(完整版)基于菲涅尔透镜的配光设计
均匀菲聂耳透镜
均匀菲涅耳透镜一、理论分析：LED 菲涅耳透镜折射面的一个切面如下图所示，取透镜中心为Y 轴，径向为X 轴，为简化问题，将LED 简化为原点处的Lambertian 点光源。
设计目标：求解使照度均匀分布的菲涅耳纹曲线方程：z=f(y)——阶梯函数。
如何实现：理论上对于Lambertian 光源，实现均匀照明需要：max max sin sin θθ=R r 其中l angle R *2max = ，angle 为设计透镜的聚光角度，l 为投射距离。
龙格库塔法求解z=f(y)需要的参数： 1、三个关键表达式：),(z f θω= ),(z f y θ= ),(z f d dz θθ= 和 ),(z θ 的一个初值。
2、自变量θ的取值范围数组： ]::[Start Stop step θθ。
3、拟合方程。
求解分析：菲涅耳纹外侧弧为有效弧段，可用类似均匀平凸程序分段求解，需要确定的参量是每段的初值。
菲涅耳纹内侧弧须与透镜内光线走向平行，以减少对光线的干扰。
需要确定的参量是光线经过分段点的角度。
设置参数：angle 、d 、1t 、 2t 、l 。
))sin (tan(arcsin )(tan n d z d y θθ-+=(1))))sin (tan(arcsin )(tan sin arctan()arctan('max zl n d z d R z l y r c --+⋅-=--=θθθω （2）2/1222/1222/32222)sin (sin sin sin cos )sin ()sin (cos cos θθωθωθθθθθ-+----⋅+-=n n n z n d d dz （3）第一段：初始条件：0=c θ , ),(),(21t t d z c ++=θθ ，定义域：]::[max θθstep c求解过程：由（1）、（2）、（3）和初始条件、定义域 ，使用四阶Runge-Kutta 法迭代可求出曲线上的一系列点的坐标。
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。
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.。
基于Zemax软件的大齿距等厚菲涅尔透镜的设计_徐欢
文章编号:1007-6735(2007)01-0099-04收稿日期:2006-02-27作者简介:徐 欢(1980-),女,硕士研究生.基于Zemax 软件的大齿距等厚菲涅尔透镜的设计徐 欢, 李湘宁, 周 果(上海理工大学光学与电子信息工程学院,上海200093)摘要:介绍了在Zemax 软件中运用多重组态进行大齿距等厚菲涅尔透镜设计的方法,并结合实例进行了设计研究,提出了用Zemax 软件设计大齿距等厚菲涅耳透镜的一种方案.通过对设计结果进行模拟,证明了其可行性.关键词:菲涅尔透镜;多重组态;Zemax 软件;大齿距;等厚中图分类号:O 435 文献标识码:ADesign of Fresnel lens with big grooves and equalthickness based on the software ZemaxXU Huan, L I Xiang 2ning, ZHO U Guo(Co llege o f O ptics and Electronics Engineering,University o f Shanghai for Science and Techno lo gy,Shanghai 200093,China)Abstr act:The design method of Fresnel lens which has big grooves and equal thickness is introduced by application of muti configuration function in the software Zemax.Via an example,the problem how to use many functions of Zemax to design Fresnel lens with big grooves and equal thickness is discussed and its feasibility is proved.Key words:Fr e snel lens;muti c onf igur ation ;Zemax sof tware;big grooves;equal thickne ss 菲涅尔透镜是由一系列同心棱形槽构成的光学系统,每个环带都相当于一个独立的折射面,这些棱形环带均能使入射光线会聚到一个共同的焦点.