基于菲涅尔透镜的配光设计

菲涅尔透镜设计实例

菲涅尔透镜设计实例菲涅尔透镜是一种特殊的透镜设计，与传统的球面透镜相比，它具有更薄、更轻、更便于制造和使用的特点。

菲涅尔透镜的设计方案广泛应用于各种领域，如航海、照明、摄影等。

本文将以菲涅尔透镜在太阳能集热器中的设计实例为例，来说明菲涅尔透镜的应用和优势。

一、菲涅尔透镜在太阳能集热器中的设计实例太阳能集热器是利用太阳辐射热能进行能量转换的装置，其中菲涅尔透镜被广泛应用于集光器的设计中。

集光器的作用是将太阳的光线集中到一个小面积上，从而提高热能的集中度，增加太阳能的利用效率。

在太阳能集热器中，菲涅尔透镜被设计成具有特殊的形状，以实现光线的聚焦效果。

其设计原理是通过透镜表面特殊的微结构，将原本通过球面透镜折射的光线改为通过透镜表面的微槽，从而达到减小透镜厚度、减轻透镜重量的目的。

二、菲涅尔透镜设计的优势相比传统的球面透镜，菲涅尔透镜设计具有以下几个优势：1. 薄型设计：菲涅尔透镜的微槽结构使得透镜的厚度大大减小，从而减轻了透镜的重量，便于集光器的制造和使用。

2. 高效集光：菲涅尔透镜的特殊结构使得光线可以更好地聚焦，提高了集光器的光能利用效率。

透过菲涅尔透镜的光线能够更集中地投射到集热器的接收面上，从而实现更高的热能转换效率。

3. 宽视场角：菲涅尔透镜的设计可以实现宽视场角，即可以从更广的角度接收太阳光线。

这使得菲涅尔透镜适用于需要广视场角的应用场景，如太阳能光伏系统中的太阳能跟踪器。

4. 易于制造：菲涅尔透镜的制造相对简单，与传统的球面透镜相比，节省了制造成本和时间。

这使得菲涅尔透镜在大规模生产中具有较高的可行性。

三、菲涅尔透镜设计的应用领域除了太阳能集热器，菲涅尔透镜的设计还广泛应用于其他领域。

以下是一些常见的应用领域：1. 航海导航：菲涅尔透镜常被用于航海灯塔中，通过将灯光聚焦，增强灯塔的可见性和远距离导航的效果。

2. 摄影器材：菲涅尔透镜的薄型设计使其成为相机镜头的理想选择之一。

它能够提供清晰、锐利的图像，同时减轻了相机的重量，便于携带和使用。

菲涅耳透镜的通光分析及设计方法探讨

文章编号:100525630(2006)0120034205菲涅耳透镜的通光分析及设计方法探讨Ξ陈　杰,李湘宁,叶宏伟(上海理工大学光电学院,上海200093) 摘要:研究了菲涅耳透镜成像质量差的原因,提出一种改进的方法,即改善轴外点的成像质量以增大菲涅耳透镜的视场。

分析了三种常用的设计菲涅耳透镜的方法,用光学设计软件Zem ax 模拟设计结果,对三种设计方法进行比较。

得出结论:像面为曲面时可校正场曲;基面和底面为曲面的菲涅耳透镜与平面型菲涅尔透镜相比彗差较小。

关键词:菲涅耳透镜;像差;设计;曲面中图分类号:O 43 文献标识码:AAna lyo is of Fresnel len s tran s m issiv ity and research of designCH EN J ie ,L I X iang 2n ing ,Y E H ong 2w ei(Co llege of Op tics and E lectronics ,U niversity of Shanghai fo r Science and T echno logy ,Shanghai 200093,Ch ina ) Abstract :T he flaw of F resnel len s w as analyzed ,and a m ethod w as b rough t up to b roaden the angle of F resnel len s and to i m p rove i m aging quality .T h ree m ethods of F resnel len s design w ere listed ,and there typ e of len s w ere si m u lated ,and the resu lts of si m u lati on s w ere com pared ,and the conclu si on is :cu rve detecto r can ligh ten field cu rvatu re .T he i m aging quality of cu rve F resnel len s is better than p lane one ,becau se com a aberrati on w as co rrected .Key words :F resnel len s ;aberrati on ;design ;cu rve1　引　言当前广泛使用的菲涅耳透镜普遍使用轴上点消球差的方法设计[1]。

蜂窝式阵列菲涅尔透镜的配光设计

蜂窝式阵列菲涅尔透镜的配光设计在2021年的法兰克福车展上，宝马公司发布消息将生产以激光为车灯光源的新型车。

其采用的激光光源为激光二极管，具有响应速度快、能耗低、寿命长等优点。

相对于LED灯而言，激光灯源还具有较强的聚束性。

用激光大灯作汽车前照灯，其照度必须符合相关照明标准，即在配光屏上近光应产生明显的明暗截止线。

为了达到标准，通常的方法是以非成像光学原理为设计基础，在光源前加特制的配光透镜。

目前以非成像光学理论为基础而设计的配光透镜，主要有自由曲面透镜、自由曲面反射镜和菲涅尔透镜等。

自由曲面透镜能控制光线的出射角，重新分配光强，从而提高光能的利用率，设计方法主要有网格划分法、偏微分方程法和SMS法等，可适用于点源或小型扩展光源，这类透镜多被用来实现以LED为光源的均匀照明。

自由曲面反射器一般以边光原理等理论，结合反射定律，根据光源的发光特性和接收面上的光强分布要求建立偏微分方程，利用数值求解的方法求出反射面，以达到均匀照明的要求。

菲涅尔透镜的设计方法与自由曲面有所不同，是由法国物理学家Augustin Jean Fresnel发明的。

普通透镜对光线起偏折作用的主要是透镜表面的曲率，将透镜中多余的平行层抽去便形成了菲涅尔透镜。

它是凸透镜的一种异化，仍具有汇聚光线和成像的特性。

与传统透镜相比，菲涅尔透镜有用材少，重量轻和体积小的特点，且具有良好的聚光性能。

因所需功能不同，菲涅尔透镜被设计成不同类型，有平板型、弧型、透射式和反射式等。

本文首次将多焦点的蜂窝式菲涅尔透镜阵列应用到平行光的配光设计中。

文中通过计算每个菲涅尔的环带角度和倾斜角度来优化出射光的分布，并设计出符合要求的菲涅尔透镜阵列，进一步通过光学仿真检测菲涅尔透镜的出光效果，结果表明设计是符合预设目标的，具有良好的投光效果。

