Zemax全新菲涅耳透镜设计
菲涅尔透镜 参数 计算
菲涅尔透镜参数计算【摘要】菲涅尔透镜是一种特殊的透镜结构，广泛应用于光学系统中。
本文从菲涅尔透镜的原理和应用出发，详细介绍了菲涅尔透镜的参数确定方法、计算公式、评估标准，以及效率和性能优化。
菲涅尔透镜参数计算的重要性在于能够准确地设计和优化光学系统，提高其性能和效率。
未来，随着光学技术的不断发展，菲涅尔透镜参数计算也将迎来更广阔的应用前景，为光学系统的设计和研发提供更加精准的技术支持。
在实际应用中，人们可以根据所需的光学系统设计要求和性能指标，进行菲涅尔透镜参数计算，以获得最佳的光学效果和性能表现。
【关键词】菲涅尔透镜、参数、计算、原理、应用、确定方法、计算公式、评估标准、效率、性能优化、重要性、发展前景、应用前景1. 引言1.1 菲涅尔透镜参数计算菲涅尔透镜参数计算是指在设计和制造菲涅尔透镜时，需要对其各项参数进行准确计算和评估的过程。
菲涅尔透镜是一种特殊的透镜，通过其特殊的表面结构可以实现对光线的聚焦和分散，广泛应用于太阳能光伏系统、车灯、舞台灯光等领域。
在进行菲涅尔透镜参数计算时，首先需要理解菲涅尔透镜的原理和应用。
菲涅尔透镜的工作原理是通过其表面的环形凸台结构，使得光线在经过透镜时可以通过反射和折射来实现聚焦或分散。
菲涅尔透镜的参数确定方法包括材料选择、几何结构设计、曲率半径等方面，需要综合考虑光学性能和制造成本等因素。
计算菲涅尔透镜的参数主要涉及到曲率半径、焦距、光学直径、透镜形状等方面。
通过适当的公式和模拟软件，可以准确地计算出菲涅尔透镜的各项参数。
评估标准则是根据设计要求和应用场景来确定透镜的性能是否符合要求。
菲涅尔透镜参数计算的重要性在于可以确保产品的光学性能和稳定性，提高生产效率和节约成本。
随着技术的不断进步和应用领域的拓展，菲涅尔透镜参数计算的发展前景和应用前景也将变得更加广阔和重要。
2. 正文2.1 菲涅尔透镜的原理和应用菲涅尔透镜是一种特殊的透镜，它是由法国物理学家菲涅尔发明的。
大视场菲涅尔透镜的聚光效率模拟和分析
大视场菲涅尔透镜的聚光效率模拟和分析第32卷第1期2010年2月光学仪器OPTICALINSTRUMENTSV o1.32.No.1February,2010文章编号:1005—5630(2010)01—0044-05大视场菲涅尔透镜的聚光效率模拟和分析吴旭婷,李湘宁,蔡伟(上海理工大学光电信息与计算机工程学院,上海200093)*摘要:大视场菲涅尔聚焦透镜在180.的范围内各个视场下均能实现较理想的聚焦.根据现有的大视场菲涅尔聚焦透镜的设计结果,利用Zemax软件在非序列环境下自定义面型的功能对该设计进行模拟分析.模拟菲涅尔透镜在不同方向的平行光照射下的聚焦情况.通过对不同方向的光线照射下探测器接收到能量的情况进行分析,得到了相应的聚光效率,为设计的可行性提供了分析依据.关键词:菲涅尔透镜;Zemax软件;大视场;聚光效率中图分类号:TP319文献标识码:Adoi:10.3969/j.issn.1005—5630.2010.01.010 ThesimulationandanalysisofthelargefieldFresnellens opticalconcentratorefficiencyWUXuting,LJXiangning,CAIWei (SchoolofOptical—ElectricalandComputerEngineering,UniversityofShanghaiforScienceandTechnology,Shanghai200093,China)Abstract:LargefieldFresnellensconcentratorcangetabetteropticalconcentratorefficiency ineachfieldofviewwithintheangleof180..OnthebasisofthedesignofthelargefieldFresnel concentratorlens.simulatebyusinguserdefinedsurfacefeatureinthenon-sequence