Geometric optics analysis on light transmission and reﬂection …ipds.korea.ac.kr/download/publication/15.pdf · 2012-01-10 · Geometric optics analysis on light transmission and

Optical Engineering 45�8�, 084004 �August 2006�

Geometric optics analysis on light transmissionand reflection characteristics of metallicprism sheets

Hwi KimByoungho Lee, FELLOW SPIE

Seoul National UniversitySchool of Electrical EngineeringKwanak-Gu Shinlim-DongSeoul 151-744, KoreaE-mail: [email protected]

Abstract. Light transmission and reflection characteristics of metallicprism sheets are investigated based on a geometric optics approach. Ananalytic method is presented for finding the radiant intensity profiles oflight transmitted through and reflected by a single metallic prism sheetfor an incident light with arbitrary radiant intensity profile. With a simpleinteraction model between adjacent prism sheets, the analysis methodfor a single prism sheet is generalized for analyzing prism sheet layerscomposed of several prism sheets. Light transmission and reflectioncharacteristics of a single prism sheet and prism sheet layers are com-pared. It is seen that the metallic prism sheet can be appropriately ap-plicable to transflective devices or brightness enhancement film for liquidcrystal displays. © 2006 Society of Photo-Optical Instrumentation Engineers.�DOI: 10.1117/1.2335871�

Subject terms: metallic prism sheet; transflective device; geometric opticsanalysis.

Paper 050926R received Nov. 26, 2005; revised manuscript received Jan. 21,2006; accepted for publication Jan. 23, 2006; published online Aug. 22, 2006.

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1 Introduction

Recently, transflective displays have attracted common in-terests of industry and academy. Transflective display de-vices have been developed for mobile applications like per-sonal digital assistants �PDAs� and cellular phones forattaining advantages such as being lighter, more efficient inenergy consumption, and lower in cost. Transflective dis-plays use both the ambient light from the environment andthe light from the embedded backlight for achieving highenergy-consumption efficiency. Liquid crystal transflectivedisplays especially require high performance transflectivedevices, i.e., transflectors.1 A requirement of good trans-flectors is to transmit the light from the backlight and re-flect the ambient light maximally. In addition, several func-tional factors such as brightness enhancement and viewingangle management are also required of transflectors. Trans-flective structures with these functions are also useful formany other applications as well as for displays.

In this work, light transmission and reflection propertiesof a periodic metallic prism structure2,3 are studied for in-specting its potential for application in a transflector. Figure1 shows the considered metallic prism structure. Prismsmade of highly reflective material are periodically ar-ranged. The solid-lined box indicates a single period of theperiodic prism structure. There is a gap between two adja-cent prisms. As a result, the empty space between two ad-jacent prisms has a trapezoidal shape. As seen in Fig. 1, alight ray propagates along zigzag paths through the gapbetween adjacent prisms. Because of the asymmetry in thetrapezoidal gap structure, the two cases presented in Fig. 1show somewhat different transmission and reflection char-

p0091-3286/2006/$22.00 © 2006 SPIE

Optical Engineering 084004-1

cteristics. In the first case, light is incident on the bottomf the trapezoidal gap, and partially reflected and transmit-ed through the prism sheet. The second case is that light isncident on the ceiling of the trapezoidal gap, and partiallyeflected and transmitted through the structure. The asym-etry in the structure produces considerable differences in

ptical characteristics of two cases. For convenience, theormer case is referred to as transmission mode and theatter case is referred to as reflection mode. Because of theifferences in light transmission and reflection characteris-ics of the transmission and reflection modes, the metallicrism structure may be used for transflectors.

Light transmission and reflection characteristics of a me-allic prism sheet are analyzed based on a geometric opticspproach. With a simple model of interaction between ad-acent prism sheets, the analysis method for a single prismheet is generalized to analyze prism sheet layers composedf several prism sheets. Light transmission and reflectionharacteristics of a single prism sheet and double prismheet layers are compared.

This work is organized into four sections. In Sec. 2, aeometric optics analysis method of the metallic prismheet is addressed. In Sec. 3, optical characteristics of aingle metallic prism sheet are presented. In Sec. 4, theresented analysis method is extended to layered structuresf the structure. Final remarks are given in Sec. 5.