通过优化设计方法和设计效率，结合集成光学中的光刻工艺可实现图像级的配光镜头设计。

1 菲涅尔透镜单元的设计方法设计目标：将平行光照射到菲涅尔透镜阵列上，并在距离透镜阵列1 m远的接收面上形成特定的图形。

用于光伏系统新型菲涅耳线聚焦聚光透镜设计

光子学报第31卷第2期 V o l131N o12 2002年2月 A CTA PHO TON I CA S I N I CA Feb ruary2002　用于光伏系统新型菲涅耳线聚焦聚光透镜设计Ξ汪　韬　李　辉　李宝霞　赛小锋　高鸿楷(中国科学院西安光学精密机械研究所,光电子学室710068)摘　要　根据边缘光线原理,优化设计太阳电池及光伏系统的菲涅耳线聚焦聚光透镜1设计光学聚光率为18×,可用于空间、地面光伏系统的聚光系统1分析了其集光角特性,表明该菲涅耳线聚焦棱镜具有大的集光角(±7°)1关键词　太阳电池;菲涅耳透镜;集光角0　引言近年来,基于太阳能、风能等可再生能源技术发展迅速1特别是基于太阳能光伏发电技术,为空间卫星供电的电源系统和地面光伏发电系统,为未来解决能源问题提供了新的广阔前景1但其面临发电价格高昂和太阳电池材料紧缺、昂贵的问题,需要进一步地降低成本和提高效率1为减少太阳电池片的实际用量,人们早已开始了太阳电池聚光器的研究1聚光系统主要为反射式1(如CPC、S M T S等)和透射式(F resnel,全息等)两种1特别是Ga InP2 GaA s Ge级联太阳电池的研制成功2,其较Si电池效率高、抗辐射、耐高温1非常适用于聚光型太阳电池1而且随光学树脂的应用发展,如聚碳酸酯、PMM A(聚甲基丙烯酸甲酯)和聚苯乙烯等,具有耐冲击强度高、相对密度小,透过率高,在太阳光谱的013～2Λm范围内透过率达92%以上,与光学玻璃相差无几1其光学性能优良,抗老化,成型工艺简单、产品成本低廉1利用光学树脂透镜和级联太阳电池合成的聚光型太阳电池极大地提高单位电池片产生的电量1大大降低了发电成本,提高了太阳能光伏发电的竞争力3,41早先点聚焦菲涅耳聚光透镜具有高的聚光率,但其必须对太阳进行二维跟踪1我们采用三维优化设计,考虑太阳能电池的热退化效应,设计具有较大集光角、只对太阳进行一维跟踪的线聚焦菲涅耳聚光透镜11　设计原理菲涅耳聚光透镜其根本目的为增加太阳电池上的太阳辐射功率的密度1由于菲涅耳非成象光学,无需考虑象的精度,在入射角范围内将能量聚焦于一定范围内,无需点聚焦51遵循折射原理(Snell定理)n1sin(i1)=n2sin(i2)当采用最小偏折角棱镜时,菲涅耳聚光透镜反射损失为最小,即为入射光线与顶面的法线的夹角等于出射光线与底面法线的夹角712　设计方法考虑因素:1)棱镜组对光的吸收随棱镜的厚度增加而变大,同时由于棱镜元的底边缘造成的通光量的损失也急剧变大,所以棱镜的厚度要尽可能的薄1单棱镜太薄将造成实际加工的困难,我们取其最大厚度为1mm12)菲涅耳聚光透镜的焦距直接影响电池组件集光角和光学聚光率的大小,同时影响电池组件的体积13)电池组件集光角的设计,集光角越大,电池组件对太阳的入射的方向不敏感,对系统瞄准太阳的能力要求低,同时它也直接影响光学聚光率的大小1对±Η截面内入射角,不同季节,每天太阳倾角的变化不同,正Ξ国家自然科学基金资助项目　收稿日期:2001206213午前后4小时夏天变化为±2°,冬天变化为±6°,太阳本身的有限长角为±015°,加上聚光器斜率误差,所以菲涅耳聚光棱镜的集光角设计值≥±615°14)折射率n 采用太阳电池吸收光谱的中心波长600nm 处折射率为114881先由0位置与接受面的相对位置设计第一棱镜元,确定其参量棱镜顶角角度Α1、棱镜倾角Β1、棱镜元宽度X 1,递进优化之1再在棱镜1基础上连接设计棱镜2,确定其参量Α2、Β2、X 2,递进优化1以此类推,得到第n 棱镜参量(Αn ,Βn ,X n )1由此得到棱镜组参量(Α1Α2…Αn ,Β1Β2…Βn ,X 1X 2…X n )1如图1,设计流程图见图21采用new ton 法逼近,至满足判据,结束该棱镜元参量的搜索1进行下一棱镜元参量的搜索1判据为 d x -d 0 <Ε,式中图1　光线在棱镜上的折射示意图F ig .1　Schem atic of rays refracti on on the F resnel lens 图2　菲涅耳线聚焦聚光棱镜的设计流程图 F ig .2　F low chart of the op ti m um line 2focu s F resnel len sd x 为入射角为Η时的光线的偏折角,d 0为光线投射到电池表面所需的偏折角,Ε为极小量1Η、Ω分别为入射角在棱镜端面和垂直端面内的投影1光学聚光率定义为E l E o ,E l 为有棱镜情况下光辐射密度,E o 为无棱镜情况下光辐射密度11光学聚光率为会聚比与光效率的积1总的光学聚光率为各棱镜元的光学聚光率的和1计算公式为c (Η,7)=6nT (Η,7,n )(A l (n ) A o (n ))T (Η,7,n )为第n 棱镜的透过率,A l (n )为第n 棱镜的出射孔径,A o (n )为第n 棱镜的入射孔径1其设计外形如图3,其光学聚光率见图41 图3　菲涅耳线聚焦聚光棱镜外形截面图 F ig .3　Schem atic of truncated the op ti m umline 2focu s F resnel lens 图4　不同Η、7菲涅耳线聚焦聚光棱镜的聚光率 F ig .4　Op tical concen trati on rati o of the op ti m umline 2focu s F resnel len s in differen t Η,73　损失分析太阳光穿过菲涅耳棱镜,在棱镜上表面和下表面分别发生反射1棱镜倾角变大时,入射角变大,反射损失变大,透射光通量与入射角和棱镜顶角有关,当入射角与出射角相等时,透射光通量为最大1另外棱镜元的边缘也造成通光量的损失1当入射角Η太大时,一部分光线将投射到棱7912期江韬等1用于光伏系统新型菲涅耳线聚焦聚光透镜设计镜的底边,只是这部分光线偏离预定方向,无法投射到太阳电池表面1所以应尽量减小棱镜元的底边宽度1即减少棱镜的厚度14　集光角特性分析如图4,在±7角平面内,其集光角达到±60°,光学聚光率对入射角的变化不敏感1在±60°之间都有较高的光学聚光率1这样在一天内不动电池组件从上午8时至下午4时都能充分利用太阳光1在±Η角平面内,其集光角达到±7°,具有较宽的集光角,大于太阳一天内南北方向的仰角变化15　焦距的影响如图5,相同的入射孔径,不同的焦距情况下的光学聚光率(7=0),大的焦距(f =360mm )有相对高的光学聚光率达21,但其集光角为±4°1当焦距变小(f =200mm )其集光角达到±8°,但其图5　不同焦距下的光学聚光率和集光角特性 F ig .5　Effect