environmentofZemax.SimulatetheopticalconcentratorsituationoftheFresnellenswhich areirradiatedbytheparallel—rayindifferentdirections.Basedonthesimulationandanalysisof thelargefieldFresnel1ensopticalconcentratorefficiencyindifferentdirection.providean analysisofthefeasibilityforthedesign.Keywords:Fresnellens;Zemaxsoftware;largefield;opticalconcentratorefficiency引言大视场菲涅尔聚焦透镜是用于会聚太阳光的一种光学元件,它要求对各个方向的太阳光均能实现聚焦,并有较高的聚光效率.对于菲涅尔透镜表面的槽沟,许多学者的研究证实,当出射面压槽沟时透镜的光学效率最高LI].设计根据大视场菲涅尔透镜的特殊聚光要求,着重研究出射面有槽沟的平板菲涅尔透镜在Zemax软件中的建模及光路的追迹,利用该软件自定义面型的功能,分析在不同方向的平行光照射下大视场菲涅尔聚焦透镜的聚光情况.从而为设计提供一个客观的评价,为实际运用提供分析依据.在大视场菲涅尔聚焦透镜的设计中主要运用了几何光学的聚焦原理,为了使太阳光照射时每个时刻收稿日期:2009—07—29作者简介:吴旭婷(1984一),女,浙江湖州人,硕士研究生,主要从事应用光学方面的研究.第1期吴旭婷,等:大视场菲涅尔透镜的聚光效率模拟和分析?45?都有正入射的光线,将整个透镜设计成半圆柱状,从而使系统具有了较大的视场.为了分析太阳光在各个时间段照射菲涅尔透镜时探测器所接受到的能量的情况,现借助Zemax软件对设计进行建模及仿真分析.Zemax软件提供了大量可供光学系统选用的内置面型,如:球面,非球面,ABCD 矩阵面,衍射面,变折射面等,除此以外用户还可以定制特殊面型.l工作原理菲涅尔透镜是一种非球面透镜,是由一系列同心棱形槽构成的.每个环带都相当于一个独立的折射面,在平行光垂直入射情况下,在其焦面上能得到一个无像差的会聚点.设计中依靠三棱镜序列实现菲涅尔的聚焦.在设计中应遵守基本的光学原理,光线入射到棱镜发生一次折射,由棱镜另一面射出发生二次折射[4].棱镜的顶角为a,棱镜材料折射率为,如图l所示.总偏向角与折射率,工作侧面角a和入射角的一般函数关系式为:/3一1一口+arcsin{sinl口一arcsinfsin(J__~i1l}(1)IL\/.JJ大视场菲涅尔聚焦透镜有非球面透镜的作用(在平行光垂直入射情况下,在其焦面上能得到一个无像差的会聚点),如图2所示.其每个棱齿都相当于一个独立的折射面,这些棱齿能使入射光线会聚到一个共同的焦点.干扰侧面,图1菲涅尔透镜的折射光学Fig.1DioptricsofFresnellens一一,}d/2,,d/2I图2焦距与透镜总宽度的比例关系示意图Fig.2Therelationshipbetweenthef~_alandlenswidth设计中的大视场菲涅尔聚焦透镜用于太阳光能的聚焦.为了使菲涅尔聚焦透镜在每个时间段都能接收正向入射的光能,并满足大视场的要求,设计中需要将所有的面元旋转180.得到一个半圆柱状的入射面.2系统模拟2.1菲涅尔透镜的结构该设计以实例做参照,选取合适的焦距.在实例中采用焦距为250mm,受光面的宽度为300mm,一个棱齿的宽度a为0.5mm.总共具有600个齿,由于齿的左右两边是对称的,所以只要计算一边的齿.材料也是关键的因素,这里选用有优质透光率的聚碳酸酯(polycarbonate,PC),折射率,z一1.587,具有高透光率(透光率可达90).菲涅尔聚焦透镜的棱齿在光线正入射的情况下使光线偏折并向焦平面会聚,这时在中心距处入射光的偏向角应是:一arctan()(2),J,工作侧面角a的一般数学表达式为:口一—arctan[sin01--—sin(0,--f1)~(3)口一～O~/*,2--sin01--COS(1一46?