encapsulation shape has been set as half-ellipsoidalwith an aspect ratio ldquoheight above radiusrdquo HR varying from03 (flat encapsulation) to 17 (oblong encapsulation) Thusdepending on the shape the volume of the encapsulationvaries accordingly from about 1mm3 to 70mm3 whichallows observing simultaneously the effect of the shape andof the volume on the module optical characteristics

Regarding the simulation analysis this model does nottake into account the die roughness as stated above Thisdoes not significantly change the results since both the LEDplane surface and a roughened surface have a lambertiandistribution However it implies that the analysis has to bedone by only comparing the results among themselves Thuswe have normalized the light extraction values which havebeen obtained through the simulations as follows

120578extraction =120578 minus 1205780

1205780

(1)

where 120578 is the light extraction efficiency of the consideredgeometry and 120578

0is the light extraction efficiency of a

reference case This reference has been arbitrarily chosen tobe a hemispherical encapsulation with a radius R of 14mm

Then we have plotted this calculated gain or loss in lightextraction 120578extraction depending on the volume and on theaspect ratio of the encapsulation The corresponding resultsare given in Figure 2

First the graph clearly evidences that due to a highamount of total internal reflexions within the encapsulationa flat encapsulation shape (119867119877 lt 07) ever provides a badlight extractionThis is in agreement with previous works [8]which were done for packaged LEDs where it was shown thata hemispherical dome gave better extraction results than a flator convex encapsulation shape

Our simulation results also indicate that above an aspectratio 119867119877 of 07 the shape of the encapsulation has a smallimpact on the light extraction and that even an oblongshape may provide an efficient LED COB module This wasalso observed in recent works [12] on silicon-based LEDpackaging Indeed above a certain aspect ratio the rayincident angles at the silicone-air interface are small enoughto limit the total internal reflexions Thus these rays willalways be able to escape from the encapsulation maintainingthe light extraction quite stable

ISRN Optics 3

01020

0 10 20 30 40 50 60 70

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

re

fere

nce (

)

Volume (mm3)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17

Figure 2 Variation of the light extraction of a LED COB moduledepending on the volume and on the aspect ratio of the LED diesilicone encapsulation (simulation results)

Then regarding the impact of the encapsulation volumepreviousworks have shown that the light extraction stabilizedfrom an encapsulation radius larger than 15119903 where 119903 isthe die size [10] In our model configuration the die sizeis 119903 = 1mm Thus a hemispherical encapsulation such as119877 = 15119903 approximately represents a volume of 7mm3 Oursimulations are also effectively in line with these resultsMoregenerally our computations evidence that above a siliconevolume of 5 to 10mm3 the light extraction efficiency of theCOB module remains quite stable and rather independent ofthe encapsulation shapeHowever for small silicone volumesthe hemispherical encapsulation shape is the most efficientgeometry

Finally we have studied the impact of the LED COBencapsulation shape on the light intensity distribution Byinserting a far-field intensity detector in the simulationmodel we have collected the angular flux emitted by theCOB geometry The light intensity distribution is plotted inFigure 3 for an encapsulation radius of 23mm

As it is currently done for packaged LED components thegraph evidences that giving a specific shape to the LED COBencapsulation allows beam shaping Indeed inserting anoblong-shape encapsulation implies that light rays impactingthe silicone-air interface will mainly be extracted along smallangles This will lead to a sharp and narrow intensity distri-bution as it is depicted by the simulation curve representingthe high aspect ratio HR = 17 On the contrary makinga hemispherical or flat encapsulation favours light angulardispersion at the silicone-air interface which will provide arather lambertian distribution

These theoretical studies indicate that the optimal opticalperformances for a LED COB module will be obtained witha geometry combining a rather high encapsulation volume(larger than 5mm3) and a hemispherical shape An oblongshape may also be considered for applications which requirestrong narrow beams

0

02

04

06

08

1

0 30 60 90

Rela

tive i

nten

sity

Angle (degrees)

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17

minus30minus60minus90

Figure 3 Light intensity distributions provided by a LED COBmodule depending on the shape of its encapsulation (simulationresults) The encapsulation radius is 23mm