on the op tical concen trato r rati oof Ηand erro r to lerance (7=Η)光学聚光率降低为161原因是焦距变小相应其f ×Η值减小,其集光角变大1焦距变小时菲涅耳聚光棱镜边缘部分偏折角变大,其反射损失加重,光效率降低,导致整个菲涅耳聚光棱镜的光学聚光率下降1在实际应用中,菲涅耳聚光棱镜应有尽量大的集光角,但是集光角设计的变大则造成光效率的相应减小,应考虑实际应用情况作相应的调整1理论上随电池表面光通量增加短路电流呈线性增加,开路电压呈指数增长1而电池的漏电电流不变化1这样V 增加,(c ×I -I l ) (I -I l )>c ,即电流增幅大于c 倍1这样电池输出功率为原先的c 倍以上,电池效率也有所升高1光学聚光率c 不能太高,否则电池表面温度太高导致电池系列电阻变大,电池效率将有所下降1以AM 115条件下1m 2太阳电池效率19%记,输出功率P 为190W ,配备18倍菲涅耳线聚焦聚光透镜后,由于电池表面温度升高不多,电池效率损失微小6,电池输出功率可达3400W 左右1大大提高了单位电池面积的发电量,降低了太阳电池组件的成本,提高了光伏发电的竞争力16　结论设计一种用于太阳电池的菲涅耳线聚焦聚光透镜,考察了焦距对其光学聚光率的影响1理论上棱镜越细密越好,但由于实际加工有一定的精度限制,所以应根据情况取舍1据此设计透射式的菲涅耳线聚焦聚光透镜,聚光量适中C =18,太阳电池的温度不高,减缓太阳电池的热退化效应,有利于延长其使用寿命1并且其较以往(±215.)具有较大的集光角±7.,便于实际应用1无须太阳跟踪系统,只需随着不同季节太阳纬度的变化,调整太阳电池组件南北方向的倾角1参考文献1　W elfo rd W T ,W in ston R .T he op tics of non i m aging concen trato rs .N er Yo rk :A cadem ic P ress ,1978,132～1382　Yeh Y C M ,et al .A dvances in p roducti on of cascade so lar cells fo r space .26th IEEE Pho tovo ltaic SpecialistsConference ,1997:827～8303　O ′N eillM J ,et al.Inflatab le len ses fo r space pho tovo ltaic concen trato r arrays .26th IEEE Pho tovo ltaic Specialists Conference ,1997:853～8564　Spence B R ,et al .T he scarlet array fo r h igh pow er GEO satellites .26th IEEE Pho tovo ltaic Specialists Conference ,1997:1027～10305　L o renzo E ,L uque A .F resnel len s analysis fo r so lar energy app licati on s .A pp l Op t ,1982,20(17):2941～29456　Ku rtz S R ,O ′N eillM J .E sti m ating and con tro lling ch rom atic aberrati on lo sses fo r tw o 2juncti on ,tw o 2term inal devicesin refractive concen trato r system s.25th IEEE Pho tovo ltaic Specialists Conference ,1996:361～3647　K ritchm an E M ,et al .(1979b )H igh ly concen trating F resnel L en ses .A pp l Op t ,1980,18(15):2688～2695891 光子学报 30卷A NE W D ESIGN OF L INE -FOCUS FRESNEL L ENSFOR PHOT OVOL TA I C POW ER S Y STE MW ang T ao ,L i H u i ,L i B aox ia ,Sai X iaofeng ,Gao HongkaiX i′an Institu te of Op tics and P recision M echan ics ,Ch inese A cad e m y of S ciences 710068R eceived date :2001206213Abstract A n arched line 2focu s F resnel len s is designed fo llow ing the edge ray p rinci p le by op ti m um m ethod .T h is k ind of F resnel len s cou ld be u sed in so lar concen trato r of sp ace and terrestrial p ho tovo ltaic pow er system .It ′s easier to track the sun in on ly one single ax is .It has op tic concen trato r rati o as 18.It also has better accep tance angle and low co st .Keywords F resnes len s ;So lar concen trato r ;A ccep tance angleW ang Tao w as bo rn in Shaanx i ,Ch ina ,in 1974.H e received the B .S degree and M .S degree from the N o rthw est U n iversity in 1996and 1999resp ectively .A t p resen t ,he is a Ph .D degree candidate in X i ′an In stitu te of O p tics and P recisi on M echan ics ,Ch inese A cadem y of Sciences .H is p resen t in terest is p ho tron ic m aterials and devices 19912期江韬等1用于光伏系统新型菲涅耳线聚焦聚光透镜设计。