因此,消球差是菲涅尔透镜固有的特点.菲涅尔透镜有时亦称环带透镜、波纹(或锯齿)透镜和螺纹透镜,它的特点是薄、轻(通常用塑料制成)及孔径大,并且可利用复制技术精确地大批生产.现代菲涅尔透镜不仅可以作聚光器、照明器和放大镜用,而且在其他成像系统中也得到了广泛应用.传统的菲涅尔透镜的设计是通过计算确定其技术参数,如槽根半径、槽峰半径及槽宽等,这样做比较精确,但过于烦琐.采用计算机软件来完成则可避免大量的光学计算,但对于目前使用最广泛的光学设计软件Zemax 而言,一般的具有细小齿距(螺距小、深度浅)的菲涅尔透镜可用其序列模式下的菲涅尔面(Fresnel)来直接进行设计和模拟,并可直接对其进行优化,得到一个较好的设计结果.但对于大齿距的菲涅尔透镜,即齿距相对于透镜的孔径来说较大的时候,这种面就不能够很好地建模.Zemax 非序列模式可以对这种较大的菲涅尔透镜进行模拟,但其缺点是无法对其进行优化,因而不能直接设计.所以,针对这个问题,本文结合设计实例得出了利用Zemax 软件中多重组态的功能来完成大齿距等厚菲涅尔透镜设计的方案.上海理工大学学报第29卷 第1期J.University of Shanghai for Science and TechnologyVol.29 No.1 20071 设计原理菲涅尔透镜是一个大孔径、适用于小视场的光学系统,它与非球面透镜的作用相同,但其形状与非球面透镜不同.非球面透镜表面是连续的,而菲涅尔透镜是由若干个以光轴为中心的圆环组成.在Ze 2max 软件中,序列模式下的Fresnel 面就是利用这个原理模拟的,它与非球面透镜具有相同的曲面方程z =cy21+1-(1+k)c 2y2+E Ni=1A 2i y 2i(1)式中,c 为表面中心处的曲率;y 为径向高度;k 为二次曲面系数;A i 为非球面系数.其中,k <-1为双曲面,k =-1为抛物面,-1<k <0为椭圆,k =0为球面,k >1时为扁椭圆.Zemax 用式(1)表示菲涅尔透镜时,是将其表示为一个平面上连续变化的曲率值,表面的截点通过计算入射光线与平面的交点来确定.一旦平面截点找到以后,面型就按该点的球面(或非球面)曲率来处理,光线再折射到下一介质中.因此,这种模拟只是对实际菲涅尔透镜的一种近似.因为实际的菲涅尔透镜有齿距,光线和每个环带的交点和平面有偏移,对于细小齿距的菲涅尔透镜,这种偏移的程度较小,Zemax 可以用平面来代替曲面,并且这种模拟近似性较好.而对于大齿距的菲涅尔透镜,这种偏移的程度较大,无法直接用平面来代替曲面,Zemax 这种模拟方法就失效了.因此,用Zemax 设计大齿距的菲涅尔透镜,主要是确定好每个环带的齿形,如图1所示.菲涅尔透镜的每个环带相当于一非球面透镜的一个环带,设计时先设计好各非球面,然后取对应的各环带,在保证其齿高相等的同时,使其像点都位于同一点,达到共焦的目的.图1 菲涅尔透镜设计原理Fig.1 T heory of Fr esnel lens design2 设计方法某光电开关需要设计一透镜作为其聚光系统,使其对能量进行会聚.由于受该产品开发过程中的尺寸限制,该透镜需设计成一大齿距等厚的菲涅尔透镜,其主要技术参数:工作距l c =10.45mm,厚度d =2mm,视场w =0.5b ,通光孔径D =12.1mm,波长K =900nm,材料为PMMA,会聚光斑直径5[1mm.从通光面积分布以及透镜尺寸考虑,取4个环带通光口径分别为D 1=5.86mm,D 2=8.42mm,D 3=10.68mm,D 4=12.1mm.由于Zemax 软件不能直接构建如图1所示的菲涅尔透镜整体,可以考虑用Zemax 对4个环带逐一设计,但这样做比较复杂,而且不直观,无法形成一个整体进行分析.因此,可尝试在Z emax 软件的序列模式中使用多重组态来进行设计.在透镜的多重组态中,每一环带可看作一个组态,菲涅尔透镜的4个环带可以定义为四组态系统.如图1所示,把中心环带设为第一组态,即基态.第二、三、四个环带分别定义为第二、三、四组态.然后根据透镜的技术参数要求给多重组态编辑器窗口中的相应运算元赋初值,如表1所示.