We employ a Monte Carlo ray-tracing technique to model light-extraction characteristics of light-emitting diodes. By relaxing restrictive assumptions on photon traversal history, our method improves upon available analytical models for estimating light-extraction efficiencies from bare LED chips, and enhances modeling capabilities by realistically treating the various processes which photons can encounter in a packaged LED. Our method is not only capable of calculating extraction efficiencies, but can also provide extensive statistical information on photon extraction processes, and predict LED spatial emission characteristics

McGill, T. C.

Ting, D. Z.-Y.

English

Caltech Authors - Main

VLSIDESIGN
1998, Vol. 6, Nos. (1-4), pp. 363-366
Reprints available directly from the publisher
Photocopying permitted by license only
(C) 1998 OPA (Overseas Publishers Association) N.V.
Published by license under
the Gordon and Breach Science
Publishers imprint.
Printed in India.
Modeling Light-Extraction Characteristics of Packaged
Light-Emitting Diodes
D. Z.-Y. TINGa’b’* and T. C. MCGILLb’*
aThomas J. Watson, Sr., Laboratory ofApplied Physics, California Institute ofTechnology Pasadena, Cali3’brnia 91125, USA;bDepartment ofPhysics, National Tsing Hua University, Hsinchu, Taiwan 300, ROC
We employ a Monte Carlo ray-tracing technique to model light-extraction characteristics of
light-emitting diodes. By relaxing restrictive assumptions on photon traversal history, our
method improves upon available analytical models for estimating light-extraction efficiencies
from bare LED chips, and enhances modeling capabilities by realistically treating the various
processes which photons can encounter in a packaged LED. Our method is not only capable
of calculating extraction efficiencies, but can also provide extensive statistical information on
photon extraction processes, and predict LED spatial emission characteristics.
Keywords: LED photon extraction, LED efficiency
I. INTRODUCTION
Analytical models[I,2] developed in the past have
been very useful for considering photon extraction
from semiconductor LED chips in limiting cases.
Taking advantage of high-speed computation plat-
forms available today, we approach the problem with
a numerical Monte Carlo ray-tracing technique which
promises greater range of validity. Photon extraction
from LED chips is difficult for several reasons.
Absorption by the medium and contacts prevent many
of the internally generated photons from ever reach-
ing exposed chip surfaces in the first place. A sub-
stantial fraction of the photons that do reach the
surface end up being internally reflected because crit-
ical angles at chip surfaces are typically small due to
the large index of refraction mismatch between the
semiconductor LED chip and its surrounding
medium. Although each photon may encounter a
number of these processes, it is straight-forward to
keep track of photon traversal history numerically.
Therefore Monte Carlo techniques well-suited for
simulating photon extraction.
II. MODEL
Figure illustrates the T-1 3/4 LED lamp, which is
used as the prototype structure in our Monte Carlo
particle simulation. The particles used are classical
photons (corpuscles) which obey the rules of geomet-
rical optics. A simulation is performed with an
ensemble of randomly generated photons, and the
processes which each photon encounters (e.g.,
medium absorption, transmission/reflection at inter-
faces) are governed by probabilistic models. We
* Tel: 886.35.715131x3246. Fax: 886.35.723052. Email: dzt@phys.nthu.tw
t Corresponding author. Tel: (818) 395-4849. Fax: (818) 568-8972. Email: tcm@ssdp.caltech.edu
363
364 D.Z.-Y. TING and T.C. MCGILL
Epoxy
/
Lens
Top
Contact
LED
,,,,,..
Anode Cathode
FIGURE Illustration of the T-1 3/4 LED lamp (not to scale) used
in our simulations. Note that the anode post, cathode post, and the
bonding wire are ignored in our simulations
assume that in the LED chip photons are generated
uniformly within a thin planar region at a height of
z hjunc from the base of the chip, and are emitted in
an isotropic spatial pattern.[ 1 We also assume mono-
chromatic photon emission for simplicity. A trivial
extension to our model would allow for the treatment
of more general emission spectra. For each photon, a
position vector on the emission plane and a direction
vector are randomly generated. A ray-polygon inter-
section algorithm[3] is used to compute the intersec-
tion of photon trajectory with one of the six chip
surfaces. Since a photon might be absorbed inside the
chip before reaching the destination surface, we use a
Monte Carlo routine to determine whether absorption
takes place en route. Let the path length between the
initial and final positions be A. The probability of a
photon being absorbed in a distance A is given by
P(A) e-zx, (1)
where o is the medium absorption coefficient. We