(完整版)基于菲涅尔透镜的配光设计

基于菲涅尔透镜的配光设计内容：一、概述二、设计方法三、设计步骤报告人：陈志强学号：************专业：光信15011、菲涅尔透镜概述菲涅尔透镜(Fresnel lens)又称螺纹透镜，是由法国物理学家奥古斯汀·菲涅尔（Augustin·Fresnel)发明的，他在1822年最初使用这种透镜设计用于建立一个玻璃菲涅尔透镜系统--灯塔透镜。

菲涅尔透镜多是由聚烯烃材料注压而成的薄片，也有玻璃制作的，镜片表面一面为光面，另一面刻录了由小到大的同心圆，它的纹理是利用光的干涉及扰射和根据相对灵敏度和接收角度要求来设计的，透镜的要求很高，一片优质的透镜必须是表面光洁，纹理清晰，其厚度随用途而变，多在1mm左右，特性为面积较大，厚度薄及侦测距离远。

2、基本原理假设一个透镜的折射能量仅仅发生在光学表面（如：透镜表面），拿掉尽可能多的光学材料，而保留表面的弯曲度。

（如图1-1）另外一种理解就是，透镜连续表面部分“坍陷”到一个平面上。

从剖面看，其表面由一系列锯齿型凹槽组成，中心部分是椭圆型弧线。

每个凹槽都与相邻凹槽之间角度不同，但都将光线集中一处，形成中心焦点，也就是透镜的焦点。

每个凹槽都可以看做一个独立的小透镜，把光线调整成平行光或聚光。

这种透镜还能够消除部分球差。

图1-13、光学特性使用普通的凸透镜，会出现边角变暗、模糊的现象，这是因为光的折射只发生在介质的交界面，凸透镜片较厚，光在玻璃中直线传播的部分会使得光线衰减。

如果可以去掉直线传播的部分，只保留发生折射的曲面，便能省下大量材料同时达到相同的聚光效果。

菲涅耳透镜就是采用这种原理的。

菲涅尔透镜看上去像一片有无数多个同心圆纹路（即菲涅耳带)的玻璃，却能达到凸透镜的效果，如果投射光源是平行光，汇聚投射后能够保持图像各处亮度的一致。

二、设计方法1、光源本设计光源采用给定的点源，在TP软件中可以找到格点光源来仿真。

2、目标光斑不同接收面的目标光斑有很大差异，具体如图3-9——图3-12。

基于Tracepro的菲涅尔聚光透镜设计与仿真

10.16638/ki.1671-7988.2020.13.028基于Tracepro的菲涅尔聚光透镜设计与仿真吴贺利1，杨帆2，罗晨晖2，柯婉頔2，吴满2（1.武汉外语外事职业学院机电技术学部，湖北武汉436500；2.武汉科技大学城市学院机电工程学部，湖北武汉436500）摘要：文章通过对太阳能聚光光伏发电研究中重要的聚光器菲涅尔透镜基本设计，完成太阳光的光谱数据提取与模拟、聚光器材料性能建模，并在光学仿真软件Tracepro中进行太阳光聚光光迹模拟追踪，实现太阳光光路仿真，并完成菲涅尔聚光透镜的结构设计分析以及其聚光光斑特性分析。

关键词：菲涅尔透镜；太阳光谱；光迹追踪中图分类号：P182.3 文献标识码：A 文章编号：1671-7988(2020)13-90-03Design and Simulation of Fresnel lens based on TraceproWu Heli1, Yang Fan2, Luo Chenhui2, Ke Wandi2, Wu Man2（1.Department of mechanical and electrical technology, Wuhan college of foreign language & foreign affairs, Hubei Wuhan 436500; 2.Department of Mechanical and Electrical Engineering, City college of WUST, Hubei Wuhan 436500）Abstract:In this paper, based on the basic design of Fresnel lens which is important concentrator in the research of solar photovoltaic power generation, complete the spectral data simulation of sunlight and the material performance modeling of concentrator, simulation tracking of sunlight spotlight in TracePro, realize the simulation of sunlight path, finally, Complete the structural design analysis and characteristic analysis of Fresnel lens.Keywords: Fresnel lens; Solar spectrum; Light trail trackingCLC NO.: P182.3 Document Code: A Article ID: 1671-7988(2020)13-90-03前言应用于高倍聚光光伏发电的菲涅尔聚光透镜是由法国物理学家Augustin Jean Fresnel在1822年所发明的一种透镜[1]，由多个同轴排列或平行排列的棱镜所形成的一序列不连续曲面取代了一般透镜的连续球面，因此，菲涅尔透镜结构简单，便于制造，在重量和体积上比一般透镜更轻、更薄，在设计上可以获得更大的孔径与焦距比[2]。