表1 菲涅尔透镜的初始值Tab.1 Or iginal data of Fr esnel设置参数参数设置面序号组态1组态2组态3组态4APMN(表面孔径最小值)10 2.93 4.21 5.34APMN(表面孔径最小值)20 2.93 4.21 5.34APMX(表面孔径最大值)1 2.93 4.21 5.34 6.05APMX(表面孔径最大值)2 2.93 4.21 5.34 6.05SDIA(半孔径)12.934.215.346.05由这些初始数据,Zemax可以生成4个初始环带分别对应的4种初始组态,如图2所示.图2 菲涅尔透镜的4个初始环带F ig.2 Four original r ings of Fresnel lens中心环带的设计与一般的非球面透镜的设计类似,通过计算给出初始结构参数,再对其进行优化得100 上海理工大学学报2007年第29卷到中心环带面型,如图3所示.其余环带的设计则以第一环带为基态来进行.图3 菲涅尔透镜的中心环带Fig.3 Central r ing of F resnel lens由于菲涅尔透镜为等厚透镜,所以在设计第二环带以及第三、四环带时必须满足它们在起始位置时环带的厚度为2mm.以第二环带设计为例,假设第二环带在光轴上的厚度为2.5mm ,则其后工作距为9.95mm.通过软件优化得到一个曲率为-0.207514mm 的环带,如图4所示.将其与图3叠加,得到一具有两个环带的菲涅尔透镜,如图5所示,此时图中x =0.5mm.图4 菲涅尔透镜的第二个环带Fig.4 The second ring of Fresnellens图5 两个环的菲涅尔透镜F ig.5 F resnel lens wit h two rings由图5可知两个环带的菲涅尔透镜实现了光束的共焦要求,但没有满足菲涅尔透镜等厚的要求,因为根据二次曲面方程z =2.5+c y 21+1-(1+k)c 2y 2可计算出当y =2.93mm 时,z =1.69096mm(小于2mm).设x c 为y =2.93mm 时透镜相对于其二次曲面顶点的距离,如图5所示,此时x c =-0.80904mm.要满足透镜的厚度要求,则需要使x =x c .经过实践分析可知,x c 随x 的增大而增大,但其增大的速度较x 要小,最后两者达到相等.所以每次取x =|x c |,对其优化,求出新的x c ,如此循环,直到两者相等($x =x -|x c |[0.01mm),如表2所示,c 为曲面的曲率.表2 第二环带中心厚度求解Tab.2 Resolves of the second ring .s center thickness x /mm c /mm -1|x c |/mm 0.500000-0.2075140.8090430.809043-0.2141650.8304250.830425-0.2146410.8319710.831971-0.2146760.8320830.832083-0.2146780.8320890.832089-0.2146790.8320930.832093-0.2146790.832093表2中的二次曲面的曲率c 是通过对第二组态的透镜进行优化得到的.而x c 的值可以从Zemax 中直接读取数据,用计算机语言编写一个计算程序求得.即当x =0.832093mm 时得到一个新的满足设计要求的两环菲涅尔透镜,此时,第二环的曲率为c =-0.214679,二次曲面系数k=- 2.203200.如图6所示.图6 两环的等厚菲涅尔透镜F ig.6 Fr esnel lens with two r ing .s and equal thickness第三、四环带的设计过程与第二环带类似,先取一个x 值,然后对第三、四组态的数据进行循环优化,求出相应的x c 值,直到x =|x c |($x =x -|x c |[0.01mm )时为止.最后得到菲涅尔透镜的4个环101 第1期徐 欢,等:基于Zemax 软件的大齿距等厚菲涅尔透镜的设计带,如图7所示.将这些环带再叠加起来,就形成了一个具有4个沟槽的等厚菲涅尔透镜,如图8所示.图7 菲涅尔透镜的4个环带F ig.7 Four rings of F resnellens图8 四环的等厚菲涅尔透镜F ig.8 Fresnel lens with four gr ooves and equal thickness3 设计结果及分析图9分别给出了视场角w =0b ,w =0.3b 及w =0.5b 的点列图.