generate a random number R between 0 and 1;
absorption takes place if R _< P(A). If a photon reaches
a destination chip surface without being absorbed by
the semiconductor, we check to see if it strikes either
the top or the bottom contact, where contact absorp-
tion processes can occur. For simplicity, we assume
that the contacts are totally absorbing, although par-
tially absorbing contacts can be modeled quite easily.
If the photon is not absorbed, we determine whether it
is transmitted or reflected by generating a random
number between 0 and 1, and comparing it to the
transmission probability given by the FresneI equa-
tions.[4] An internally reflected .photon continues on
its path within the LED chip until it is eventually
absorbed or transmitted. A photon emitted by the
LED chip is then ray-traced to the reflector dish, and
then to the epoxy lens. For speed and simplicity, we
assume that the three stages of the simulation occur
sequentially (chip, then reflector, then lens). There-
fore photon re-entrance into the LED chip is not con-
sidered, nor the possibility of internally reflected
photons in the lens re-striking the reflector dish. The
error associated with the sequential approximations
has been estimated to be a few percent. Throughout
the different stages of the simulation, extensive statis-
tics are gathered for subsequent analyses.
III. RESULTS AND DISCUSSION
We demonstrate the potential usefulness of the Monte
Carlo method by varying the junction height hjunc to
examine the effect it has on light-emission character-
istics. We also consider the effect of varying the value
of epoxy index of refraction. We assume that the
absorption coefficient for the semiconductor chip is
a 10 cm-1. This corresponds to a weakly absorbing
medium, with a characteristic absorption length 1/c
of 1000 gm, or 3.75 times the width of the cubic chip.
Note that simulation of a realistic device would
require that we use experimentally measured absorp-
tion coefficient spectrum o(E) for the LED material.
The index of refraction for the semiconductor chip is
taken to be 3.1, and for the epoxy, both 1.5 and 1.7 are
considered. Figure 2(a) shows the light-extraction
efficiency for the LED as functions of the light-emit-
ting junction height, which ranges from 0 to 265 gm
(the height of the chip is 266.7 gm, or 1.05 rail.), for
MODELING LIGHT-EXTRACTION CHARACTERISTICS OF PACKAGED LIGHT-EMITTING DIODES 365
two different values of epoxy index of refraction.
Note that the efficiency for the n 1.5 case is consist-
ently lower than the n 1.7 case by a significant
amount. This is because the critical angle at the chip-
epoxy interface is 29 for n 1.5, and 33 for n 1.7.
(In practice, epoxy indices do not exceed 1.51.) In
both cases, efficiency is low when the junction is near
the bottom of the chip where most of the downward
pointing photons generated at the junction are
absorbed by the bottom contact. As the junction is
raised, the efficiency increases until reaching a maxi-
mum at around hjunc 190 tm, and then decreases
by a small amount. At its maximum, the efficiency is
nearly twice the hjunc 0 value. Figure 2(b) shows
the emission patterns as functions of azimuthal angle
0 for a particular LED structure after each of the three
simulation stages (chip, dish, and lens). The chip
emission tends to be broadly distributed, the reflector
dish brings all emission to 0 < 90, and the lens
tightly focuses a portion of the emission into 0 < 20,
while scattering the remainder to a much broader dis-
tribution.
In summary, we employ a Monte Carlo ray tracing
technique to model light-extraction characteristics of
light-emitting diodes. By effectively utilizing readily
available computational resources and relaxing
restrictive assumptions on photon traversal history,
our method improves upon available analytical mod-
els for estimating light-extraction efficiencies from
bare LED chips, and enhances modeling capabilities
by realistically treating the various processes which
photons can encounter in a packaged LED. Our
method is not only capable of calculating extraction
efficiencies, but can also provide extensive statistical
information on photon extraction processes, and pre-
dict LED spatial emission characteristics. Simulations
using our method can be performed very rapidly on
modern workstations, making it a good candidate for
an effective design tool. Several areas of our model
could be improved to make it more realistic and ver-
satile; a more detailed account of our model is given
elsewhere[5]. We believe that, with some refinement,
our method could become a valuable LED design
tool.
E)_ 0.30
0.20
nEPoxY 1.5
LL! rlEPOX 1.7
’
0.10
0.000 0.005 0.010 0.015 0.020 0025
Light Emitting Junction Height (cm)
2,5
1.5
"P-. 1.0
0.5
0.0 "--’;" -’"
0.0
(b hi== 190 l,m nEPOxy=1.5
LEE) Chip
Reflector Dish
Epoxy Lens
30.0 60.0 90.0 120.0 150.0 180.0