光学仪器第32卷在Zemax建模时只考虑正向人射时的情况,即式(3)中01—0.,sin01—0的情况,再结合齿的宽度即可求得每个齿的高度h=a*Ot,理想的聚光情况如图3所示.根据设计要求需要将透镜面旋转180.,得到一个半圆柱的聚光表面,从而使之能接收到各个时间段正向入射的光线.在实际聚焦时,由于每个齿都有一定的宽度,在宽度范围内只有一条光线是满足严格的点聚焦,而并不是宽度范围内的所有光线都是严格的点聚焦过程,所以在焦点附近是一个有一定宽度的线聚焦.在设计中,探测器的宽度为5mm,长度为500mm,放置在菲涅尔聚焦透镜的焦平面上.2.2建模和光线模拟按上述要求及计算结果完成大视场菲涅尔聚焦透镜的结构尺寸的设定,可以在Zemax非序列模式下对整个系统建模进行光路模拟,从而观察其实际效果[5].建模方式:运用Zemax中的列表径向,面元阵列,并以TOB为副档名进行建模.根据上述程序运行所得的计算结果,得到构成透镜齿棱的每个点的位置(在Zemax中,,成右手坐标系),即每一个值对应一个值,这些Y,值可以组成一个TOB格式的数据文件.由于一个TOB文件的最大容纳的数据为246,在设计中需要有多个点构成整个聚光板,因此需要用多个TOB文件相拼接来完成整个系统的设计,从而在Y,平面上得到一个菲涅尔聚焦透镜的一个截面.由于根据数据所建的模型只是菲涅尔聚焦透镜的一个截面,为了得到一个立体的半圆柱状的聚光面,需要在此基础上再将其绕z轴旋转180.得到模型,如图3所示.在建模中为了能使光源,探测器以及菲涅尔聚焦透镜的受光照面在同一轴上,需要将整个菲涅尔聚焦透镜绕Y轴转--90..在设计的建模中,为了更好地使光线经过菲涅尔透镜后聚焦,在菲涅尔聚焦透镜的截面旋转180.时,尽可能地运用多次平滑,使得菲涅尔聚焦透镜趋近于半圆柱状,从而在模拟中得到更好的效果,如图4所示.在运行前,按工作要求设置好参数,将长500mm,宽5mm的探测器放置在焦平面位置上,即可进行光路模拟.图3各棱齿理想偏向角示意图Fig.3Theidealangulardeviation图4菲涅尔聚焦透镜模型图Fig.4ModelofFresnellens利用Zemax软件模拟不同视场的光照射菲涅尔聚焦透镜的情况,在模拟前设置好光源的各项参数,使光能以不同视场角度的平行光人射,即可模拟不同时刻下光照射时的情形,观察探测器上的能量情况.3分析与讨论设计以覆盖整个透镜齿棱的光能为单位,通过旋转光源的办法,得到以不同视场的平行光照射菲涅尔聚焦透镜的情形.根据在长250mm,宽5ram的探测器上接收到的能量分布情况进行分析,组图5(a),(b)为0.时探测器上接收到的能量,组图6(a),(b)为4O.时探测器上接收到的能量. 由图5,图6可以看出,大部分光能集中在探测器的5mm宽度内.按照前面的分析,同样的方法再取入射光束宽度为整个人射光能量的一半时(所取光束是正入射方向附近的光),两组光束都以每隔10.为测量对象取点,根据得到的有关数据得到如图7所示的分布曲线.第1期吴旭婷,等:大视场菲涅尔透镜的聚光效率模拟和分析?47?(a)0.角入射能量分布图(a)Energydistributionof0.incidentXcoordinatevalueInc0herentirradiance(b)0.角入射能量横向分布图(b)Transverseenergydislribufionof0.incident图5O.角入射时能量探测Fig.5EnergydetectorofO.incident(a)40.角入射能量分布图(a)Energydistributionof40.incidentXcoordinatevalueIncoherentirradianee(b)4O.角入射聚焦能量横向分布图(b)Transverseenergydistributionof40.incident图640.角入射时能量探测Fig.6Energydetectorof40.incident图7中z轴表示光源以不同角度的入射情况,Y轴表示长500mm宽5ram的探测器上所对应接收到的全部光能的百分比(即光能利用率).