从图9中可以看出,该菲涅尔透镜的零视场像差基本为零,当w =0.5b 时,主光线在像面上的高度为0.068mm,光斑半径为0.142mm,即满足会聚光斑直径小于1mm 的要求.图9 点列图Fig.9 Spot diagram4 光路模拟透镜的结构尺寸设计完成后,可以在Zemax 非序列模式下对菲涅尔透镜作整体建模进行光路模拟,从而观察其实际效果.建模方式是由序列模式下所得到的参数算出菲涅尔透镜表面不同半径环上的点相对于基面的高度,即每一个y 值对应一个z 值(如图6所示).这些y 、z 值可以组成一个n 行两列(行数可任取)的矩阵,组成一个TOB 格式的数据文件.Zemax 通过读取这些数据,构建相应的菲涅尔透镜模型,如图10所示.在运行前,按工作要求设置好参数,即可进行光路模拟,如图11所示.图11 菲涅尔透镜光路图Fig.11 F resnel lens .opticalroad图10菲涅尔透镜模型图Fig.10 Model of Fres 2nel lens5 结束语本文在实际的设计过程中,通过结合使用Ze 2max 的两种模式,很好地设计、优化并模拟了一个大沟槽等厚的菲涅尔透镜.既解决了Zemax 不能对这种透镜直接建模进行设计的难题,又避免了传统设计所需的烦琐计算.参考文献:[1] 王之江.光学技术手册[M].北京:机械工业出版社,1987.[2] 王之江.光学设计理论基础[M].北京:科学出版社,1983.[3] Zemax Development Corporation.Zemax 光学设计程式使用手册[M].上海:讯技光电有限公司,2003.[4] 王成良,李湘宁,贺莉清.应用Zemax 软件构造特殊面型[J].光学仪器,2001,23(3):23-26.[5] 杨力,阴旭,陈强,等.大型菲涅尔透镜的设计和制造[J].光学技术,2001,27(6):499-502.102 上海理工大学学报2007年第29卷。
菲涅尔聚光透镜的一般设计方法及效率分析
镜元的入射光偏向角 ; f 和 f ′分别为 F 和 F′到光轴 O′点的距离 ; R 为 Fresnel 透镜的圆弧曲率半径 ; r 为球
冠的外廓半径 。根据图 2 所示几何关系有 θi =θγ +θν = α′i +βi , 其中 θi 为第 i 楞尖劈透镜元的顶角 ,θγ =
W′i ,则
αi = ui + W′i
收稿日期 :2009210217. 基金项目 :国家高技术研究发展计划 (2007AA05Z444) . 作者简介 :李 鹏 (19682) ,男 ,博士 ,副教授. E2mail :lpwhut @live. whut . edu. cn
第 32 卷 第 6 期 李 鹏 ,吴贺利 ,杨培环 ,等 :菲涅尔聚光透镜的一般设计方法及效率分析 63
导致部分光线发散引起的光学损失 ,例如 ,对于平面朝外的 Fresnel 透镜 ,由于楞高会遮挡部分折射光线 ,使
得从第二楞开始就出现部分透射光发散 ;对于平面朝内的 Fresnel 透镜 ,当 F 数小于某临界值时 ,出射界面上
入射角大于其全反射角 ,使透射光不能到达设定的焦斑范围内而损失 ,如图 3 (a) 所示 。反射损失和结构损
Abstract : A general design formula for t he Fresnel lens is obtained t hrough a simple deduction which is initially based on an
optical model for t he design of t he Fresnel lens wit h a curved base. A met hod to calculate optical efficiency of t he Fresnel lens is brought forward and t he comparisons are made between different shapes Fresnel lens which are commonly used now. The quali2 tative evaluation of t heir adaptability , t he advantages and t he disadvantages has finally been done in t his paper.