Azimuthal Angle 0 (degree)
FIGURE 2 (a) Computed photon extraction efficiencies as func-
tions of light-emitting junction height in LED chip for two differ-
ent epoxy indices of refraction. (b) Azimuthal distributions of
photons emitted from a LED structure with hiunct 190 tm, and
epoxy index of n 1.5. Emission patterns after each of the three
simulation stages (chip, dish, and lens) are shown
Acknowledgements
The authors would like to thank J. F. Swenberg, M.
W. Wang, F. M. Steranka, M. G. Craford, and P.
Mahowald for helpful discussions. This work was
supported by the Office of Naval Research (ONR)
under Grant No. N00014-92-J- 1845. DZT acknowl-
edges partial support from Department of Physics,
National Tsing Hua University (Hsinchu).
References
[1 W.N. Cart, "Photometric figures of merit for semiconductor
luminescent sources operating in spontaneous decay mode,"
Infrared Physics 6, 1-19 (1966).
[2] W.B. Joycc, R. Z. Bachrach, R. W. Dixon, and D. A. Scaler,
"Geometrical properties of random particles and the extrac-
tion of photons from electroluminescent diodes," J. App.
Phys. 45(5), 2229-2253 (1974).
366 D.Z.-Y. TING and T.C. MCGILL
[3] D. Badouel, "An efficient ray-polygon intersection," in
Graphics Gems, A. S. Glassner, Ed., pp.390-399, Academic
Press, Boston, MA (1990).
[4] See, for example, E. Hecht, Optics, 2nd Ed., Addison-Wes-
ley, Reading, MA (1987).
[5] D.Z.-Y. Ting and T. C. McGill, "Monte Carlo simulation of
LED light-extraction characteristics," to appear in Optical
Engineering 34(12) (1995).
Biographies
David Z.-Y. Ting is an Associate Professor of Phys-
ics at the the National Tsing Hua University in Hsin-
chu, Taiwan, ROC. His research activities include the
theoretical studies of electronic and optical properties
of semiconductor alloys, quantum wells, superlat-
tices, and heterostructure tunnel devices, quantum
transport in nanostructure, and optical simulations.
(E-mail: dzt@phys.nthu.edu.tw)
Thomas C. MeGill is the Fletcher Jones Professor
of Applied Physics at the California Institute of Tech-
nology. His research interests are in the broad area of
microstructures for modem electronics, semiconduc-
tor physics and devices.
EURASIP Book Series on Signal Processing and Communications
Edited by: J. Astola, and L. Yaroslavsky
Digital signal transforms are of a fundamental value in digital signal and image processing. Their role is manifold. Transforms selected 
appropriately enable substantial compressing signals 
and images for storage and transmission. No signal 
recovery, image reconstruction, and restoration task can 
be efficiently solved without using digital signal transforms. 
Transforms are successfully used for logic design and digital data encryption. 
Fast transforms are the main tools for acceleration of computations in digital 
signal and image processing.
The volume collects in one book most recent developments in the theory and 
practice of the design and usage of transforms in digital signal and image 
processing. It emerged from the series of reports published by Tampere 
International Centre for Signal Processing, Tampere University of Technology. 
For the volume, all contributions are appropriately updated to represent the 
state of the art in the field and to cover the most recent developments in 
different aspects of the theory and applications of transforms.
The book consists of two parts that represent two major directions in the field: 
development of new transforms and development of transform-based signal 
and image processing algorithms. The first part contains four chapters devoted to recent advances in transforms for image 
compression and switching and logic design and to new fast transforms for digital holography and tomography. In the second 
part, advanced transform-based signal and image algorithms are considered: signal and image local adaptive restoration 
methods and two complementing families of signal and image resampling algorithms, fast transform-based discrete sinc-
interpolation and spline-theory-based ones.
Topics and Features:
 The subject of the book is of a fundamental importance in digital signal and image processing.
 A variety of signal and image processing tasks are considered and treated on the common methodological base of 
transform domain processing.
 Theoretical results are strongly application-oriented.
Advances in Signal Transforms:
Theory and Applications
Limited-Time Promotional Offer. Buy this title NOW at 20% discount plus Free Shipping.
EURASIP Book Series on SP&C, Volume 7, ISBN 977-5945-55-0.
Please visit http://www.hindawi.com/spc.7.html for more information about the book. To place an order 
while taking advantage of our current promotional offer, please contact books.orders@hindawi.com
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Modeling Light-Extraction Characteristics of Packaged Light-Emitting Diodes