Geometric Optics Analysis Method of theMetallic Prism Sheet

n this section, a geometric optics analysis method of theetallic prism structure is described. It is assumed that the

ight source illuminating the prism sheets is incoherent andan be completely characterized by radiant intensity

4,5
rofile. For convenience, electromagnetic rigor with re-
August 2006/Vol. 45�8�

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Kim and Lee: Geometric optics analysis on light transmission¼

spect to reflection coefficients and material parameters isneglected. It is assumed that prisms are made of completeconductors so that light with an arbitrary incidence angleand polarization is reflected without loss. A specific raytracing method is devised for providing an intuitive and fastanalytic algorithm useful for understanding a collective be-havior of numbers of rays. As indicated in Fig. 2, the mir-rored ray trace �indicated by a black line� equivalent to thereal ray trace �indicated by a white line� in the trapezoidalgap between two adjacent prisms can be represented as astraight line inside the cylindrical geometry. Figure 2�a�shows that the transversal trace of a ray through the trap-ezoidal gap between two adjacent prisms is equivalentlyinterpreted as a straight ray through a circularly unfoldedextension of the trapezoidal gap, considering the mirrorsymmetry of the incident and reflective rays at the bound-aries. The trapezoidal gap is parametrized by inner circleradius r, outer circle radius R, and central angle of thetrapezoidal gap �, as indicated in Fig. 2�a�. For conve-

Fig. 1 Two modes of the metallic prism sheet: �a� transmissionmode and �b� reflection mode.

nience, the central angle of the trapezoidal gap is set to � e


2� /N. Thus, the number of the pieces comprising theomplete circle is exactly N. For 3-D analysis, the cylindri-al object shown in Fig. 2�b� is used. The real trace of anncident ray traveling in the trapezoidal gap can be de-cribed by a straight ray, which passes inside the cylindricalbject. With the aid of this geometrical setup, we can ana-yze the transmission and reflection modes of the metallicrism sheet.

.1 Transmission Modes mentioned before, the transmission mode refers to the

ase that rays are incident from the bottom facet of therapezoidal gap. In the cylindrical geometry, rays go fromhe inside of the inner circle with radius of r to the outsidef the outer circle with radius of R. In this case, all raysoing along any directions can exit the outer circle as indi-ated in Fig. 3. Figure 3�a� shows a real ray trace in therapezoidal gap. The ray starts at the bottom of the trapezoi-al gap and propagates along the zigzag path. The motionf the ray can be simply and intuitively analyzed by usinghe cylindrical extension, as shown in Fig. 3�b�. The trap-zoidal gap is a piece of a complete circle that consists ofany same pieces of the trapezoidal gap. In the transmis-

ion mode, a ray is incident from the bottom of the trap-

ig. 2 �a� Mirrored equivalent ray trace of a real ray trace in therapezoidal gap and �b� cylindrical geometry for 3-D ray trace.

zoidal gap. The ray of the direction vector �l ,m ,n� passes


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an incident position �x , y , z� on the bottom, where−r sin�� /2�� x�r sin�� /2�, y=r cos�� /2�, and z=0. Theray equation is given by

�x,y,z� = �lt + x,mt + y,nt + z� for m � 0. �1�

The intersection point of the straight ray with the outercircle of radius R can be obtained easily. Doing it enablesus to know all information as the direction of the ray exit-ing the trapezoidal gap, the number of reflections inside thegap, and the exact ray trace.

At first, the parameter t at the intersection point is givenby

t =− �l,m� · �x, y� + ��l,m� · �x, y��2 − �l2 + m2��x2 + y2 − R2��1/2

�l2 + m2�

�� t � 0� . �2�

Fig. 3 �a� Trace of a ray incident from the bottom of the trapezoidalgap and �b� geometrical analysis of the equivalent ray trace usingthe cylindrical geometry.

Then from Eq. �1�, the intersection point is given by t


x, y, z� = �lt + x,mt + y,nt + z� . �3�

et the clockwise directional angle of the vector connectingrom the origin to the intersection point with respect to theaxis be denoted by �. If 0� x and 0� y, the angle of the

ntersection point from the x axis is given by

= sin−1�y/R� −�

2. �4�

f x�0 and 0� y, the angle � is given by

=�

2− sin−1�y/R� . �5�

he case of y�0 occurs only in the reflection mode that isxplained in the next section. If y�0, the angle � is ob-ained as

=3�

2− cos−1�x/R� . �6�

et the index mr of the reference area where the ray startsnitially be mr=0. Then the index me of the exit area where

ig. 4 �a� Trace of a ray incident from the ceiling of the trapezoidalap and �b� geometrical analysis of the equivalent ray trance usinghe cylindrical geometry.

he ray exits the trapezoidal gap is located in the range


m

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�


N

2�� −

1

2� me �

N

2�� +

1

2. �7�

Let the index of the area where the end point of a ray meetsthe outer circle be defined by

Fig. 5 Simulation setups for a single metallic prism sheet: �a� trans-mission mode and �b� reflection mode.