菲涅尔透镜设计方法介绍

The Fresnel LensCenturies ago, it was recognized that the contour of the refracting surface of a conventional lens deﬁnes its focusing properties. The bulk of material between the refracting sur-faces has no effect (other than increasing absorption losses) on the optical properties of the lens. In a F resnel (point focus) lens the bulk of material has been reduced by the extraction of a set of coaxial annular cylinders of material, as shown in Figure 1. (Positive focal length Fresnel lenses are almost universally plano-convex.) The contour of the curved surface is thus approximated by right circular cylindrical portions, which do not contribute to the lens’ optical proper-ties, intersected by conical portions called “grooves.” Near the center of the lens, these inclined surfaces or “grooves”are nearly parallel to the plane face; toward the outer edge, the inclined surfaces become extremely steep, especially for lenses of low f–number. The inclined surface of each groove is the corresponding portion of the original aspheric surface, translated toward the plano surface of the lens; the angle of each groove is modiﬁed slightly from that of the original aspheric proﬁle to compensate for this translation.The earliest stepped-surface lens was suggested in 1748by Count Buffon, who proposed to grind out material from the plano side of the lens until he was left with thin sections of material following the original spherical surface of the lens, as shown schematically in F igure 2a). Buffon’s work was followed by that of Condorcet and Sir D. Brewster, both of whom designed built-up lenses made of stepped annuli. The aspheric Fresnel lens was invented in 1822 by Augustin Jean F resnel (1788–1827), a F rench mathematician and physicist also credited with resolving the dispute between the classical corpuscular and wave theories of light through his careful experiments on diffraction. Fresnel’s original lens was used in a lighthouse on the river Gironde; the main innovation embodied in Fresnel’s design was that the center of curvature of each ring receded along the axis according to its distance from the center, so as practically to eliminate spherical aberration. Fresnel’s original design, including the spherical-surfaced central section, is shown schematically in Figure 2b). The early Fresnel lenses were cut and polished in glass – an expensive process, and one limited to a few large grooves. Figure 3 shows a Fresnel lens, constructed in this way, which is used in the lighthouse at St Augustine, Florida, USA. The large aperture and low absorption of F resnel lenses were especially important for use with the weak lamps found in lighthouses before the invention of high-brightness light sources in the 1900s. The illustrated system is catadioptric: the glass rings above and below the Fresnel lens band in the center of the light are totally-internally-reflecting prisms, which serve to collect an additional frac-tion of the light from the source. The use of catadioptric sys-tems in lighthouses was also due to Fresnel.Until the 1950’s, quality Fresnel lenses were made from glass by the same grinding and polishing techniques used in 1822. Cheap Fresnel lenses were made by pressing hot glass into metal molds; because of the high surface tension of glass, Fresnel lenses made in this way lacked the necessary detail, and were poor indeed.In the last forty years or so, the advent of optical-quality plastics, compression and injection molding techniques,Figure 1 Construction of a Fresnel lens from its correspond-ing asphere. Each groove of the Fresnel lens is asmall piece of the aspheric surface, translated to-ward the plano side of the lens. The tilt of each sur-face must be modified slightly from that of theoriginal portion of aspheric surface, in order tocompensate for the translation.Figure 2 Early stepped–surface lenses. In both illustrations the black area is material, and the dashed curvesrepresent the original contours of the lenses. a)shows the lens suggested by Count Buffon (1748),where material was removed from the plano sideof the lens in order to reduce the thickness. b)shows the original lens of Fresnel (1822), the cen-tral ring of which had a spherical surface. InFresnel’s lens, the center of curvature of each ringwas displaced according to the distance of thatring from the center, so as to eliminate sphericalaberration.a)b)© Copyright Fresnel Technologies, Inc. 20032© Copyright Fresnel Technologies, Inc. 20033and computer-controlled machining have made possible the manufacture and wide application of F resnel lenses of higher optical quality than the ﬁnest glass F resnel lenses.Modern computer-controlled machining methods can be used to cut the surface of each cone precisely so as to bring all paraxial rays into focus at exactly the same point, avoid-ing spherical aberration. Better still, newer methods can be used to cut each refracting surface in the correct aspheric contour (rather than as a conical approximation to this con-tour), thus avoiding even the width of the groove (typically 0.1 to 1 mm) as a limit to the sharpness of the focus. Even though each groove or facet brings light precisely to a focus,the breaking up of the wavefront by the discontinuous sur-face of a F resnel lens degrades the visible image quality.Except in certain situations discussed later, Fresnel lenses are usually not recommended for imaging applications in the visible light region of the spectrum.The characteristics of the aspheric “correction”The grinding and polishing techniques used in the manufac-ture of conventional optics lead to spherical surfaces. Spher-ical surfaces produce optics with longitudinal spherical aberration, which occurs when different annular sections of the optic bring light rays to a focus at different points along the optical axis. This phenomenon is illustrated for a positive focal length, plano-convex conventional lens in Figure 4 (in all optical illustrations in this brochure, light is taken to propagate from left to right). The lens illustrated is a section of a sphere with 1" (25 mm) radius of curvature, 1.6"(36 mm) in diameter; the index of refraction of the material is 1.5, typical both for optical glasses and for our plastics materials. The focal length of the illustrated lens is thus 2"(50 mm), and the aperture is /1.3. As is evident from the ﬁgure, the longitudinal spherical aberration is very strong.Single-element spherical lenses are typically restricted to much smaller apertures (higher –numbers) than this,because longitudinal spherical aberration of the magnitude shown in Figure 4 is generally unacceptable. Figure 5 shows an aspheric lens of the same focal length and –number;note that the surface contour is modiﬁed from the spherical proﬁle in such a way as to bring rays passing through all points on the lens to a focus at the same position on the opti-cal axis. A lens made with the aspheric proﬁle illustrated in Figure 5, therefore, exhibits no longitudinal spherical aber-ration for rays parallel to the optical axis.Since Fresnel lenses are made from the beginning to the correct aspheric proﬁle, the notion of “correcting for spheri-cal aberration” is not meaningful for F resnel lenses. The lenses are more accurately characterized as “free from spherical aberration.” The combination of the aspheric sur-face (which eliminates longitudinal spherical aberration)and the thinness of the lens (which substantially reduces both absorption losses in the material and the change of those losses across the lens proﬁle) allows F resnel lenses with acceptable performance to be made with very large apertures. In fact, F resnel lenses typically have far larger apertures (smaller –numbers) than the /1.3 illustrated in Figure 4.Figure 6 compares an aspheric plano-convex lens with an aspheric F resnel lens (the F resnel lens’ groove structure isf f f f f Figure 3 The light from the St Augustine, Florida (USA) light-house, showing the glass Fresnel optical system used in the lighthouse. The optical system is about 12 feet (3.5 m) tall and 7 feet (2 m) in diameter.Figure 4Illustration of longitudinal spherical aberration.The rays shown were traced through an /1.3 spherical-surface lens; the focus is evidentlyspread out over a considerable distance along theoptical axis.f© Copyright Fresnel Technologies, Inc. 20034tive focal length (EFL), quential, so that the Fresnel lens.focus. (This type of F application and reversed.for a given focal length tion (where object distances, i.e. the conjugates), and are found to be and for the conjugate ratio 3:1. Even though a lens may be designed for conjugates in some particular ratio, it can be used at other ﬁnite conjugate ratios as well. The error introduced is usually reasonably small.Fresnel lenses are normally fabricated so that they are correct for the case of grooves toward the collimated beam,plano side toward the focus (grooves “out”). They can, how-ever, be fabricated so that they are correct for the case of grooves toward the focus, plano side toward the collimated beam (grooves “in”). In this case, there is no refraction at all on the plano side for a collimated beam traveling parallel to the optical axis. In the grooves “out” case, both surfaces refract the light more or less equally. The case of grooves toward the collimated beam (“out”) is the optically preferred case. The main difference is that in the grooves “in” case, the grooves at the outer periphery of the lens are canted at muchf f f 1f ⁄1i ⁄1o ⁄+=i 4f 4f 3⁄ Figure 6 Comparison between an aspheric conventionallens and an aspheric Fresnel lens, illustrating the optical quantities discussed in the text.smaller angles to the plano surface than they would be in spherical or grooves “out” lenses. Because the angles made with the plano surface are relatively small toward the periphery of the lens, any small warpage or tilt of the lens surface, or any small deviation of a light ray from parallelism with the optical axis, leads to a very large deviation from the ideal in the angle between the light ray and the lens surface.These errors lead directly to a decrease in the collection efﬁ-ciency of a grooves “in” lens relative to a grooves “out” lens of the same focal length and –number.A third case which is sometimes encountered is that of