3 Experiments

In order to validate the simulation results which have beenpresented above and to evaluate the potential of such encap-sulation shapes and volumes for improving the performancesof LED COB modules we have mounted several LED dies ina COB configurationThen we have performed different testson these modules to check their optical characteristics A topview of one of thesemodules (microscopic imaging) is shownin Figure 4

The modules include a SemiLEDS LED die of 1 times1mm2 surface area with a typical dominant wavelength 120582domequal to 4625 nm (reference SL-V-B40AC2 with a typicalradiant flux at 350mA of 350mW) The LED die has beenmounted on a ldquostarrdquo PCB with a silver paste adhesive (EpoxyTechnology reference EPOTEK H20E-HC)

Encapsulation was carried out using a dispensing processwith silicone from NuSil having a refractive index 119899 = 14for blue-range incident wavelengths Volume and shape havebeen adjusted by varying the dispensing parameters

Finally we have used a 610158401015840

integrating sphere coupledto a spectrophotometer from LabSphere (SphereOptics) tomeasure the radiant flux of these encapsulated modules Inorder to be able to compare the experimental results with theray-tracing simulations which were detailed in the previoussection we have followed the same analysis procedure (see(1)) First we have calculated the light extraction of eachmodule by doing the ratio between the radiant fluxes emittedby the system after and before encapsulation Then we havechosen a sample which presents a hemispherical encapsula-tion of 2mm radius and we have set its light extraction value1205780as reference for the others Finally we have normalized

all of the sample extraction values to this reference caseand we have plotted the graph which is given in Figure 5 Ithas to be noted that due to the different geometries of thetwo reference samples which have been taken for analysingthe experimental and the simulation results (encapsulationradius of 2mm versus 14mm for the simulations) the

4 ISRN Optics

Figure 4 Top view of one LED COB module

10

0 5 10 15 20 25 30

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

r

efer

ence

()

minus10

minus30

minus50

minus70

minus90

minus110

HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13

Volume (mm3)

Figure 5 Gain of light extraction as a function of the encapsulationvolume for various HR ratio (experimental results)

maximal gain of light extraction 120578extraction is different betweenthese two graphs

First the graph confirms the simulation results whichstipulated that a flat encapsulation never provides a goodlight extraction Whatever the encapsulation volume is thesampleswhich present an aspect ratioHR smaller than 06 alllead to a poor light extraction In addition the absolute valuesof light extraction measured for these samples (not shown inthe graph) also indicate that the radiant flux emitted by someof these modules is even lower than the initial flux of 350mWemitted by the LED die without silicone encapsulation

Then the measurement dispersion is also larger than thesimulated oneThis is mainly due to the fact that the encapsu-lation shapes are not always ellipsoidal as it was modelled inthe simulations Indeed we found that some of them presenta ball-shape (diameter at the contact interface of the PCBlower than the encapsulation diameter) Such shapes whichappear to be a consequence of our manual dispense processmay effectively influence the light extraction efficiency ofthe COB modules In order to check this phenomenon wehave chosen two of our samples and we have performedadditional simulations by modelling their real encapsulationshapes The results are summarized in Table 1 The results ofthe simulations done with ellipsoidal encapsulation shapesof similar volumes are also given For comparison the light

Table 1 Comparative light extraction efficiencies for COBmodulesdepending on their encapsulation shapes (ellipsoidal or ball-shape)

Sample Encapsulation Gain of light extraction(simulation)

COB 1

Ellipsoidal shape 1

Real shape

1045

COB 2

Ellipsoidal shape 1

Real shape

1033

extraction obtained with these ellipsoidal encapsulations wasarbitrarily normalized to 1 and it has been taken as referencefor the simulations of the ball-shape encapsulations

These simulations evidence that ball shapes improve thelight extraction efficiency of several percents compared to anellipsoidal encapsulation of similar volume Thus an encap-sulation shape variationmay effectively be at the origin of themeasurement dispersion compared to simulation results

Nevertheless these light extractionmeasurements gener-ally show the same trend than the one which was observedwith the simulations For instance when considering thesmall-volume encapsulations the light extraction ratherincreases with the silicone volume