Fig. 6 Radiant intensity profiles of �a� input La
central angles �b� �=� /2, �c� �=� /4, �d� �=� /8, �e� �

e = �N�

2�+

1

2� , �8�

here the square brackets � � represent the nearest integerot greater than. It is noted that if me=N, me is effectivelyquivalent to 0. Hence we can know that the total reflectionumber of the ray inside the trapezoidal gap is me. Also, theirection of the exiting ray can be obtained. Then the angleetween the center axis of the exit area and that of theeference area is given by 2�me /N. To achieve the exit rayirection, first the center axis of the exit area must beatched to �0,1,0� by an appropriate counterclockwise ro-

ating transformation of the coordinate. In the rotated coor-inate, the exit ray direction vector �l� ,m� ,n�� reads as

l�,m�,n�� = �l cos2�me

N� + m sin2�me

N��,

�− l sin2�me

N� + m cos2�me

N��,n� . �9�

he longitudinal angle �out of the ray direction to the cen-ral axis and the azimuth angle �out of the ray can be ob-ained by using the following equation

sin �out sin �out,sin �out cos �out,cos �out� = �n�,l�,m�� .

�10�

an light and transmitted light for the trapezoid
mberti =� /16, and �f� �=� /32.

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2.2 Reflection ModeThe reflection mode refers to the case that rays are incidentfrom the ceiling of the trapezoidal gap. In the cylindricalgeometry, there are two possibilities, as shown in Fig. 4�b�:a ray goes from the outside of the outer circle and meets theinner circle or meets the outer circle again. The first casemeans that the ray is transmitted to the bottom of the prismsheet. The second case indicates that the ray is repeatedlyreflected inside the structure and eventually goes back tooutside the outer circle.

In the case of reflection, the ray does not meet the innercircle. The ray of the direction vector �l ,m ,n� passes anincident position �x , y , z� on the ceiling place, where−R sin�� /2�� x�R sin�� /2�, y=R cos�� /2�, and z=0. Theray equation is given by

�x,y,z� = �lt + x,mt + y,nt + z� for m � 0. �11�

By the same manner as in the previous section, the inter-section point of the outer circle and the ray is obtained as

t =− �l,m� · �x, y� + ��l,m� · �x, y��2 − �l2 + m2��x2 + y2 − R2��

�l2 + m2�

�� t � 0� . �12�

Then the intersection point is given by

¯ ¯ ¯ ¯ ˜ ¯ ˜ ¯ ˜

Fig. 7 Radiant intensity profiles of �a� input Lareflected light, �c� the transmitted light and radiincidence angle of 45�deg�, �e� the transmitted

�x,y,z� = �lt + x,mt + y,nt + z� . �13� r


On the other hand, in the case of transmission, the inter-ection point of the ray with the inner circle is given as

x±, y±, z±� = �lt± + x,mt± + y,nt± + z� , �14�

here the parameter t± is given by

± =− �l,m� · �x, y� ± ��l,m� · �x, y��2 − �l2 + m2��x2 + y2 − r2��

�l2 + m2�.

�15�

he solution of having a larger y component is selected toet the physical meaning. The area index of the exit areaan be found by the same manner stated in the previousection. The index of the area where the end point of a rayeets the outer circle can be obtained by

e± = �N�±

2�+

1

2� . �16�

f me+=me− is satisfied, the ray does not meet the bottomacet of the trapezoidal gap. Thus the ray meets the outerylinder structure. As a result, the ray is reflected by thetructure. If me+�me− is satisfied, the ray does meet theottom facet of the trapezoidal gap. The index mr of theeference area is also set to be mr=0. By the same mannern the previous section, the exit ray direction �l� ,m� ,n�� isbtained by Eq. �9�. It is noted that m� is negative in the

n light with incidence angle of 0�deg�, �b� thensity profiles of �d� input Lambertian light with

nd �f� the reflection light.

mbertiaant inte

eflection mode. The longitudinal angle �out of the ray di-


Faincidence angle and central angle �.