用于LED均匀照明的自由曲面菲涅耳TIR透镜光学设计
第50卷第2期Vol.50No.22021年2月Feb.2021红外与激光工程Infrared and Laser EngineeringOptical design of freeform Fresnel TIR lens forLED uniform illuminationHu Tiantian1,2,Zeng Chunmei12,Rui Congshan1-2,Hong Yang12.Ma Suodong1,2(1.School of Optoelectronic Science and Engineering,Soochow University,Suzhou215006,China;2.Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province&Key Lab of Modem OpticalTechnologies of Education Ministry of China,Soochow University,Suzhou215006,China)Abstract:A new design of total internal reflection(TIR)lens was presented which had a freeform Fresnel surface in the central part of the front to improve the heat dissipation capability.Snell's law and the reflection law were applied to construct the freeform refractive surface and the freefonn reflective surface for the TIR lens.The freeform refractive surface was transformed into the freefonn Fresnel surface with universal design method of Fresnel lens.The simulation result for the freeform Fresnel TIR lens obtained by Monte Carlo ray tracing shows that the far field illumination uniformity of82.0%and the luminous efficiency of96.6%are achieved for the light source size of2mm><2mm,in the meanwhile the lens weight is only21.94g.The freeform Fresnel TIR lens has nearly20%reduction in lens weight and volume,only a2%reduction in luminous efficiency,and no reduction in illumination uniformity compared to the TIR lens without the Fresnel surface.The result indicates that the Fresnelization for freeform surface of TIR lens can significantly reduce the volume and weight of TIR lens and shorten the optical path length,thus effectively improve its heat dissipation efficiency and service life while maintaining a high performance.Key words:optical design;Fresnel TIR lens;Snell's law;heat dissipationCLC number:0439Document code:A DOI:10.3788/IRLA20200183用于LED均匀照明的自由曲面菲涅耳TIR透镜光学设计胡甜甜込曾春梅叫芮丛珊"，洪洋迢马锁冬2(1.苏州大学光电科学与工程学院，江苏苏州215006；2.江苏省先进光学制造技术重点实验室&教育部现代光学技术重点实验室，江苏苏州215006)摘要：为了提高透镜的散热能力，设计了一种新型全内反射(TIR)透镜，该透镜的出射面中央为自由曲面菲涅耳面'采用斯涅尔定律和全反射定律分别求解TIR透镜折射部分和反射部分自由曲面的面形。