VLSIDESIGN
1998, Vol. 6, Nos. (1-4), pp. 363-366
Reprints available directly from the publisher
Photocopying permitted by license only
(C) 1998 OPA (Overseas Publishers Association) N.V.
Published by license under
the Gordon and Breach Science
Publishers imprint.
Printed in India.
Modeling Light-Extraction Characteristics of Packaged
Light-Emitting Diodes
D. Z.-Y. TINGa’b’* and T. C. MCGILLb’*
aThomas J. Watson, Sr., Laboratory ofApplied Physics, California Institute ofTechnology Pasadena, Cali3’brnia 91125, USA;
bDepartment ofPhysics, National Tsing Hua University, Hsinchu, Taiwan 300, ROC
We employ a Monte Carlo ray-tracing technique to model light-extraction characteristics of
light-emitting diodes. By relaxing restrictive assumptions on photon traversal history, our
method improves upon available analytical models for estimating light-extraction efficiencies
from bare LED chips, and enhances modeling capabilities by realistically treating the various
processes which photons can encounter in a packaged LED. Our method is not only capable
of calculating extraction efficiencies, but can also provide extensive statistical information on
photon extraction processes, and predict LED spatial emission characteristics.
Keywords: LED photon extraction, LED efficiency
I. INTRODUCTION
Analytical models[I,2] developed in the past have
been very useful for considering photon extraction
from semiconductor LED chips in limiting cases.
Taking advantage of high-speed computation plat-
forms available today, we approach the problem with
a numerical Monte Carlo ray-tracing technique which
promises greater range of validity. Photon extraction
from LED chips is difficult for several reasons.
Absorption by the medium and contacts prevent many
of the internally generated photons from ever reach-
ing exposed chip surfaces in the first place. A sub-
stantial fraction of the photons that do reach the
surface end up being internally reflected because crit-
ical angles at chip surfaces are typically small due to
the large index of refraction mismatch between the
semiconductor LED chip and its surrounding
medium. Although each photon may encounter a
number of these processes, it is straight-forward to
keep track of photon traversal history numerically.
Therefore Monte Carlo techniques well-suited for
simulating photon extraction.
II. MODEL
Figure illustrates the T-1 3/4 LED lamp, which is
used as the prototype structure in our Monte Carlo
particle simulation. The particles used are classical
photons (corpuscles) which obey the rules of geomet-
rical optics. A simulation is performed with an
ensemble of randomly generated photons, and the
processes which each photon encounters (e.g.,
medium absorption, transmission/reflection at inter-
faces) are governed by probabilistic models. We
* Tel: 886.35.715131x3246. Fax: 886.35.723052. Email: dzt@phys.nthu.tw
t Corresponding author. Tel: (818) 395-4849. Fax: (818) 568-8972. Email: tcm@ssdp.caltech.edu
363
364 D.Z.-Y. TING and T.C. MCGILL
Epoxy
/
Lens
Top
Contact
LED
,,,,,..
Anode Cathode
FIGURE Illustration of the T-1 3/4 LED lamp (not to scale) used
in our simulations. Note that the anode post, cathode post, and the
bonding wire are ignored in our simulations
assume that in the LED chip photons are generated
uniformly within a thin planar region at a height of
z hjunc from the base of the chip, and are emitted in
an isotropic spatial pattern.[ 1 We also assume mono-
chromatic photon emission for simplicity. A trivial
extension to our model would allow for the treatment
of more general emission spectra. For each photon, a
position vector on the emission plane and a direction
vector are randomly generated. A ray-polygon inter-
section algorithm[3] is used to compute the intersec-
tion of photon trajectory with one of the six chip
surfaces. Since a photon might be absorbed inside the
chip before reaching the destination surface, we use a
Monte Carlo routine to determine whether absorption
takes place en route. Let the path length between the
initial and final positions be A. The probability of a
photon being absorbed in a distance A is given by
P(A) e-zx, (1)
where o is the medium absorption coefficient. We
generate a random number R between 0 and 1;
absorption takes place if R _< P(A). If a photon reaches
a destination chip surface without being absorbed by
the semiconductor, we check to see if it strikes either
the top or the bottom contact, where contact absorp-
tion processes can occur. For simplicity, we assume
that the contacts are totally absorbing, although par-
tially absorbing contacts can be modeled quite easily.
If the photon is not absorbed, we determine whether it
is transmitted or reflected by generating a random
number between 0 and 1, and comparing it to the