F


rection to the central axis and the azimuth angle �out of theray can be obtained by Eq. �10�.

3 Light Transmission and ReflectionCharacteristics of a Single MetallicPrism Sheet

With the ray tracing method mentioned in the previous sec-tion, the traces of ray bundles with specific radiant intensityprofiles can be analyzed. However, we are mainly inter-ested in the radiant intensity profiles of the transmitted andreflected light. In our analysis, the prism sheet is a trans-former that transforms an input incoherent diffused lightwith a specific radiant intensity profile to transmitted lightand reflected light with respective radiant intensity profiles.Transmission and reflection rates can be calculated fromrespective radiant intensity profiles. Since it is assumed thatthe material of a prism is a perfect conductor, the sum oftransmission power rate and reflection power rate is exactlyone.

Intuitively, we can see that the reflection and transmis-sion rates in the transmission mode are fixed to �1−r /R�and r /R, respectively, while the reflection and transmissionrates in the reflection mode are highly dependent on theinput radiant intensity profile. Figure 5 shows simulation

Fig. 8 �a� Functional dependence of the reflection rate to incidenceangle and inner circle radius and �b� that of the transmission rate toincidence angle and inner circle radius.

setups of transmission and reflection modes of a single �


ig. 9 �a� Functional dependence of the reflection rate to incidencengle and central angle �, and �b� that of the transmission rate to

ig. 10 Simulation setups for a crossed double prism sheet layer:
a� transmission mode and �b� reflection mode.

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prism sheet. In the transmission mode simulation, a Lam-bertian light is used as an input light. The radiant intensityprofiles of the reflected and transmitted light for prismsheets with several central angles of trapezoidal gap arevisualized. In the reflection mode, input light with a narrowradiant intensity profile is used as the input light. Transmis-sion and reflection rates are obtained for input light withseveral incidence angles.

In the transmission mode, the incident Lambertian lightis transformed to light with narrower radiant intensity pro-files. Figure 6 presents the transmitted light profiles forprism sheets with several central angles in the transmissionmode. In Fig. 6�a�, the radiant intensity profiles of inputincident Lambertian light is shown. For prism sheets withseveral central angles, radiant intensity profiles of the trans-mitted light are presented in Figs. 6�b� through 6�f�. Theinner circle radius r and outer circle radius R are set to 0.3and 1, respectively. As the central angle becomes smaller,the width of the radiant intensity profile decreases. The ra-diant intensity profile of the transmitted light can be ad-justed by controlling the height and the central angle of thetrapezoidal gap.

In the reflection mode simulation, the input light with

Fig. 11 �a� Recursive light transition model andlight transition model and �d� its flow chart for th

radiant intensity profile of a narrow cone shape is incident c


n the prism sheet. The reflection and transmission rates arenspected for several values of incidence angle. Figure 7hows two distinctive radiant intensity profiles of illuminat-ng light source. Figure 7�a� shows the input radiant inten-ity profile with incidence angle of 0 �deg�. The radiantntensity profiles of the reflected and transmitted light areresented in Figs. 7�b� and 7�c�, respectively. Figure 7�d�hows the input radiant intensity profile with incidencengle of 45 �deg�. The radiant intensity profiles of the re-ected and transmitted light are shown in Figs. 7�e� and�f�, respectively. In Fig. 6, it is indicated that the patternsf the radiant intensity profiles, the transmission rates, andhe reflection rates of two cases are different and varied forhe incidence angle of the input light.

Also, the reflection and transmission rates with the inci-ence angle are varied for the structural parameters as theatio of r and R, and the central angle �. These relationshipsre plotted in Figs. 8 and 9. Figure 8 shows that the func-ional relationship of the reflection and transmission rates tohe incidence angle and the structural parameter r �R=1�.he incidence angle of the input light is defined as the peakoint of the radiant intensity profile of the input light. Be-

flow chart for the reflection mode; �c� recursivesmission mode.

�b� its

ause of the assumption of no loss, the sum of the reflection


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incidence angle of 45�deg�, �e� the transmitted light, a



nd transmission rates is one. As the incidence angle goeso zero, the reflection rate decreases monotonically andeaches the minimum value at the incidence angle of zero.s the aperture opens wider, the reflection rate decreases.ince the input light has wide spatial frequencies, i.e., wideadiant intensity profile, the reflection rate is slightlymaller than the ratio of r /R.