Finally among the different modules which were real-ized the maximal light extraction is obtained for a ratherhemispherical encapsulation with a volume of about 15mm3This is in line with the simulation results which predicteda stabilization of the light extraction at its optimum withencapsulation volumes larger than 10mm3 We have mea-sured the radiant flux emitted by this module we founda light extraction value of about 30 compared to theradiant flux emitted by LED die without silicone which isof the same order than the light extraction gains which havebeen measured for silicone packaged LEDs [13] Thus thisconfirms the potential of COB technology for providing high-efficient LED light sources

In order to check the impact of the encapsulation shapeon themodule intensity distribution we have also performedangular measurements with a LED spectrogoniometer toobtain the light intensity distribution of themodules depend-ing on their encapsulation aspect ratioThe results are shownin Figure 6

This graph confirms experimentally the phenomenawhichwere observed in simulationsThemoduleswhichwereencapsulated with an oblong encapsulation shape (119867119877 gt 1)

ISRN Optics 5

0010203040506070809

1

0 25 50 75 100

Rela

tive i

nten

sity

Angle (degrees)minus100 minus75 minus50 minus25

HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13

Figure 6 Light intensity distributions provided by a LED COBmodule depending on the shape of its encapsulation (experimentalresults)

provide a sharper and narrower distribution than the mod-ules covered with a lower aspect ratio encapsulation this evi-dences that light extraction at small exit angles is favoured Astheoretically expected the hemispherical and encapsulationshapes rather provide lambertian distributions

4 Conclusions

In this paper we have studied theoretically and experimen-tally the impact of the encapsulation shape and the volume ofa LED COB module on its performances in terms of bothlight extraction and intensity distribution We have shownthat flat encapsulation shapes never provide an efficientCOB light source while hemispherical encapsulation shapeslead to lambertian distributions with a light extraction gainwhich is rather independent of the encapsulation shape abovevolumes of 10mm3 Despite providing more dispersed datadue to the process parameter variations the experimentsconfirmed the simulation results Presenting up to a 30encapsulation gain in light extraction they evidenced that theoptimal performances are obtained with a nearly hemispher-ical encapsulation with a volume for a 1mm2 LED die largerthan 5 to 10mm3This work is seen to gain an insight into thepotential of LED COB modules for providing high-efficientand custom light sources Next studies will be devoted toapply these results to white modules and to optimize theinsertion of phosphors particles within the encapsulation toobtain efficient white LED COB light sources

Acknowledgments

The authors would like to gratefully acknowledge NEOLUX(La Chapelle-Vendomoise France) and BEST (Gevrey-Chambertin France) for partially funding this study

References

[1] F M Steranka J Bhat D Collins et al ldquoHigh power LEDsmdashtechnology status andmarket applicationsrdquoPhysica Status SolidiA vol 194 no 2 pp 380ndash388 2002

[2] P Hartmann F P Wenzl C Sommer et al ldquoWhite LEDs andmodules in Chip-On-Board technology for general lightingrdquoProc of SPIE vol 6337 Article ID 63370I 2006

[3] E F Schubert Light-Emitting Diodes Cambridge UniversityPress 2006

[4] T Fujii Y Gao R Sharma E L Hu S P DenBaars and SNakamura ldquoIncrease in the extraction efficiency of GaN-basedlight-emitting diodes via surface rougheningrdquo Applied PhysicsLetters vol 84 no 6 pp 855ndash857 2004

[5] J H Lee J T Oh S B Choi J G Woo S Y Lee and M B LeeldquoExtraction-efficiency enhancement of InGaN-based verticalLEDs on hemispherically patterned sapphirerdquo Physica StatusSolidi C vol 4 no 7 pp 2806ndash2809 2007

[6] C Nuese J Tietjen J Gannon and H Gossenberger ldquoOpti-mization of electroluminescent efficiencies for vapor-grownGaAs1-xPx diodesrdquo Journal of The Electrochemical Society vol116 no 2 pp 248ndash253 1969

[7] FWMont J K KimM F Schubert H Luo E F Schubert andRW Siegel ldquoHigh refractive index nanoparticle-loaded encap-sulants for light-emitting diodesrdquo in Light-Emitting DiodesResearch Manufacturing and Applications XI Procceedings ofSPIE January 2007