transmission probability given by the FresneI equa-
tions.[4] An internally reflected .photon continues on
its path within the LED chip until it is eventually
absorbed or transmitted. A photon emitted by the
LED chip is then ray-traced to the reflector dish, and
then to the epoxy lens. For speed and simplicity, we
assume that the three stages of the simulation occur
sequentially (chip, then reflector, then lens). There-
fore photon re-entrance into the LED chip is not con-
sidered, nor the possibility of internally reflected
photons in the lens re-striking the reflector dish. The
error associated with the sequential approximations
has been estimated to be a few percent. Throughout
the different stages of the simulation, extensive statis-
tics are gathered for subsequent analyses.
III. RESULTS AND DISCUSSION
We demonstrate the potential usefulness of the Monte
Carlo method by varying the junction height hjunc to
examine the effect it has on light-emission character-
istics. We also consider the effect of varying the value
of epoxy index of refraction. We assume that the
absorption coefficient for the semiconductor chip is
a 10 cm-1. This corresponds to a weakly absorbing
medium, with a characteristic absorption length 1/c
of 1000 gm, or 3.75 times the width of the cubic chip.
Note that simulation of a realistic device would
require that we use experimentally measured absorp-
tion coefficient spectrum o(E) for the LED material.
The index of refraction for the semiconductor chip is
taken to be 3.1, and for the epoxy, both 1.5 and 1.7 are
considered. Figure 2(a) shows the light-extraction
efficiency for the LED as functions of the light-emit-
ting junction height, which ranges from 0 to 265 gm
(the height of the chip is 266.7 gm, or 1.05 rail.), for
MODELING LIGHT-EXTRACTION CHARACTERISTICS OF PACKAGED LIGHT-EMITTING DIODES 365
two different values of epoxy index of refraction.
Note that the efficiency for the n 1.5 case is consist-
ently lower than the n 1.7 case by a significant
amount. This is because the critical angle at the chip-
epoxy interface is 29 for n 1.5, and 33 for n 1.7.
(In practice, epoxy indices do not exceed 1.51.) In
both cases, efficiency is low when the junction is near
the bottom of the chip where most of the downward
pointing photons generated at the junction are
absorbed by the bottom contact. As the junction is
raised, the efficiency increases until reaching a maxi-
mum at around hjunc 190 tm, and then decreases
by a small amount. At its maximum, the efficiency is
nearly twice the hjunc 0 value. Figure 2(b) shows
the emission patterns as functions of azimuthal angle
0 for a particular LED structure after each of the three
simulation stages (chip, dish, and lens). The chip
emission tends to be broadly distributed, the reflector
dish brings all emission to 0 < 90, and the lens
tightly focuses a portion of the emission into 0 < 20,
while scattering the remainder to a much broader dis-
tribution.
In summary, we employ a Monte Carlo ray tracing
technique to model light-extraction characteristics of
light-emitting diodes. By effectively utilizing readily
available computational resources and relaxing
restrictive assumptions on photon traversal history,
our method improves upon available analytical mod-
els for estimating light-extraction efficiencies from
bare LED chips, and enhances modeling capabilities
by realistically treating the various processes which
photons can encounter in a packaged LED. Our
method is not only capable of calculating extraction
efficiencies, but can also provide extensive statistical
information on photon extraction processes, and pre-
dict LED spatial emission characteristics. Simulations
using our method can be performed very rapidly on
modern workstations, making it a good candidate for
an effective design tool. Several areas of our model
could be improved to make it more realistic and ver-
satile; a more detailed account of our model is given
elsewhere[5]. We believe that, with some refinement,
our method could become a valuable LED design
tool.
E)_ 0.30
0.20
nEPoxY 1.5
LL! rlEPOX 1.7
’ 0.100.000 0.005 0.010 0.015 0.020 0025
Light Emitting Junction Height (cm)
2,5
1.5
"P-. 1.0
0.5
0.0 "--’;" -’"
0.0
(b hi== 190 l,m nEPOxy=1.5
LEE) Chip
Reflector Dish
Epoxy Lens
30.0 60.0 90.0 120.0 150.0 180.0
Azimuthal Angle 0 (degree)
FIGURE 2 (a) Computed photon extraction efficiencies as func-
tions of light-emitting junction height in LED chip for two differ-
ent epoxy indices of refraction. (b) Azimuthal distributions of
photons emitted from a LED structure with hiunct 190 tm, and
epoxy index of n 1.5. Emission patterns after each of the three
simulation stages (chip, dish, and lens) are shown
Acknowledgements
The authors would like to thank J. F. Swenberg, M.