In Fig. 9, the reflection and transmission rates are plottedor several values of the central angle of the trapezoidal gapith r fixed to 0.3. The dependency of the reflection rate on

he central angle of the trapezoidal gap is weaker than thatn the structural parameter r /R. The reflection and trans-ission rates in the reflection mode is somewhat insensitive

o the variation in the central angle, while the radiant inten-ity profile of the transmitted light in the transmission modes strongly dependent on the central angle of the trapezoidalap, as shown in Fig. 6. This point indicates that the centralngle of the trapezoidal gap is a meaningful design factor.he central angle is adjusted to modify the radiant intensityrofile of the transmitted light in the transmission modeithout considerable loss of reflection rate in the reflectionode.The metallic prism sheet can highly reflect the ambient

ight with oblique incidence angle and transmit the incom-ng Lambertian light incident on the bottom facet of therism sheet with transmission rate of r /R. In practice, whenhe metallic prism sheet should be attached between theacklight unit and LC cells in practical LCDs, by the re-ycle mechanism of the backlight unit, the real transmis-ion rate is greater than aperture coverage r /R. These be-

an light with incidence angle of 0�deg�, �b� thensity profiles of �d� input Lambertian light with

Fig. 12 Radiant intensity profiles of the transmitted lights �a� in thetransmission mode and �b� in the reflection mode.

Fig. 13 Radiant intensity profiles of �a� input Lambertireflected light, �c� the transmitted light and radiant inte

nd �f� the reflection light.


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haviors of the metallic prism sheet show considerablepotential for its application to transflective devices.

4 Light Transmission and ReflectionCharacteristics of a Crossed DoublePrism Sheet Layer

In this section, the geometric optics analysis method pre-sented in Sec. 2 is generalized to analyze multiple layerstructures of metallic prism sheets. An intuitive interactionmodel of each prism sheet comprising the layer is de-scribed. By using the generalized analysis method, lighttransmission and reflection characteristics of double prismsheets are studied. The simulation setups of double prismsheets are similar to those of the single prism sheet. Figure10 shows the simulation setups of transmission and reflec-tion modes of a double prism sheet layer. In the transmis-sion mode simulation, a Lambertian light is used as aninput light. The radiant intensity profiles of the reflectedand transmitted light for prism sheets with several central

Fig. 14 �a� Comparison of the reflection rates of a single prismsheet and crossed double prism sheet and �b� that of the transmis-sion rates of a single prism sheet and crossed double prism sheet.

angles are visualized. In the reflection mode, a light with p


arrow radiant intensity profile is used as the input light.ransmission and reflection rates are obtained for input

ight with several incidence angles.For the double prism layer, the transmission rate in the

ransmission mode is not simply given by r /R because ofultiple reflections in the space between the upper prism

heet and lower prism sheet. The multiple reflections be-ween two prism sheets can be simply modeled by a recur-ive process as addressed in Fig. 11. In Fig. 11, the recur-ive multiple reflection processes in the reflection mode andransmission modes are presented. The functions, reflec-ion_mode1 and transmission_mode1, are to calculate theadiant intensity profiles of the reflected and transmittedight in the reflection and transmission modes of the lowerrism sheet, respectively. Similarly, the functions reflec-ion_mode2 and transmission_mode2 are to calculate theadiant intensity profiles of the reflected and transmittedight in the reflection and transmission modes of the upperrism sheet, respectively.

By using the analysis method, we first consider the ra-iant intensity profile of the transmitted light in the trans-ission mode. Figures 12�a� and 12�b� show the radiant

ntensity profiles of the transmitted and reflected light, re-pectively. As compared with the results of Fig. 6, the ra-iant intensity profile in Fig. 12�a� shows that the lightnergy is condensed near the normal direction �the center inig. 12�a��. This behavior is due to the crossed prism sheeteometry and is similar to that of the brightness enhance-ent film �BEF� of 3M.4 Thus the metallic prism sheetould be potentially used for brightness enhancement andiewing angle management for LCDs. In the reflectionode simulation, the input light with the same radiant in-