用于光伏系统新型菲涅耳线聚焦聚光透镜设计(1)
*-./,/(正午前后!小时夏天变化为"#$%冬天变化为"&$%太阳本身的有限长角为"’()$%加上聚光器斜率误差%所以菲涅耳聚光棱镜的集光角设计值*"&()$(!+折射率,采用太阳电池吸收光谱的中心波长&’’-.处折射率为/(!00(先由’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1/2棱镜倾角3/2棱镜元宽度4/%递进优化之(再在棱镜/基础上连接设计棱镜#%确定其参量1#23#24#%递进优化(以此类推%得到第,棱镜参量51,%3,%4,+(由此得到棱镜组参量51/1#61,%3/3#63,%4/4#64,+(如图/%设计流程图见图#(采用-789:-法逼近%至满足判据%结束该棱镜元参量的搜索(进行下一棱镜元参量的搜索(判据为;<=><’;?@%式中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"所以应尽量减小棱镜元的底边宽度"即减少棱镜的厚度"#集光角特性分析如图$!在%&角平面内!其集光角达到%’()!光学聚光率对入射角的变化不敏感"在%’()之间都有较高的光学聚光率"这样在一天内不动电池组件从上午*时至下午$时都能充分利用太阳光"在%+角平面内!其集光角达到%,)!具有较宽的集光角!大于太阳一天内南北方向的仰角变化"-焦距的影响如图.!相同的入射孔径!不同的焦距情况下的光学聚光率/&0(1!大的焦距/203’(441有相对高的光学聚光率达56!但其集光角为%$)"当焦距变小/205((441其集光角达到%*)!但其卷!"#$%#&’(")*+’"#,*)-.&*/#&"#++#"&*)/01)2)3)+2!’-0)$#/&4&2#56789:7;<=>?@><=>A 7;B >7<C 7>D >7;E F 89<G 7;?;89H 7>I J K L MN M O P J P Q P R S TU V P J W O L M XY Z R W J O J S M[R W \L M J W O <]\J M R O R ^W L X R _‘S Ta W J R M W R Ob c d d e f g F h F >i F jj 7k Fl m d d c n d e n c o !p q r s t u r v 87w h x F jy >8F n E ;h @z{w F z 8F y y F 8z>zj F z >98F jE ;y y ;|>89k x FF j 9Fw 7}~w >8h >~y F !};~k >"@""Fk x ;j #:x >zH >8j ;E{w F z 8F yy F 8zh ;@y j !F@z F j >8z ;y 7wh ;8h F 8k w 7k ;w;Ez ~7h F 78j k F w w F z k w >7y ~x ;k ;i ;y k 7>h ~;|F w z }z k F "#$k K z F 7z >F w k ;k w 7h Hk x F z @8>8;8y };8F z >89y F 7B >z #$k x 7z ;~k >h h ;8h F 8k w 7k ;ww 7k >;7z c f #$k 7y z ;x 7z !F k k F w 7h h F ~k 78h F 789y F 78jy ;|h ;z k#%&’()s *q {w F z 8F z y F 8z +C ;y 7w h ;8h F 8k w 7k ;w +v h h F ~k 78h F 789y F$t ,-2t )|7z !;w 8>8C x 778B ><.x >87<>8c /b 0#?Fw F h F >i F jk x FA #Cj F 9w F F78j 1#Cj F 9w F FE w ;"k x F 2;w k x |F z k 38>i F w z >k }>8c //e 78j c///w F z ~F h k >i F y }#v k ~w F z F 8k <x F >z 74x #5j F 9w F F h 78j >j 7k F >8D >K 78$8z k >k @k F ;E6~k >h z 78j 4w F h >z >;81F h x 78>h z <.x >8F z F v h 7j F "};E C h >F 8h F z #?>z ~w F z F 8k>8k F w F z k >z ~x ;k w ;8>h "7k F w >7y z 78jj F i >h F z7//c m 期江韬等7用于光伏系统新型菲涅耳线聚焦聚光透镜设计。
