,, [7-9] 1, n 1,, n, [10] [11-1], LED, θ,,, Solidworks TracePro, 1 Fig.1 Schematicofbeampropagation, ( ) s p r s = Er = n1cosαi-ncosαt, (1a) E i n 1co

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1 34 6 Vol.34,No ACTAOPTICASINICA June,014 (, 36101) (LED), TracePro, (PMMA) (PC), 0.5, 0.5,, 93% ; ; ; O435 A doi: /aos ResearchofGrazingIncidenceDiffuserwith Microstructureof Double-SidedTriangularPrism Arrays LiangDejuan LaiLiping ChenChunyu DuTuanjie ZhuangQiren (ColegeofInformation Scienceand Engineering,Huaqiao University,Xiamen36101,China) Abstract Agrazingincidencedifuserwithdouble-sidedtriangularprismarraysisresearched,whichissuitablefor edge-lightinglightemitingdiode(led)flatpanellightwithoutlightguideplate.basedonfresnelequations,the anti-reflectionprinciplesoftriangularprismarraysareanalyzed.theinfluenceofparametersofthetriangularprism arrays,i.e.theratioofdepthtowidthandthebotom width,onthedifusertransmitanceisinvestigatedbyusing thesimulationofraytracingsoftwaretracepro.simulationsrevealthatthetransmitanceofentrysurfaceincreases withtheratio ofdepthto width,bothfor polymethyl methacrylate (PMMA)and polycarbonate (PC).The transmitanceachievesthemaximum whiletheratioofdepthtowidthisabout0.5,andkeepsinvariantwhenthe ratioincreases.thetransmitanceofexitsurfacedecreaseswhentheratioofdepthtowidthiscloseto0.5,because thelighthasbeentotalreflectedtwiceinthedifuser.theresultsshowthatthetransmitanceofgrazingincidentray canbeupto93%intheoptimizeddifuser. Keywords opticaldesign;difuser;fresnelequation;microstructureoftriangularprism OCIScodes ; ;0.00; ,, (LED), [1],LED [-4] LED LED, LED [5-6],, LED, LED LED LED LED : ; : : (01H009) : (1988 ),,, LED liangdejuanok@163.com : (1960 ),,, qrzhuang@hqu.edu.cn( )

2 ,, [7-9] 1, n 1,, n, [10] [11-1], LED, θ,,, Solidworks TracePro, 1 Fig.1 Schematicofbeampropagation, ( ) s p r s = Er = n1cosαi-ncosαt, (1a) E i n 1cosαi+n cosαt r p = Er = ncosαi-n1cosαt, (1b) E i n cosαi+n 1cosαt αi,αt,n 1 n n 1sinαi =n sin αt, R 槡 [ ] 烄 n 1cos(αi)-n 1- n1 n ) 烌烄 sin(αi n 1 1- n1 R =r s +r n ) sin(αi -n cos(αi) 烌 p = 烅烍 + n 1cos(αi)+n 1- n1 sin(αi 烆槡 [ n ) 烅 n ] 1 1- n1 sin(αi 烎槡 [ n ) 烍. () ] +n cos(αi ) 烆烎 h, D, β, c = h /D, cotβ, =c β =arccot(c ) 1,αi =β -θ, θ 1, 槡 [ ] sinαi =sinβ cosθ-cos β sinθ sin [ (c cot-1 ]-θcoscot [ -1 (c ] ( 3) cosαi =cosβ cosθ+sin β (c sinθ coscot-1 [ ] +θsin [ cot -1 (c ]. (4), 1, T ()~(5) T =1-R. (5)