由图中所示的数据曲线显示,设计虽然在一定程度上实现了聚光板的聚光效果,但是聚光效率比较低,而且从图中可以看出光从正入射到以20.角人射的范围内探测器所接收的能量几乎是线性下降的.从模拟本身看,设计存在缺陷,光能的利用率比较低,不能得到理想的效果.经过图7中两组分布曲线的比较,发现在入射光束宽度缩减为原入射光能量的一半时(所取光线是正入射方向附近的光),由图得知探测器上所聚集到的能量几乎是原来能量的80左右.这就证明了,离正入射方向较远的光能对最终探测器接收到的能量是比较小的,光能的利用率较低,探测器上接收的主要光能大多来自于正入射附近的光能.Incidentangle/(.)图7光能利用率随入射光角度变化图Fig.7Condenserenergyratiowiththedifferentincidentangles通过运用Zemax软件的自定义功能进行建模,并模拟了各个不同方向平行光人射后的聚光情况,使设计者比较直观地看到设计的效果,大大提高了设计的效率,也使今后改进时有了更好的方向.4结束语在实际的建模模拟过程中,通过结合使用Zemax的TOB文件结构在非序列下的建模,较好地模拟了Q31宣量口苦—IouIITo0—rB_【口HJ【I10.IIIoII_|o/0/o焉矗.1u矗sllQpu0u48?光学仪器第32卷大视场菲涅尔聚焦透镜的实际聚焦情况,得到了一个比较客观的效果,对设计的可行性提供了分析依据.在对探测器所接收到的能量进行分析后,对整个设计的光学效率有了详实的了解,使整体设计效果在付诸于实践之前有了一个比较直观的判断,大大提高了设计的效率,有着充分的实际意义.也使类似的光学设计能依此相似的方法得到很好的建模分析,以求达到比较理想的效果.参考文献:[1]KRASINAEA,TVERIYAOVICHEV,RC)MANKEVICHA V.Opticalefficiencyofsol arengineeringFresnellensesEJ].AppliedSolarEnergy,1989,(6):6—1O.[2]张明,黄良甫,罗崇泰,等.空间用平板形菲涅尔透镜的设计和光学效率研究[J].光电工程,2001,28(5):l8—21.[3]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.E4]郁道银,谈恒英.光学工程[M=].北京:机械工业出版社,2004.[5]徐欢,李湘宁,周果.基于Zemax软件的大齿距等厚菲涅尔透镜的设计_J].上海理工大,2007,29(1):99—1O2.量子级联激光器研究获重大突破新型中红外激光二极管转换效率超50%美国西北大学的研究人员研制出了一种小型中红外激光二极管,其转换效率超过5o.有关报道称这一成果是量子级联激光器(QCL)研究的重大突破,使量子级联激光器向多个领域的实际应用,包括对危险化学品的远程探测,迈出了重要一步.相关研究成果刊发在最近的《自然?光子学》杂志网络版上.量子级联激光器是一种发光机制异于传统半导体激光器的新型二极管激光器,根据量子力学原理设计,其发光波长可覆盖中红外区域.与传统的二极管激光器不同,量子级联激光器是单极器件,仅需电子即可运作,利用电子在一维量子化的导带问的跃迁来实现发光.经过多年的研究和工业化开发,现代近红外(波长在1m左右)激光二极管的转换效率已接近极值,而中红外(波长大于3ym)激光二极管却很难达到效率极值.先前的报道认为,即使冷却到低温状态,高效量子级联激光器的转换效率也不会高于40.美国西北大学量子器件研究中b(CQD)的研究人员通过优化激光器设备的材料质量,在量子级联激光器效率方面取得了突破性进展.他们剔除了在低温条件下激光器操作中非必要的设计元素,研制出的新型激光器在温度冷却到40K时,4.85ym波长光的转换效率达到了53%.该研究小组的领导者,美国西北大学麦考密克工程与应用科学学院电气工程和计算机科学教授玛尼杰?拉泽吉认为,这种高效激光器的问世是一个重大突破,这是科学家们首次使激光器发出的光能超过热能.她强调,激光器的转换效率突破5O这个门槛,是一个里程碑式的成就.报道称,提高转换效率依然是目前激光器研究的首要目标.而新型设备所展现的高效率,可大大扩展量子级联激光器的功率标定范围.最近的研究表明,伴随着量子级联激光器的广泛发展,单体脉冲激光器的输出功率已高达120W,而在一年前,只有34W.该研究得到了美国国防部高级研究计划局高效中红外激光器(EMIL)项目和美国海军研究所的共同资助.(摘自《科技日报》)。