基于菲涅尔透镜的室内LED射灯配光设计
图 ４ 调 整 前 后 的 角度 值
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（ ｐ ｒｍｅ ｔ ｆ ｐｉｄＰ ｙ ｉ ，Ｚ ｅｉ ｇＵｎ ｖ ｒｉ ｆ ｃ ｎ ｌｇ ， ｎ ｚ ｏ １ ０ ３ Ｃ ｉａ Ｄｅ ａ ｔ ｎ ｏ Ａｐ ｌ ｈ ｓｃ ｅ ｓ ｈ ｉ ｎ ｉ ｓ ｙｏ ｈ ｏｏ ｙ Ｈａ ｇ ｈ ｕ３ ０ ２ ， ｈ ｎ ） ａ ｅ ｔ Ｔｅ
基于菲涅尔透镜与抛物面反射镜光伏系统设计
基于菲涅尔透镜与抛物面反射镜光伏系统设计王娅妮;刘建胜【摘要】在菲涅尔透镜具有聚光特性的基础上,提出一种同时利用抛物面反射镜焦点发出的光线可反射成平行光的特性混合式聚光光伏系统.利用Zemax软件,对整个聚光光伏系统进行仿真并得到初步仿真数据,参考仿真结果对聚光系统进行改进优化,提高了光能吸收率和有效几何聚光比,同时降低了系统实现成本提高了实用性.【期刊名称】《电子科技》【年(卷),期】2015(028)012【总页数】4页(P10-13)【关键词】菲涅尔透镜;抛物面反射镜;Zemax;光能吸收率;有效几何聚光比【作者】王娅妮;刘建胜【作者单位】北京航空航天大学电子信息工程学院,北京 100191;北京航空航天大学电子信息工程学院,北京 100191【正文语种】中文【中图分类】TK513.1太阳能是取之不尽、用之不竭的可再生能源,现今世界各国都在通过研究聚光光伏系统利用太阳能解决能源短缺问题。
聚光光伏系统利用聚光器将一定面积上的太阳光汇聚到极小的区域上,通过对太阳能的集中进行进一步利用;提高聚光效率、降低系统成本成为了需解决的首要问题。
传统的聚光器分为折射式聚光器、反射式聚光器以及混合式聚光器等[1];折射式聚光是使用一个光学透镜,使入射光聚焦到太阳能电池上从而增大照射面积[2];折射式聚光器的典型代表即为菲涅尔透镜,因其高透光率、高汇聚比、便于加工且大规模使用,抛物面反射镜则常用于反射式聚光器。
本文根据菲涅尔透镜的聚光特性与抛物面反射镜的反射特性设计了一种新型混合式聚光系统。
太阳光在此聚光系统中将进行二次聚光再到达聚光光伏电池(CPV)接收面上。
这种设计在保证较高的聚光效率及几何汇聚比的同时,相较于传统聚光光伏系统,改变了CPV接收光能的位置,将其置于太阳光入射同侧,可更好地实现光能的后续利用。
聚光光伏系统主要通过两个性能指标进行评估,光能吸收效率ELC和有效几何聚光比Cg。
光能吸收效率ELC代表了总入射光能与后级太阳能电池表面能够接收到的有效出射光光能的比值。
基于菲涅尔透镜的室内LED射灯配光设计
基于菲涅尔透镜的室内LED射灯配光设计
祝华;贺叶美;李栋;梁雪;张航
【期刊名称】《光学仪器》
【年(卷),期】2011(033)002
【摘要】为了将LED发出的光均匀投射到3m远直径为1m的圆形区域内,设计了一种LED(发光二极管)射灯.采用菲涅尔透镜对射灯进行二次光学配光设计,并通过调整菲涅尔透镜的各个独立环带的倾角来优化投射光的分布.文中对菲涅尔透镜的投光效果、安全性和加工误差等方面进行了考察,结果表明设计是安全的、可靠的并具有良好的投光效果.
【总页数】5页(P38-42)
【作者】祝华;贺叶美;李栋;梁雪;张航
【作者单位】浙江工业大学,应用物理系,浙江,杭州,310023;浙江工业大学,应用物理系,浙江,杭州,310023;浙江工业大学,应用物理系,浙江,杭州,310023;浙江工业大学,应用物理系,浙江,杭州,310023;浙江工业大学,应用物理系,浙江,杭州,310023
【正文语种】中文
【中图分类】TU113.6
【相关文献】
1.蜂窝式阵列菲涅尔透镜的配光设计 [J], 张航;周海波;刘超;徐军;陈钢
2.评价LED道路照明灯具配光性能的两个重要指标——从配光设计角度谈LED道路照明节能 [J], 邹吉平
3.基于菲涅尔透镜的大功率LED均匀照明系统设计 [J], 聂佳林;胡淼;阮泽辉;崔恩楠;汪延安;蔡美伶