[8] J K Kim H Luo E F Schubert J Cho C Sone and YPark ldquoStrongly enhanced phosphor efficiency in GaInN whitelight-emitting diodes using remote phosphor configuration anddiffuse reflector cuprdquo Japanese Journal of Applied Physics vol44 no 20ndash23 pp L649ndashL651 2005

[9] H Luo J K Kim E F Schubert J Cho C Sone and Y ParkldquoAnalysis of high-power packages for phosphor-based white-light-emitting diodesrdquo Applied Physics Letters vol 86 no 24Article ID 243505 pp 1ndash3 2005

[10] H C Chen K J Chen C H Wang et al ldquoA novel randomlytextured phosphor structure for highly efficient white light-emitting diodesrdquo Nanoscale Research Letters vol 7 article 1882012

[11] I Moreno D Bermudez and M Avendano-Alejo ldquoLight-emitting diode spherical packages an equation for the lighttransmission efficiencyrdquo Applied Optics vol 49 no 1 pp 12ndash202010

[12] B Cao S Yu H Zheng and S Liu ldquoSilicon-based system inpackaging for light emitting diodesrdquo in Proceedings of the IEEE62nd Electronic Components and Technology Conference pp1267ndash1272 2012

[13] S Liu and X Luo LED Packaging for Lighting ApplicationsChemical Industry Press 2011

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Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

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ThermodynamicsJournal of

2 ISRN Optics

PCB

HR = 03

(a)

PCB

HR = 1

2R

H

(b)

PCB

HR = 17

(c)

Figure 1 Cross-sections of the geometries which have been modelled for evaluating the impact of the encapsulation shape and size on a LEDCOB performance (a) Nearly flat encapsulation with an aspect ratio HR of 03 (b) hemispherical encapsulation (c) oblong encapsulationwith an aspect ratio HR = 17

works stayed at the theoretical stage and they were notdemonstrated experimentally

That is why we propose in this paper to combine botha ray-tracing and an experimental approach for optimizingthe light extraction and intensity distribution of a LED COBmodule Thanks to the Monte-Carlo ray-tracing simulationswe have determined the encapsulation shape and the volumeallowing to maximize light extraction Then the originalityof this study is that these results have been correlated withexperimental measurements done on COB samples whichwere made from a 1mm2 LED die encapsulated with siliconeThe experimental results are found to be in good agreementwith the simulations

2 Simulations

In order to determine the parameters which are critical forthe LEDCOBencapsulation performance we have developeda simulation model which calculates the amount of lightextracted from a blue light-emitting die depending on theshape and on the size of its encapsulation

We have used the Zemax software which is based ontheMonte-Carlo ray-tracingThe typical LEDCOB geometryincludes a 1times1mm2 GaNLEDdie (refractive index 119899 = 242for a 450 nm incident wavelength) on a large board Thenthe die emission has been modelled as a lambertian intensitydistribution The light-emitting wavelength has been fixedequal to 450 nm which is close to the typical wavelengthof Royal Blue LEDs For simplicity reasons we have alsochosen not to take into account the die roughness in thesesimulations As will be detailed later this does not impactthe trend of the results but it implies to carefully analysethem Then the board has been considered as a reflectiveelement In order to reproduce the behaviour of the printedcircuit board (PCB) which will be used for the comparativeexperimental tests and which comprises a white solder maskwe have fixed its reflectivity to 70 with a surface lambertiandiffusion Finally this module has been covered with asilicone encapsulation (119899 = 14 for a 450 nm incidentwavelength) whose shape and size have been modified asdepicted in Figure 1 119867 is the height and 119877 is the radius ofthe encapsulation

The encapsulation shape has been set as half-ellipsoidalwith an aspect ratio ldquoheight above radiusrdquo HR varying from03 (flat encapsulation) to 17 (oblong encapsulation) Thusdepending on the shape the volume of the encapsulationvaries accordingly from about 1mm3 to 70mm3 whichallows observing simultaneously the effect of the shape andof the volume on the module optical characteristics