W. Wang, F. M. Steranka, M. G. Craford, and P.
Mahowald for helpful discussions. This work was
supported by the Office of Naval Research (ONR)
under Grant No. N00014-92-J- 1845. DZT acknowl-
edges partial support from Department of Physics,
National Tsing Hua University (Hsinchu).
References
[1 W.N. Cart, "Photometric figures of merit for semiconductor
luminescent sources operating in spontaneous decay mode,"
Infrared Physics 6, 1-19 (1966).
[2] W.B. Joycc, R. Z. Bachrach, R. W. Dixon, and D. A. Scaler,
"Geometrical properties of random particles and the extrac-
tion of photons from electroluminescent diodes," J. App.
Phys. 45(5), 2229-2253 (1974).
366 D.Z.-Y. TING and T.C. MCGILL
[3] D. Badouel, "An efficient ray-polygon intersection," in
Graphics Gems, A. S. Glassner, Ed., pp.390-399, Academic
Press, Boston, MA (1990).
[4] See, for example, E. Hecht, Optics, 2nd Ed., Addison-Wes-
ley, Reading, MA (1987).
[5] D.Z.-Y. Ting and T. C. McGill, "Monte Carlo simulation of
LED light-extraction characteristics," to appear in Optical
Engineering 34(12) (1995).
Biographies
David Z.-Y. Ting is an Associate Professor of Phys-
ics at the the National Tsing Hua University in Hsin-
chu, Taiwan, ROC. His research activities include the
theoretical studies of electronic and optical properties
of semiconductor alloys, quantum wells, superlat-
tices, and heterostructure tunnel devices, quantum
transport in nanostructure, and optical simulations.
(E-mail: dzt@phys.nthu.edu.tw)
Thomas C. MeGill is the Fletcher Jones Professor
of Applied Physics at the California Institute of Tech-
nology. His research interests are in the broad area of
microstructures for modem electronics, semiconduc-
tor physics and devices.
EURASIP Book Series on Signal Processing and Communications
Edited by: J. Astola, and L. Yaroslavsky
Digital signal transforms are of a fundamental value in digital signal and image processing. Their role is manifold. Transforms selected 
appropriately enable substantial compressing signals 
and images for storage and transmission. No signal 
recovery, image reconstruction, and restoration task can 
be efficiently solved without using digital signal transforms. 
Transforms are successfully used for logic design and digital data encryption. 
Fast transforms are the main tools for acceleration of computations in digital 
signal and image processing.
The volume collects in one book most recent developments in the theory and 
practice of the design and usage of transforms in digital signal and image 
processing. It emerged from the series of reports published by Tampere 
International Centre for Signal Processing, Tampere University of Technology. 
For the volume, all contributions are appropriately updated to represent the 
state of the art in the field and to cover the most recent developments in 
different aspects of the theory and applications of transforms.
The book consists of two parts that represent two major directions in the field: 
development of new transforms and development of transform-based signal 
and image processing algorithms. The first part contains four chapters devoted to recent advances in transforms for image 
compression and switching and logic design and to new fast transforms for digital holography and tomography. In the second 
part, advanced transform-based signal and image algorithms are considered: signal and image local adaptive restoration 
methods and two complementing families of signal and image resampling algorithms, fast transform-based discrete sinc-
interpolation and spline-theory-based ones.
Topics and Features:
 The subject of the book is of a fundamental importance in digital signal and image processing.
 A variety of signal and image processing tasks are considered and treated on the common methodological base of 
transform domain processing.
 Theoretical results are strongly application-oriented.
Advances in Signal Transforms:
Theory and Applications
Limited-Time Promotional Offer. Buy this title NOW at 20% discount plus Free Shipping.
EURASIP Book Series on SP&C, Volume 7, ISBN 977-5945-55-0.
Please visit http://www.hindawi.com/spc.7.html for more information about the book. To place an order 
while taking advantage of our current promotional offer, please contact books.orders@hindawi.com


An efficient ray-polygon intersection,&quot;

Geometrical properties of random particles and the extraction of photons from electroluminescent diodes,&quot;

Photometric figures of merit for semiconductor luminescent sources operating in spontaneous decay mode,&quot;

Ting

https://authors.library.caltech.edu/9255/1/TINvd98a.pdf

Modeling Light-Extraction Characteristics of Packaged Light-Emitting Diodes

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