4.基于复合抛物面反光杯和菲涅尔透镜组合的洗墙灯LED条形光斑设计优化 [J], 王勇恒
5.室内LED射灯光生物安全分析 [J], 顾芳波;朱腾飞;钱枫;魏婷;陈华才
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基于自由曲面和菲涅尔透镜的LED汽车后雾灯设计
基于自由曲面和菲涅尔透镜的LED汽车后雾灯设计
引言
LED是新一代具有竞争力的新型固体光源，具有效率高、光色纯、能耗低、寿命长、可靠耐用、无污染、控制灵活、响应快、尺寸小、抗冲击等优点[1]。
由于LED芯片输出的光符合朗伯分布，如果不经过适当的配光处理而直接应用于实际的汽车照明系统将无法达到所需标准。
所以需对以LED为光源的照明系统进行二次光学设计，设计结果直接影响到照明系统的发光效率、能耗、以及汽车的安全性能[2-4]。
目前汽车照明技术的发展非常迅猛。
随着汽车产业的高速发展和市场的激烈竞争，现代汽车照明系统对发光效率、安全性能、以及美观的要求也越来越高。
汽车照明中的自由曲面反射镜及LED照明系统的设计和加工是至关重要的。
有别于传统光学系统的设计。
汽车照明系统的非成像光学的设计是个多学科、复杂的过程[5]。
和传统的抛物面反射镜加配光透镜的组合相比，采用自由曲面和菲涅尔原理结合透镜可以同时实现会聚和配光的功能，这样一来后雾灯就既节省使用空间又降低安装成本。
自由曲面的设计使得后雾灯变得更加灵活性和紧凑。
至今为止，LED主要应用在例如刹车灯、驻车灯、转向灯、倒车灯等汽车信号系统中。
目前LED前照灯之所以还没大规模应用的一个重要因素就是散热，而汽车LED前雾灯因为所需要的能量相对前照灯的要少，所用的LED 也相应较少，并且随着单颗LED的光效不断提高，产生的废热减少，这个约束汽车LED前照灯的技术瓶颈在汽车LED后雾灯中可以轻易地解决，因此汽车LED后雾灯的研究具有很大的使用价值。
后雾灯的设计。
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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1501
1、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1-1
3、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。
3、环结构设计
设定环数为3个。
4、目标面
此设计目标接收面设置了4个，可参见图3-6。
三、设计步骤
1、光源格点光源参数如图3-1
图3-1
2、确定环带数
按照设计要求可知环带数为3
3、求多环带母线
由Matlab程序可求出环带母线坐标，如下表。
4、导入SW建模，TP仿真
a、母线绘制
将上述三维坐标点存为.txt格式的文件可以直接导入SW画出菲涅尔透镜母线，如图3-2
图3-2
b、构建三维模型
透镜三维模型如图3-3
图3-3
c、TP仿真
将三维模型导入TP并设定好所有参数
由图3-4可以明显观察到焦点分布，并列分布在同一条直线上，前后位置不一。
图3-5为完整的TP模型
图3-4
图3-5
如图3-6，设置了4个不同的接收面，其中接受面1在第一个焦点之前，接收面2位于第二个交点处，接收面3位于第二和第三个焦点中间，接收面4位于第三个焦点之后。
这样设置接收面的优点在于可以清楚的获得不同位置的光照分布，便于对比后分析结果。
图3-6
图3-7——3-8是光线相对比较多的TP仿真三维模型
图3-7
图3-8
5、结果分析
图3-9——3-12依次为接收面1——接收面4的照度、均匀度分布图.
如图3-9，为接收面1的照度、均匀度分布图，可以明天观察到3个环，达到设计目标。
图3-9
如图3-10，当接收面位于第一个焦点处，中心亮度明显很高，但边缘亮度低，这说明在这个面上，中心处的能量相对较与非中心处较高。
另一方面也说明在此焦点上，光线能够很好的会聚，这对于菲涅尔透镜来说即为目的，达到最好的聚焦效果以满足需求。
图3-10
图3-11
如图3-12，为接收面4接收到的光线照度、均匀度分布。
此时环带变宽，暗环消失，说明在此位置出，亮环可以把周围照亮。
图3-12
参考文献：
［1］祝华，贺叶美,李栋,等.基于菲涅尔透镜的室内LED射灯配光设计［Ｊ］．光学仪器，2011，33(2):38-42．
［2］张航，周海波，刘超，等.蜂窝式阵列菲涅尔透镜的配光设计［Ｊ］. 光学仪器,2016,38(1): 53-58。