a Fresnel lens which is correct for grooves “out,” used with its grooves toward the focus (grooves “out” turned groovesf© Copyright Fresnel Technologies, Inc. 20035for angles of intersection between a light ray and the normalto a surface larger than the critical angle = ,where the ray is traveling from a medium of index of refrac-tion into a medium of index of refraction . It is evident that total internal reﬂection only occurs for , since in the case is greater than π /2 and therefore not physically meaningful.) This phenomenon makes the portion of a grooves “out” lens turned grooves “in” lens past about /1 useless. The phenomenon is easily observed as an appar-ent “silvering” of the outer portion of a grooves “out” lens when its grooves are turned to face the shorter conjugate.Total internal reﬂection does not occur for grooves “out”lenses used in their correct orientation because the only large-angle intersection between the light and the lens sur-face occurs at a transition from low to high refractive index.MaterialsOur standard materials for visible light applications are acrylic, polycarbonate and rigid vinyl. These materials are suitable for some near infrared applications as well, as dis-cussed later in this brochure. Figure 9 shows useful transmis-sion ranges for a variety of plastics materials. Materials suitable for infrared applications are described in detail in our POLY IR® brochure.The ﬁrst step in choosing a material is to match the mate-rial to the spectral domain of the application. Other consid-erations include thickness, rigidity, service temperature,weatherability, and other physical properties listed in the table of properties on the next page.AcrylicOptical quality acrylic is the most widely applicable mate-rial, and is a good general-purpose material in the visible. Its transmittance is nearly ﬂat and almost 92% from the ultravi-olet to the near infrared; acrylic may additionally be speci-ﬁed to be UV transmitting (UVT acrylic) or UV ﬁltering (UVF acrylic). The transmittance of our standard acrylic materials between 0.2 µm and 2.2 µm is shown in F igure 10 for a thickness of 1/8" (3.2 mm). Standard acrylic thicknesses are 0.060" (1.5 mm), 0.090" (2.3 mm), and 0.125" (3.2 mm). Rigid vinylRigid vinyl has a number of characteristics which make it both affordable and very suitable for certain applications. It has a high index of refraction; it is reasonably inexpensive;and it can be die-cut. However, polycarbonate has very sim-ilar properties, without the problems associated with rigid vinyl, and its use is encouraged over that of rigid vinyl in new applications. Rigid vinyl has about the same tempera-ture range as acrylic and is naturally ﬁre-retardant. The trans-mittance of rigid vinyl between 0.2 µm and 2.5 µm is shown in F igure 11 for a nominal thickness of 0.030" (0.76 mm).Standard thicknesses for rigid vinyl are 0.010" (0.25 mm),0.015" (0.38 mm), 0.020" (0.51 mm), and 0.030" (0.76 mm). PolycarbonatePolycarbonate is spectrally similar to acrylic, but is useful at higher temperatures and has a very high impact resistance.The transmittance of polycarbonate between 0.2 µm and 2.2 µm is shown in Figure 12 for a nominal thickness of 1/8"θc sin –1n n '⁄()n n 'n 'n >n 'n <θc f Figure 7 Illustration of the strong asymmetry of the asphericFresnel lens. The illustrated lens is correct for the grooves facing the longer conjugate (grooves “out”). When it is turned around so that thegrooves face the shorter conjugate (grooves “out” turned grooves “in”), on-axis performance suffers. As discussed in the text, however, in the case where the grooves must face the shorter conjugate, a grooves “out” lens turned grooves “in” has some advantages over a lens correct for grooves “in.”Figure 8 Aspheric Fresnel lens correct for the grooves facingthe shorter conjugate (grooves “in”).© Copyright Fresnel Technologies, Inc. 20037Figure 12 Transmittance of polycarbonate as a function ofwavelength. Sample thickness = 1/8" (3.2 mm) nominal.Figure 13 The three typical configurations for producing acollimated beam of light: lens only, mirror only, and a combination of lens and mirror.(3.2 mm). Standard thicknesses available in polycarbonate are 0.010” (0.25 mm), 0.015” (0.38 mm), 0.020” (0.5 mm),0.030" (0.76 mm), 0.040” (1 mm), 0.050" (1.3 mm), 0.060"(1.5 mm), and 0.125" (3.2 mm).Focal length in a given materialThe focal lengths listed in the table at the end of this bro-chure are the effective focal lengths in optical grade acrylic.The effective focal length is different when a lens is manu-factured from a different material, but is easily calculated.The effective focal length in any other material iswhere is the refractive index of the material in question.T ypical Fresnel Lens ApplicationsCollimatorProducing a collimated beam from a point source could be said to be a perfect application for F resnel lenses. In this case the spatial distribution of light from the point source tends to favor the central portion of the lens, so that the total lens transmittance can be as much as 90%. The best optical results are obtained when the grooved side faces the longer conjugate.In practice, the point source is never actually a point source, but is extended, so that the imperfection of the coni-cal approximation to the aspheric groove shapes is never noticed.Figure 13 shows the three cases usually encountered in collimation: lens only, mirror only, and lens/mirror combina-tion. Note that adding a lens to the mirror-only case would produce extremely poor results. The mirror must be specially designed to image the light source very near itself.CollectorFocusing a collimated beam of light at a point is another popular use of F resnel lenses, and one for which F resnel lenses are at least adequate. Again, the grooved side toward the inﬁnite conjugate is the optically preferred conﬁgura-tion. Because the collimated beam is assumed to be uni-form, there is a substantial loss through the lens in this case for marginal rays. The loss is caused by the increasing angles of incidence and emergence as the margin of the lens is approached. It can be predicted using Fresnel’s equations,which describe the reﬂection and transmission of light at an interface between media of differing refractive index. The loss due to reﬂection is graphed as a function of the angle between the incident ray and the (plane) interface in Figure 14.There are two additional losses which must be considered in demanding applications. One is due to the unavoidable width of the vertical step between grooves. This loss is gen-erally reasonably small in well-made F resnel lenses, but light scattered from the step brightens the focal plane and thereby reduces the contrast of an image.The other loss is due to shadowing and blocking effects caused by the vertical step. This loss does not exist for rays parallel to the optical axis striking grooves “in” lenses, but is present in all other cases. For rays making a large angle (20°EFL 1.491–n 1–--------------------EFL acrylic ,=n© Copyright Fresnel Technologies, Inc. 20038cant loss. F and invites your inquiries.Condenserdenser lens will even be frosted.plano–plano sheet.Field lenses (Fresnel screen “brighteners”)A Fresnel lens can be used to redirect the light at the edges of a frosted rear-projection display screen toward the viewer’s eyes, thus eliminating the “hot spot” often observed in such screens by brightening the edges of the display.Screens of this type include camera focusing screens. The grooves must face the light source in this application; the grooves often must therefore face the shorter conjugate, an exception to the usual rule.Conjugates for the ﬁeld lens should be the distance from the projector lens on the grooved side, and the distance to the viewer on the frosted side. Fresnel Technologies, Inc. can supply suitable lenses with the plano side either optically polished or frosted.MagniﬁersAn aspheric lens is an ideal magniﬁer from several points of view. When used at its conjugates, there is no distortion of the image (a rectangular grid remains a rectangular grid afterwhere is the lens’ focal length. This is usually taken astrue for a virtual image at inﬁnity. A magniﬁer with a focallength of 50 mm will then have a power of 5X.Because they can be made large, Fresnel lenses are gen-erally used to magnify objects slightly, perhaps as little as 1.2 or 1.5X. One usually expects to see the entire object at once within the Fresnel lens, so that the lens must then be 1.2 or 1.5 times the size of the object in both length and width.Please observe caution when using a F resnel lens as a magniﬁer around strong light sources, lasers, and in sun-light.ImagingFresnel Technologies, Inc. does not generally recommend its Fresnel lenses for image formation in the visible region of the spectrum, but there are some important exceptions.