菲涅尔太阳能聚光镜的设计
菲涅尔太阳能聚光镜的设计朴聪;张国玉【期刊名称】《应用光学》【年(卷),期】2011(32)1【摘要】讨论并设计了一种超薄的菲涅尔聚光镜,根据费玛原理设计出以非球面为截面的中心折射区域和TIR(内部全反射)棱镜为锯齿部分的折反区域,用ZEMAX软件优化得到最佳聚光态,并利用ZEMAX软件模拟出菲涅尔聚光镜聚光性及其能量分布,最终得到总厚度仅为30 mm的折反复合型菲涅尔聚光镜.实验结果表明:折反复合型菲涅尔聚光镜不仅能提高太阳能的利用率,同时也使会聚到光电池表面上的能量分布更均匀,复合式菲涅尔聚光镜的性能优于传统的菲涅尔聚光镜.%An ultra-thin Fresnel condenser lens was discussed and designed. According to Fema principle, an aspheric surface was designed as central refraction area, and a total internal reflection (TIR) prism was designed as a catadioptric area in saw-teeth part. The optimal condense performance was achieved with ZEMAX. ZEMAX was used to simulate the concentration and distribution of Fresnel condenser, and a Fresnel condenser with thickness of 30 mm was designed. The compounded Fresnel lens improves the utilization of solar energy and provides a better uniformity of energy distribution. The design method generates a better compound condenser than conventional Fresnel condenser.【总页数】4页(P23-26)【作者】朴聪;张国玉【作者单位】长春理工大学,光学工程学院,吉林,长春,130022;长春理工大学,光学工程学院,吉林,长春,130022【正文语种】中文【中图分类】O435【相关文献】1.基于DSP的线性菲涅尔太阳能集热系统设计与实现 [J], 王浩林;张津;王魏2.微弧线性菲涅尔太阳能集热器的设计 [J], 欧阳海玉;牛玉刚;王浩林;闫柏玲3.线性菲涅尔反射式太阳能集热系统的设计与试验研究 [J], 朱艳青;李育坚;王雷雷;邓育军;史继富;徐刚4.基于射线追踪法的线性菲涅尔聚光镜场阴影与遮挡分析 [J], 马军;夏荣斌5.滑移式线性菲涅尔太阳能集热器的设计及实验研究 [J], 卢梓健;黄金;胡艳鑫;王海;陈友鹏因版权原因，仅展示原文概要，查看原文内容请购买。
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。
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。
基于Zemax的光学透镜设计与激光打标机的应用
基于Zemax的光学透镜设计与激光打标
机的应用
简介
本文旨在探讨基于Zemax的光学透镜设计在激光打标机中的应用。
光学透镜是激光打标机中至关重要的光学组件，其设计合理性直接影响到激光打标机的性能和质量。
Zemax光学透镜设计软件