3 T =1- 烄 n 1 {cos[cot -1 (c )]+θsin[cot -1 (c -n 烅 n 1 {cos[cot -1 (c )]+θsin[cot -1 (c +n 烆烄烅烆 n 1 n 1 槡槡 1- n1 1- n1 : 槡槡 1- n1 {sin[cot -1 (c )]-θcos[cot -1 (c { 烌 n } 烍 - {sin[cot -1 (c )]-θcos[cot -1 (c n 烎 1- { } n1 {sin[cot -1 (c )]-θcos[cot -1 (c { n } {sin[cot -1 (c )]-θcos[cot -1 (c +n { n } {cos[cot -1 (c )]+θsin[cot -1 (c -n {cos[cot -1 (c )]+θsin[cot -1 (c 烌烍.(6) 烎 [ ] n1 θ =β -arcsin n ) sin(αi =arctan(c )- [ ] arcsin n1 n ), sin(αi ( ) T T =1- 烄 n {cos[cot -1 (c 1 )]+θ sin[cot -1 (c 1 -n 1 烅 n {cos[cot -1 (c 1 )]+θ sin[cot -1 (c 1 +n 1 烆烄烅烆 n n 槡槡 1- n 1- n 槡槡 1- n {sin[cot -1 (c 1 )]-θ cos[cot -1 (c { 1 烌 n 1 } 烍 - {sin[cot -1 (c 1 )]-θ cos[cot -1 (c 1 n 1 烎 1- { } n {sin[cot -1 (c 1 )]-θ cos[cot -1 (c 1 { n 1 } {sin[cot -1 (c 1 )]-θ cos[cot -1 (c 1 +n { n 1 } 1 {cos[cot -1 (c 1 )]+θ sin[cot -1 (c 1 c 1=h 1 /D 1, n sin [ cot -1 (c 1 n ) ]-θ coscot -1 (c { { [ 1 ] 1 }, T t ) 1 T t = T T. (8) (6)~(8) -n 1 {cos[cot -1 (c 1 )]+θ sin[cot -1 (c 1 烌,(7) 烍烎, θ, T c c 1 c Fig. TransmitancesofincidentplaneTvary (PMMA), 1.49, 3 (6)~ withtheratioofdepthtowidthc (8) [14], [15-16],LED, 0~0.3, θ T t PMMA( 1.49) (PC)( ) 40 mm 300mm mm, 1, LED D D 1, h h 1 4, LED ( ),,, [13], 40mm 300mm

4 c,,, 5, θ c 0.5, c >0.5, c θ, PMMA PC 3 5 (a)θ=3 ;(b)θ=6 (a) PMMA;(b) PC Fig.3 Efectoftheratioofdepthtowidthofmicrostructure Fig.5 Transmitancecurvesasafunctionofdiferentdepth ontotaltransmitanceofdifuser.(a)θ=3 ;(b)θ=6 widthratiosoftriangularprism araysonincident 4 Fig.4 Schematicdiagramofsimulationmodel 3.1 (a), c >0.5,, TracePro 4, 1mm 5, LED ( θ= 6 ), c 0.5, c, c >0.5,c 6, (a) (a) PMMA;(b) PC c Fig.6 Influenceofdepthwidthratioofmicrostructureon c,, totaltransmitanceofdifuserwithmaterialof(a), PMMAand (b)pc,, c planewithmaterialof(a)pmmaand(b)pc , c >0.5,, c =0.7, c 1 T t,

5 : c 1<0.5, PMMA PC 6,, 3, 6 c 1 0.5, 1,, 3 c (a) ; c 1 0.5, 1, 3, 3, 7(b), 5 6,LED, θ,pmma PC c 1, c 1>1, 1, ( 4),,, PMMA 6,,, LED θ, LED PMMA, 7 Fig.7 Schematicpathofbeaminthedifuser 3.3 D, 9 (c 1=1.5,c =0.7), ( ), 8(a) (D 1=0.mm) D 1=0.mm, (D 1=0.6 mm), D 8(b), D =0.858mm, (D ), D 1, D 1 D =0.858 mm, (D 1 ) 8 (a)d ;(b)d1 Fig.8 Variationcurvesoftransmitanceasafunctionofthewidth (a)dand (b)d1 :θ=3,c =0.7, PMMA c 1=1.5,D 1=0.858mm,D =0.mm, (84.%), [9] 10, (9%) 93%, 90% PC [17] PMMA (PS)

6 9 (a)d1=0.mm;(b)d1=0.6mm Fig.9 Uniformityofiluminationasafunctionofthewidthofexitsurfacetriangularprismarrays. (a)d1=0.mm;(b)d1=0.6mm 10 (a) (b) Fig.10 (a)iluminationmapand (b)distributioncurveofdifuserwithdouble-sidedtriangularprismarrays