θff M θ'θ---250mm f-------------------== ,Imaging generally demands some substantial ﬁeld of view, or the image is uninteresting. With simple plano-convex lenses, coma degrades the image only a degree or so off axis. Chromatic aberration blurs the image as well. As in camera or copy lenses, the faster the lens (the smaller the f–number), the worse the problem becomes – and the small f–numbers of Fresnel lenses are very tempting.The important exceptions include two cases: rays pre-cisely parallel to the axis of the lens (laser rangeﬁnder, for example) and imaging onto a large detector (for instance, a pyroelectric detector or a thermopile).Imaging can be treated as a generalization of collection. Near-infrared applicationsAll of the above applications remain relevant into the near infrared, and the preferred materials (acrylic, polycarbonate, and rigid vinyl) from the visible region can be used to about 1.3 µm without difﬁculty. The refractive index of each of these materials is slightly lower there, but our plastics are not strongly dispersive.Process monitoring at 3.4 µmAll hydrocarbons – solids, liquids, and gases – exhibit a strong absorption of 3.4 µm radiation. (3.4 µm is the wave-length of the C–H stretch.) POLY IR® 5 is specially formu-lated to contain no hydrogen, and is thus free of the C–H stretch absorption. It can be used to monitor hydrocarbons in a wide variety of applications: uses have ranged from methane monitoring above landﬁlls to process control on production lines.Passive infrared applicationsThe collection of infrared radiation emitted by humans and other warm-blooded animals has become a major applica-tion area for Fresnel lenses. This application requires that the lenses be transparent between approximately the wave-lengths of 8 µm and 14 µm, the region of maximum contrast betwen warm bodies and typical backgrounds.Passive infrared applications are discussed in our bro-chure on POLY IR® infrared-transmitting materials, and in the notes accompanying our passive infrared lens array data sheets.ThermometryOptical pyrometry can be extended toward infrared wave-lengths (and therefore lower temperatures) with appropriate sensors and optics. Fresnel lenses made from our POLY IR®infrared-transmitting materials are used with a variety of bolometers and thermopiles. Our POLY IR® 1 and 2 materi-als are most appropriate for higher temperatures (shorter wavelengths); they can be used for lower-temperature appli-cations as well. Our POLY IR® 4 material is also useful there, particularly in white. Please refer to our POLY IR®infrared-transmitting materials brochure for more informa-tion.Solar Energy CollectionFresnel lenses have often been used as concentrators for photovoltaic cells or arrays of cells in solar energy devices. We can certainly recommend them for this application,though reﬂectors and nonimaging concentrators are often superior. However, Fresnel Technologies, Inc. does not man-ufacture any Fresnel lenses with uniform energy distribution over typical photovoltaic cell areas; our products all have a damaging “hot spot” in the focal plane. We therefore do not recommend our own products for this application; neither do we manufacture mirrors or nonimaging collectors useful for solar devices.Please use caution with our Fresnel lenses in sunlight. The sun's image can easily ignite ﬂammable materials quickly, and can damage materials which are not ﬂammable. These cautions particularly apply to clothing, skin, and eyes, in both sunlight and laser light.Special OpticsFresnel Technologies, Inc. offers several types of optical ele-ments related to Fresnel lenses. These include:Cylindrical Fresnel lensesA cylindrical Fresnel lens is a collapsed version of a conven-tional cylindrical lens. These lenses can be used in any application which requires focusing in only one dimension of the focal plane. In some cases, two separate cylindrical lenses may be combined to obtain different focal properties in the x and y dimensions of the focal plane; these conﬁgu-rations are representative of one type of anamorphic optic. A variety of cylindrical Fresnel lenses is available, with typical –numbers between /1 and /2. Both positive and negative focal lengths are available.Fresnel prism (array of prisms)A Fresnel array of prisms is made up of many small prisms, each with the same vertex angles as the large prism mim-icked by the array. This type of array allows the redirection of light with the advantage of constant transmission over the entire array, instead of the varying losses of a comparably capable conventional prism. The lack of bulk may also be used to advantage when redirection of light is required and space is limited. Not all the incident light emerges on the other side of the array, because some undergoes multiple reﬂections or refractions at various surfaces, or is totally internally reﬂected. For our item #400, a collimated beam of light incident on the smooth side is tilted by 20°. The angle of minimum deviation, as deﬁned in optics texts, is 15°. Hexagonal lens arraysWe manufacture two types of lens arrays with closely-packed hexagonal lenslets: those with conventional lenslets and those with Fresnel lenslets. Fresnel lenslets are appropri-ate for larger apertures and shorter focal lengths, where the thickness and weight of conventional lenslets would be pro-hibitive.Rectangular lens arraysAll of our catalogued rectangular lens arrays are arrays of Fresnel lenses, and they are all actually square arrays. We offer some types correct for the inﬁnite conjugate on the smooth side, as well as the more usual circumstance of the inﬁnite conjugate on the grooved side. All are made using Fresnel lenses with aspherically contoured groove surfaces f f f© Copyright Fresnel Technologies, Inc. 20039© Copyright Fresnel Technologies, Inc. 200310and constant groove depths. Rectangular lens arrays can be used to illuminate an area evenly with a matching array of light emitting diodes, or to track motion via an array of pho-todiodes. They can be cut into strips to form linear arrays.Lenticular arraysA lenticular array is a closely-packed array of conventional cylindrical lenslets. These arrays are quite suitable as one-dimensional diffusers, and some are acceptable for 3D pho-tography (the focus must be located at the back (plano) side of the array). Light striking the lenticular array is diffused only in the direction across the cylindrical lenslets; there is no diffusion along the lenslets. As the –number of the lens-lets decreases, the angle of diffusion increases depending on the relative size of the light source as compared with the lenslet spacing. A variety of diffusion angles are possible as our arrays have lenslet –numbers ranging from /1.2 to /5.4. Often it is desired to diffuse light in more than one dimension. For this case, we offer crossed lenticular arrays,such that the same or a different lenticular array can be molded on the back side of the sheet.Special ProductsFresnel Technologies, Inc. through its predecessors has man-ufactured F resnel lenses since the 1960s and has gained extensive experience in custom lens fabrication. A large variety of standard lens products is offered, and these stan-dard products may be modiﬁed to suit individual needs at a small additional cost. Fresnel Technologies, Inc. also offers custom lens array systems which may be developed to achieve certain performance requirements. Some of the cus-tom services provided are:Lens FrostingSpeciﬁc Modiﬁcation of Standard Lenses Diffusing SurfacesCustom Lens Array Tooling and ProductionCutting of Lenses and Lens Arrays to Custom Shapes Custom Material DevelopmentWe invite your inquiries about these services.BibliographyA good entry level reference on optics, both geometrical and physical, is E. Hecht, Optics , 3nd edition, Addison-Wesley (Reading, MA), 1997.A more advanced treatment of optics can be found in Princi-ples of Optics , Max Born and Emil Wolf, 7th edition, Cam-bridge University Press (Cambridge, UK), 1999.For a thorough discussion both of the limitations of imaging optical systems in the collection of radiant energy and of the nonimaging collectors which can be used to collect energy efﬁciently, see W.T. Welford and R. Winston, High Collec-tion Nonimaging Optics , Academic Press (San Diego), 1989.A very interesting article describing an 1822 monograph on lighthouse lenses by F resnel is B.A. Anicin, V .M. Babovic,and D.M. Davidovic, Am. J. Phys. 57, 312 (1989).f f f f Lighthouse lens illustration (F igure 3) created with Canvas 3.5, courtesy Deneba Software, Miami, F lorida, USA and the St Augustine Lighthouse and Museum, St Augustine,Florida, USA.The Fresnel Technologies Product ListAt the end of this brochure are listed the standard stock opti-cal elements that Fresnel Technologies Inc. offers in optical quality acrylic. In the list values for optical quality acrylic material only are shown; some of the speciﬁcations apply also to other materials. Fresnel size refers to the size of the optical active area. Overall size refers to the dimensions of the optical element, possibly including a border for mount-ing purposes. All 11” x 11” overall size items have a 1.2”(31mm) x 45° chamfer at each corner. Thickness is speciﬁed for the border area (not the grooved area) and carries a toler-ance of ±40%. Much improved tolerances are possible:please contact our factory for assistance. The single piece prices listed are current at the catalog copyright date, and may be changed at any time. Contact us for the latest pricing and for quantity discounts, which can be substantial.Many of our positive focal length F resnel lenses are offered either as blanks with overall size tolerances of ±0.050" or as well centered disks with tolerances on the diameter of ±0.005" in the sizes less than 7" (180 mm) and ±0.008" in the larger sizes, centered to 0.010" to the optical axis. Improved tolerances can be held, and other cuts can be accommodated as special orders. The negative focal length Fresnel lenses listed are the only ones that are offered as stock items; a negative focal length version of most of our positive focal length Fresnel lenses is available as a special order.The grooves and the optical axis plane of items #72–85.1lie in the direction of the second dimension listed for the Fresnel size. There is no border along that dimension, but there is a 1/8" border perpendicular to the grooves, except for item #85.The sampler sheet (item #160) contains nine 2.5" diame-ter lenses in an array on a single sheet. The focal lengths of these lenses are: 2.4" (two), 2.6", 2.8", 3.0", 3.3", 3.15", 3.3",3.6", and 3.9".The lenticular arrays, items #200–260, are normally sup-plied with positive focal length lenslets. Negative focal length arrays are also available on special order, and work well as diffusers in some instances. If an array is to be used for 3D photography, please specify this in your order, so that we can send an array with thickness in the proper range.Item #300 is made of conventional lenslets (the "F ly’s-Eye" lens array) and it is suitable for one type of 3D photog-raphy, for moiré pattern work, or as a high efﬁciency diffuser.Item #310, suitable as a diffuser, is made of Fresnel lenses.When used as diffusers, both items diffuse light in all direc-tions. These arrays are normally supplied with positive focal length lenslets, but can be supplied with negative focal length lenslets upon request.The triangle formed by each prism in items #4xx has angles as shown in the columns marked “Facet angle with base.” This refers to the angle that each refracting surface makes with the plano side of the prism array. The thickness is measured from the center of the groove to the smooth side.。