ensity profile of a narrow cone shape is incident on therism sheet. The reflection and transmission rates are in-pected for several values of incidence angle. Figure 13hows two distinctive radiant intensity profiles of illuminat-ng light source. Figure 13�a� shows the input radiant inten-ity profile with incidence angle of 0�deg�. The radiant in-ensity profiles of the reflected and transmitted light areresented in Figs. 13�b� and 13�c�, respectively. Figure3�d� shows the input radiant intensity profile with inci-ence angle of 45�deg�. The radiant intensity profiles of theeflected and transmitted light are shown in Figs. 13�e� and3�f�, respectively. Comparing the results with those of theingle prism sheet shown in Fig. 7, the effect of the mul-iple reflections between two prism sheets is reflected in theadiant intensity patterns. Figure 14 shows a comparison ofhe reflection and transmission rates of a single prism sheetnd crossed double prism sheet in the reflection mode. Theentral angle and the inner radius are set to �=� /8 and r0.3, respectively. In the reflection mode, the multiple re-ections between two prism sheets and the crossed geom-try lead to a slight increase in the reflection rate. The de-endence of the reflection rate of the crossed double prismheet on the incidence angle is similar to that of the singlerism sheet.

Conclusiongeometric optics analysis method for analyzing light

ransmission and reflection characteristics of a metallicrism sheet is presented. It is inspected that the metallic
rism sheet can be appropriately applicable to transflective

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devices or brightness enhancement film for LCDs. It isshown that the central angle of the trapezoidal gap can beadjusted to modify the radiant intensity profile of the trans-mitted light in the transmission mode without considerableloss of reflection rate in the reflection mode. Also, thecrossed double prism sheet layer can condense the lightnear the normal direction more strongly. The metallic prismsheet can highly reflect the ambient light with an obliqueincidence angle, and transmit the incoming Lambertianlight incident on the bottom facet of the prism sheet with atransmission rate of r /R. In practice, when the metallicprism sheet should be attached between the backlight unitand LC cells in practical LCDs, by the recycle mechanismof the backlight unit, the real transmission rate is greaterthan aperture coverage r /R. Conclusively, it is expectedthat the metallic prism sheet can be an appropriate structurefor transflective devices for transflective displays.

References

1. K. Fujimori, Y. Narutaki, and N. Kimura, “High-transmissive ad-vanced TFT LCD technology,” SHARP Tech. J. 85, 34–38 �2003�.

2. R. W. Clikeman, N. D. Lubart, and C. R. Mayfield, “Device havingreflective and transmissive properties,” U.S. Patent No. 6919981�2005�.

3. R. W. Clikeman, N. D. Lubart, and C. R. Mayfield, “Film havingtransmissive and reflective properties,” U.S. Patent No. 6819465�2004�.

4. H. Kim, Y. J. Lim, B. Yang, K. Choi, and B. Lee, “Geometricalanalysis on optical transmission characteristics of prism sheet layers,”Opt. Eng. 44, 128001 �2005�.

5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics,
Cambridge University Press, New York �1995�.

Hwi Kim received BS and MS degrees fromthe School of Electrical Engineering inSeoul National University, Korea, in 2001and 2003, respectively. He is currently acandidate for his PhD degree in the Schoolof Electrical Engineering, Seoul NationalUniversity. His primary research interestsare in the areas of diffractive optics andnanophotonics.

Byoungho Lee received BS and MS de-grees in 1987 and 1989, respectively, fromSeoul National University, Korea, in elec-tronics engineering. He received a PhD de-gree in 1993 from the University of Califor-nia at Berkeley in electrical engineering andcomputer science. In 1994, he joined thefaculty of the School of Electrical Engineer-ing, Seoul National University, where he isnow a professor. He became a Fellow ofSPIE in 2002 and a Fellow of OSA in 2005.

e is currently a director-at-large of the OSA. He has served as aommittee member for various international conferences. He hasuthored or coauthored more than 170 papers in international jour-als and more than 250 international conference papers. In 1999,is laboratory was honored as a National Research Laboratory byhe Ministry of Science and Technology of Korea. In 2002, he re-eived the Presidential Young Scientist Award of Korea. His re-earch fields are hologram applications, 3-D displays, optical fiberratings, and nanophotonics.

August 2006/Vol. 45�8�0

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Geometric optics analysis on light transmission and reﬂection …ipds.korea.ac.kr/download/publication/15.pdf · 2012-01-10 · Geometric optics analysis on light transmission and