7 : 80% 85% 68% θ=3 10(b) 1, θ=3 36%~41% 60 ( ),, ( ) 3.4, 11% ~14%,,, PC PMMA PS (93%), PC PMMA PS,, 1 PC PMMA PS, 0.8 mm [17],, PC PMMA PS 1 0% 15% 3%, 1 (θ=3 ) Table1 Comparisonofuniformity,transmitanceandsoftlightingefectofexistingdifusers(θ=3 ) Typesof difuser Surfaceof microspheres Surfaceof micro-cones Surfaceof Dopedplate micro-pyramids PC Dopedplate PMMA Dopedplate PS Surfaceofnew microstructure Transmitance/% Uniformity/% Softlightinggrade B B B A + A + A + A 4 LED 009,94(9): , array[j].optexpress,01,0(s6):a788-a798., Tracepro, 3 ~5, PMMA PC, [J].OptExpress,01,0(6): , [J].OptExpress,010,18(6): , 93%,, 3LiJungyu, Chen Shihpu, Lin Yiping,et al.. A lighting mechanismforflatelectronemissionlamp [J].ApplPhysLet, 4Lee Hsiao Wen,Lin BorShyh.Improvementofilumination uniformityforledflatpanellightbyusingmicro-secondarylens 5C H Tsuei,JW Pen,W SSun.Simulatingtheiluminanceand theeficiencyoftheled andfluorescentlightsusedinindoor lightingdesign[j].optexpress,008,16(3): M D Tsai,JJChen,K L Huang.AdesignofLEDpanellamp for indoor ilumination [C]. Inteligent Technologies and EngineeringSystems.SpringerNew York,013: X H Lee,JLTsai,S H Ma,etal..Surface-structureddifuser byiterativedown-sizemolding withglasssinteringtechnology 8CSun,W T Chien,IMoreno,etal..Calculatingmodeloflight transmissioneficiencyofdifusersatachedtoalightingcavity 9SYu,R Hu,M Chen,etal..Improvementoflightextraction eficieneyofwhiteledsusingmicrostructurearrayonphosphor siliconelayer [C].01InternationalConferenceon Electronic PackagingTechnology & HighDensityPackaging,01: ZhuangXiaolei,ZhouFang,ShenSu,etal..Characteristicsof difuserswithcascaded-microlensarrays[j].actaopticasinica, 010,30(11): Wang Hong,Ye Feifei,Huang Huamao,etal..Design and,,,. realizationofreflectivecurrentbarrierforhigh-brightnessled [J].,010,30(11): chips[j].joptoelectronics Laser,01,3(6): Sun Yanyan, Han Lu,Shi Xiaoyu,etal..Generallaws of,,,. LED reflectionandrefractionformetasurfacewithphasediscontinuity [J].,01,3(6): [J].ActaPhysicaSinica,013,6(10): Y KPark,JYJoo,CBLee,etal..Designandfabricationofa,,,. lightemitingdiode-baseddifusersheet-lesslightguideplatefor [J].,013,6(10): lighting applications [J].International Journal of Precision 1JG Chang,YBFang.Dot-paterndesignofalightguideinan Engineeringand Manufacturing,013,14(6): edge-litbacklightusingaregionalpartitionapproach [J].Opt

8 Eng,007,46(4): JinJi,Yu Guiying,Lin Min.Researchofhighlightcolection eficiencyofledparabolicreflectorbasedonnon-imagingoptics [J].ChineseJLasers,010,37(3): ,,. LED [J].,010,37(3): LiuZhengquan,Sun Yaojie,Lin Yandan.Freeform reflector design for rectangular iluminance distribution based on diferentialgeometry [J].Acta OpticaSinica,01,3(10): ,, [J].,01,3(10): LaiLiping,ZhuangQiren,LiangDejuan.Designofaneficient projectorfor LED flatlamp withoutlight guide plate [J]. OptoelectronicsLeters,013,9(6): HuangQilu,WuFengtie.Investigationofuniformilumination ofnear-fieldtargetsusingaconiclight-emitingdiodearray [J]. ActaOpticalSinica,010,30(10): ,. LED [J].,010,30(10): He Xiaoxiang, Wu Daming, Zheng Xiuting. Efect of microstructure of light difuser plate on uniformity and transmitance[j].chinesejliquidcrystalsanddisplays,01,. 7(): ,,. [J].,01,7(): :

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