用于光伏系统新型菲涅耳线聚焦聚光透镜设计

光子学报第31卷第2期 V o l131N o12 2002年2月 A CTA PHO TON I CA S I N I CA Feb ruary2002　用于光伏系统新型菲涅耳线聚焦聚光透镜设计Ξ汪　韬　李　辉　李宝霞　赛小锋　高鸿楷(中国科学院西安光学精密机械研究所,光电子学室710068)摘　要　根据边缘光线原理,优化设计太阳电池及光伏系统的菲涅耳线聚焦聚光透镜1设计光学聚光率为18×,可用于空间、地面光伏系统的聚光系统1分析了其集光角特性,表明该菲涅耳线聚焦棱镜具有大的集光角(±7°)1关键词　太阳电池;菲涅耳透镜;集光角0　引言近年来,基于太阳能、风能等可再生能源技术发展迅速1特别是基于太阳能光伏发电技术,为空间卫星供电的电源系统和地面光伏发电系统,为未来解决能源问题提供了新的广阔前景1但其面临发电价格高昂和太阳电池材料紧缺、昂贵的问题,需要进一步地降低成本和提高效率1为减少太阳电池片的实际用量,人们早已开始了太阳电池聚光器的研究1聚光系统主要为反射式1(如CPC、S M T S等)和透射式(F resnel,全息等)两种1特别是Ga InP2 GaA s Ge级联太阳电池的研制成功2,其较Si电池效率高、抗辐射、耐高温1非常适用于聚光型太阳电池1而且随光学树脂的应用发展,如聚碳酸酯、PMM A(聚甲基丙烯酸甲酯)和聚苯乙烯等,具有耐冲击强度高、相对密度小,透过率高,在太阳光谱的013～2Λm范围内透过率达92%以上,与光学玻璃相差无几1其光学性能优良,抗老化,成型工艺简单、产品成本低廉1利用光学树脂透镜和级联太阳电池合成的聚光型太阳电池极大地提高单位电池片产生的电量1大大降低了发电成本,提高了太阳能光伏发电的竞争力3,41早先点聚焦菲涅耳聚光透镜具有高的聚光率,但其必须对太阳进行二维跟踪1我们采用三维优化设计,考虑太阳能电池的热退化效应,设计具有较大集光角、只对太阳进行一维跟踪的线聚焦菲涅耳聚光透镜11　设计原理菲涅耳聚光透镜其根本目的为增加太阳电池上的太阳辐射功率的密度1由于菲涅耳非成象光学,无需考虑象的精度,在入射角范围内将能量聚焦于一定范围内,无需点聚焦51遵循折射原理(Snell定理)n1sin(i1)=n2sin(i2)当采用最小偏折角棱镜时,菲涅耳聚光透镜反射损失为最小,即为入射光线与顶面的法线的夹角等于出射光线与底面法线的夹角712　设计方法考虑因素:1)棱镜组对光的吸收随棱镜的厚度增加而变大,同时由于棱镜元的底边缘造成的通光量的损失也急剧变大,所以棱镜的厚度要尽可能的薄1单棱镜太薄将造成实际加工的困难,我们取其最大厚度为1mm12)菲涅耳聚光透镜的焦距直接影响电池组件集光角和光学聚光率的大小,同时影响电池组件的体积13)电池组件集光角的设计,集光角越大,电池组件对太阳的入射的方向不敏感,对系统瞄准太阳的能力要求低,同时它也直接影响光学聚光率的大小1对±Η截面内入射角,不同季节,每天太阳倾角的变化不同,正Ξ国家自然科学基金资助项目　收稿日期:2001206213午前后4小时夏天变化为±2°,冬天变化为±6°,太阳本身的有限长角为±015°,加上聚光器斜率误差,所以菲涅耳聚光棱镜的集光角设计值≥±615°14)折射率n 采用太阳电池吸收光谱的中心波长600nm 处折射率为114881先由0位置与接受面的相对位置设计第一棱镜元,确定其参量棱镜顶角角度Α1、棱镜倾角Β1、棱镜元宽度X 1,递进优化之1再在棱镜1基础上连接设计棱镜2,确定其参量Α2、Β2、X 2,递进优化1以此类推,得到第n 棱镜参量(Αn ,Βn ,X n )1由此得到棱镜组参量(Α1Α2…Αn ,Β1Β2…Βn ,X 1X 2…X n )1如图1,设计流程图见图21采用new ton 法逼近,至满足判据,结束该棱镜元参量的搜索1进行下一棱镜元参量的搜索1判据为 d x -d 0 <Ε,式中图1　光线在棱镜上的折射示意图F ig .1　Schem atic of rays refracti on on the F resnel lens 图2　菲涅耳线聚焦聚光棱镜的设计流程图 F ig .2　F low chart of the op ti m um line 2focu s F resnel len sd x 为入射角为Η时的光线的偏折角,d 0为光线投射到电池表面所需的偏折角,Ε为极小量1Η、Ω分别为入射角在棱镜端面和垂直端面内的投影1光学聚光率定义为E l E o ,E l 为有棱镜情况下光辐射密度,E o 为无棱镜情况下光辐射密度11光学聚光率为会聚比与光效率的积1总的光学聚光率为各棱镜元的光学聚光率的和1计算公式为c (Η,7)=6nT (Η,7,n )(A l (n ) A o (n ))T (Η,7,n )为第n 棱镜的透过率,A l (n )为第n 棱镜的出射孔径,A o (n )为第n 棱镜的入射孔径1其设计外形如图3,其光学聚光率见图41 图3　菲涅耳线聚焦聚光棱镜外形截面图 F ig .3　Schem atic of truncated the op ti m umline 2focu s F resnel lens 图4　不同Η、7菲涅耳线聚焦聚光棱镜的聚光率 F ig .4　Op tical concen trati on rati o of the op ti m umline 2focu s F resnel len s in differen t Η,73　损失分析太阳光穿过菲涅耳棱镜,在棱镜上表面和下表面分别发生反射1棱镜倾角变大时,入射角变大,反射损失变大,透射光通量与入射角和棱镜顶角有关,当入射角与出射角相等时,透射光通量为最大1另外棱镜元的边缘也造成通光量的损失1当入射角Η太大时,一部分光线将投射到棱7912期江韬等1用于光伏系统新型菲涅耳线聚焦聚光透镜设计镜的底边,只是这部分光线偏离预定方向,无法投射到太阳电池表面1所以应尽量减小棱镜元的底边宽度1即减少棱镜的厚度14　集光角特性分析如图4,在±7角平面内,其集光角达到±60°,光学聚光率对入射角的变化不敏感1在±60°之间都有较高的光学聚光率1这样在一天内不动电池组件从上午8时至下午4时都能充分利用太阳光1在±Η角平面内,其集光角达到±7°,具有较宽的集光角,大于太阳一天内南北方向的仰角变化15　焦距的影响如图5,相同的入射孔径,不同的焦距情况下的光学聚光率(7=0),大的焦距(f =360mm )有相对高的光学聚光率达21,但其集光角为±4°1当焦距变小(f =200mm )其集光角达到±8°,但其图5　不同焦距下的光学聚光率和集光角特性 F ig .5　Effect on the op tical concen trato r rati oof Ηand erro r to lerance (7=Η)光学聚光率降低为161原因是焦距变小相应其f ×Η值减小,其集光角变大1焦距变小时菲涅耳聚光棱镜边缘部分偏折角变大,其反射损失加重,光效率降低,导致整个菲涅耳聚光棱镜的光学聚光率下降1在实际应用中,菲涅耳聚光棱镜应有尽量大的集光角,但是集光角设计的变大则造成光效率的相应减小,应考虑实际应用情况作相应的调整1理论上随电池表面光通量增加短路电流呈线性增加,开路电压呈指数增长1而电池的漏电电流不变化1这样V 增加,(c ×I -I l ) (I -I l )>c ,即电流增幅大于c 倍1这样电池输出功率为原先的c 倍以上,电池效率也有所升高1光学聚光率c 不能太高,否则电池表面温度太高导致电池系列电阻变大,电池效率将有所下降1以AM 115条件下1m 2太阳电池效率19%记,输出功率P 为190W ,配备18倍菲涅耳线聚焦聚光透镜后,由于电池表面温度升高不多,电池效率损失微小6,电池输出功率可达3400W 左右1大大提高了单位电池面积的发电量,降低了太阳电池组件的成本,提高了光伏发电的竞争力16　结论设计一种用于太阳电池的菲涅耳线聚焦聚光透镜,考察了焦距对其光学聚光率的影响1理论上棱镜越细密越好,但由于实际加工有一定的精度限制,所以应根据情况取舍1据此设计透射式的菲涅耳线聚焦聚光透镜,聚光量适中C =18,太阳电池的温度不高,减缓太阳电池的热退化效应,有利于延长其使用寿命1并且其较以往(±215.)具有较大的集光角±7.,便于实际应用1无须太阳跟踪系统,只需随着不同季节太阳纬度的变化,调整太阳电池组件南北方向的倾角1参考文献1　W elfo rd W T ,W in ston R .T he op tics of non i m aging concen trato rs .N er Yo rk :A cadem ic P ress ,1978,132～1382　Yeh Y C M ,et al .A dvances in p roducti on of cascade so lar cells fo r space .26th IEEE Pho tovo ltaic SpecialistsConference ,1997:827～8303　O ′N eillM J ,et al.Inflatab le len ses fo r space pho tovo ltaic concen trato r arrays .26th IEEE Pho tovo ltaic Specialists Conference ,1997:853～8564　Spence B R ,et al .T he scarlet array fo r h igh pow er GEO satellites .26th IEEE Pho tovo ltaic Specialists Conference ,1997:1027～10305　L o renzo E ,L uque A .F resnel len s analysis fo r so lar energy app licati on s .A pp l Op t ,1982,20(17):2941～29456　Ku rtz S R ,O ′N eillM J .E sti m ating and con tro lling ch rom atic aberrati on lo sses fo r tw o 2juncti on ,tw o 2term inal devicesin refractive concen trato r system s.25th IEEE Pho tovo ltaic Specialists Conference ,1996:361～3647　K ritchm an E M ,et al .(1979b )H igh ly concen trating F resnel L en ses .A pp l Op t ,1980,18(15):2688～2695891 光子学报 30卷A NE W D ESIGN OF L INE -FOCUS FRESNEL L ENSFOR PHOT OVOL TA I C POW ER S Y STE MW ang T ao ,L i H u i ,L i B aox ia ,Sai X iaofeng ,Gao HongkaiX i′an Institu te of Op tics and P recision M echan ics ,Ch inese A cad e m y of S ciences 710068R eceived date :2001206213Abstract A n arched line 2focu s F resnel len s is designed fo llow ing the edge ray p rinci p le by op ti m um m ethod .T h is k ind of F resnel len s cou ld be u sed in so lar concen trato r of sp ace and terrestrial p ho tovo ltaic pow er system .It ′s easier to track the sun in on ly one single ax is .It has op tic concen trato r rati o as 18.It also has better accep tance angle and low co st .Keywords F resnes len s ;So lar concen trato r ;A ccep tance angleW ang Tao w as bo rn in Shaanx i ,Ch ina ,in 1974.H e received the B .S degree and M .S degree from the N o rthw est U n iversity in 1996and 1999resp ectively .A t p resen t ,he is a Ph .D degree candidate in X i ′an In stitu te of O p tics and P recisi on M echan ics ,Ch inese A cadem y of Sciences .H is p resen t in terest is p ho tron ic m aterials and devices 19912期江韬等1用于光伏系统新型菲涅耳线聚焦聚光透镜设计。