Zemax是一种专业的光学设计软件，具有强大的光学设计和分析功能。
通过使用Zemax，设计师可以对光学透镜进行高精度的设计和优化，以实现激光打标机需要的精确焦距、聚光效果和光斑质量。
光学透镜设计原理
光学透镜的设计原理涉及到光学的折射、反射、透射等基本规律。
在使用Zemax进行光学透镜设计时，需要考虑到激光打标机的工作波长、光斑直径、工作距离等参数。
设计师可以通过调整透镜的曲率半径、厚度和材料来实现所需的光学功能。
光学透镜在激光打标机中的应用
光学透镜在激光打标机中扮演着关键的角色。
通过合理设计光
学透镜，可以实现激光的聚焦、扩束、从而控制光斑的形状、大小
和质量。
光学透镜的设计应考虑到激光的工作波长、功率以及所需
的聚光效果。
优化的光学透镜设计可以提高激光打标机的标记质量、速度和精度。
结论
基于Zemax的光学透镜设计在激光打标机中具有重要的应用价值。
使用Zemax进行光学透镜的设计和优化，可以帮助设计师实现所需的激光聚光效果，提高激光打标机的性能和质量。
因此，深入
理解Zemax光学透镜设计软件的原理和使用方法，对激光打标机的设计与应用具有重要意义。
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Zemax○R菲涅耳透镜设计工具（UDS）--VR/AR解决方案
Zemax○R自定义面型（UDS）提供了复杂曲面建模的解决方案,使得复杂建模成为可能。
下面在序列模式下以菲涅耳透镜为例，简要概述其建模，仿真及优化能力。
序列模式下，对菲涅耳透镜的建模尤其是对锯齿建模一直是个难点，以前一直没有好的解决方案。
以前只能通过非序列模式，或者混合序列-非序列模式采用内置的Fresnel 1对锯齿建模。
但非序列模式下（或者混合非序列模式下）Fresnel 1实体建模有一些局限性，体现在：
1.锯齿结构都是小平面结构，如果是成像像质方面有要求的设计如VR，其像质很难达到
要求。
这种平面结构主要用于照明等领域，像质要求相对较低。
2.锯齿结构的基底面都是平面，使用性受到限制。
目前越来越多的VR使用球面等弧面作
为基底，因此弧面基底建模无法完成。
3.优化能力很困难，这主要是基于当某些光线打在无效的锯齿端面，所导致的杂散光造成。
杂散光的形成导致弥散斑尺寸难于控制及评价，因此几乎无法优化或者要经过一些光线筛选等冗繁的工作后，优化才能进行。
4.公差评估几乎无法实现，其目前的建模方法使得公差分析几乎无法进行，比如无法分析
面型加工公差等影响，所以无法预判加工的可靠性，给加工及评估带来非常大的困难。
序列模式下，虽然内置有多个菲涅耳面型，但都是理想的菲涅耳面（没有锯齿结构，或者说锯齿非常非常浅），这样的建模方式实际上导致了与实际菲涅耳透镜（带锯齿结构）的不符，导致了根本无法评价其性能参数与实际的成像质量。
本文通过自开发的自定义面型（UDS）在序列模式下实现了菲涅耳透镜的灵活建模，扩展了Zemax○R菲涅耳透镜的建模能力，并且自带有锯齿结构，更符合实际，也可直接用于优化及公差分析，可以导出为CAD文件。
核心功能点：
1.基底可以是平面，球面或者是柱面
2.锯齿选择可以是小平面近似或者完全光滑的曲面（更高的像质需求）
3.菲涅耳折射面可以用高的非球面来表征（至r^10项），用于满足高的像质需求
4.可以选择屏蔽杂散光，只对主要像斑点做出评价如点列图尺寸，MTF等
5.可以选择锯齿特征，如等深度锯齿，还是等宽度锯齿
6.可以设置拔模角（draft angle）
7.可直接优化，无需繁琐的杂散光线筛选
8.可用于公差分析等
9.可以输出面型格点数据或者CAD文件
1.基底为球面的菲涅耳透镜
2.基底为平面的菲涅耳透镜
3.基底为柱面的菲涅耳透镜
锯齿结构：
小切平面锯齿光滑锯齿面（较高像质）
矢高图
1.平面锯齿
2.光滑锯齿
平滑锯齿与光滑锯齿对比
CAD输出
杂散光与移除杂散光之后
设计实例比较：
VR单片透镜设计：全视场角96度
1.对前后表面采用偶次非球面进行设计
中心厚度：11mm
2.采用UDS菲涅耳透镜设计，前表面偶次非球面，后表面菲涅耳面
中心厚度：7mm。