Regarding the simulation analysis this model does nottake into account the die roughness as stated above Thisdoes not significantly change the results since both the LEDplane surface and a roughened surface have a lambertiandistribution However it implies that the analysis has to bedone by only comparing the results among themselves Thuswe have normalized the light extraction values which havebeen obtained through the simulations as follows

120578extraction =120578 minus 1205780

1205780

(1)

where 120578 is the light extraction efficiency of the consideredgeometry and 120578

0is the light extraction efficiency of a

reference case This reference has been arbitrarily chosen tobe a hemispherical encapsulation with a radius R of 14mm

Then we have plotted this calculated gain or loss in lightextraction 120578extraction depending on the volume and on theaspect ratio of the encapsulation The corresponding resultsare given in Figure 2

First the graph clearly evidences that due to a highamount of total internal reflexions within the encapsulationa flat encapsulation shape (119867119877 lt 07) ever provides a badlight extractionThis is in agreement with previous works [8]which were done for packaged LEDs where it was shown thata hemispherical dome gave better extraction results than a flator convex encapsulation shape

Our simulation results also indicate that above an aspectratio 119867119877 of 07 the shape of the encapsulation has a smallimpact on the light extraction and that even an oblongshape may provide an efficient LED COB module This wasalso observed in recent works [12] on silicon-based LEDpackaging Indeed above a certain aspect ratio the rayincident angles at the silicone-air interface are small enoughto limit the total internal reflexions Thus these rays willalways be able to escape from the encapsulation maintainingthe light extraction quite stable

ISRN Optics 3

01020

0 10 20 30 40 50 60 70

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

re

fere

nce (

)

Volume (mm3)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17






0

02

04

06

08

1

0 30 60 90

Rela

tive i

nten

sity

Angle (degrees)

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17



3 Experiments







4 ISRN Optics


10

0 5 10 15 20 25 30

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

r

efer

ence

()

minus10

minus30

minus50

minus70

minus90

minus110

HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13

Volume (mm3)







COB 1

Ellipsoidal shape 1

Real shape

1045

COB 2

Ellipsoidal shape 1

Real shape

1033







ISRN Optics 5

0010203040506070809

1

0 25 50 75 100

Rela

tive i

nten

sity


HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13



4 Conclusions


Acknowledgments


References



















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



ISRN Optics 3

01020

0 10 20 30 40 50 60 70

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

re

fere

nce (

)

Volume (mm3)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17






0

02

04

06

08

1

0 30 60 90

Rela

tive i

nten

sity

Angle (degrees)

HR = 03

HR = 07

HR = 1

HR = 13

HR = 17



3 Experiments







4 ISRN Optics


10

0 5 10 15 20 25 30

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

r

efer

ence

()

minus10

minus30

minus50

minus70

minus90

minus110

HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13

Volume (mm3)







COB 1

Ellipsoidal shape 1

Real shape

1045

COB 2

Ellipsoidal shape 1

Real shape

1033







ISRN Optics 5

0010203040506070809

1

0 25 50 75 100

Rela

tive i

nten

sity


HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13



4 Conclusions


Acknowledgments


References



















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



4 ISRN Optics


10

0 5 10 15 20 25 30

Gai

n of

ligh

t ext

ract

ion

com

pare

d to

r

efer

ence

()

minus10

minus30

minus50

minus70

minus90

minus110

HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13

Volume (mm3)







COB 1

Ellipsoidal shape 1

Real shape

1045

COB 2

Ellipsoidal shape 1

Real shape

1033







ISRN Optics 5

0010203040506070809

1

0 25 50 75 100

Rela

tive i

nten

sity


HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13



4 Conclusions


Acknowledgments


References



















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



ISRN Optics 5

0010203040506070809

1

0 25 50 75 100

Rela

tive i

nten

sity


HR lt 05

06 lt HR lt 08

09 lt HR lt 11

12 lt HR lt 13



4 Conclusions


Acknowledgments


References



















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Documents

Research Article Combined Experimental and Monte-Carlo Ray …downloads.hindawi.com/archive/2013/385345.pdf · 2019. 7. 31. · ISRN Optics 0 10 20 0 10203040506070 Gain of light