薄透镜系统的初级像差方程组新方案

第二章薄透镜系统的初级像差理论2.1概述2.2薄透镜系统的初级像差方程组2.3薄透镜组像差的普遍性质2.4像差特性参数的P，W，C的规化2.5单透镜的、、和结构参数的关系2.6双胶合透镜组结构参数的求解2.7平行玻璃板的初级像差公式2.8光学系统消场曲的条件——petzval条件Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.1.初级像差和y、h的关系：(2)初级彗差(3)初级子午场曲(细光束场曲)(4)初级弧矢场曲(5)初级畸变(6)初级轴向色差(7)初级垂轴色差2.1概述(1)初级球差（跟材料的色散系数有关，与y、h无关）Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.薄透镜的概念如果一个透镜组的厚度和它的焦距比较可以忽略，这样的透镜组称为薄透镜组。由若干个薄透镜组构成的系统，称为薄透镜系统（透镜组之间的间隔可以是任意的）。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.2薄透镜系统的初级像差方程组AByy’B’A’孔径光阑O已知：，，，，，第一辅助光线：，第二辅助光线：，外部参数（与具体结构参数（r,d,n）无关）第二辅助光线第一辅助光线Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.薄透镜系统的初级像差方程组(1)(2)(3)(4)(5)(6)(7)对薄透镜组求和Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.其中的参数：对单透镜求和对单透镜求和对透镜组中每个折射面求和Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.薄透镜系统的初级像差方程组(1)(2)(3)(4)(5)(6)(7)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.(1)(2)(3)(4)(5)(6)(7)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.像差方程组的用途：可以得到薄透镜组的像差性质。2.已知像差的数值，反求结构参数。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.3薄透镜组像差的普遍性质2.3.1薄透镜组的单色像差性质1．一个薄透镜组只能校正种初级单色像差两Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2．光阑位置对像差的影响与无关，所以光阑位置对球差没有影响。(1)球差(2)彗差彗差与光阑位置有关。但球差为零时，彗差即与光瞳位置无关。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.(3)像散像散与光阑位置有关，但球差、彗差都为零时，像散与光瞳位置无关。(4)光阑和薄透镜组重合时像散与透镜组的结构无关，无法校正。(5)光阑和薄透镜组重合时畸变为零。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.(6)单薄透镜的petzval场曲对单薄透镜组来说，与结构无关。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.3.2薄透镜组的色差性质1．一个薄透镜组消除了轴向色差必然同时消除垂轴色差。2．薄透镜组必须采用不同材料的玻璃组合消色差。3．消色差的条件与物体位置无关。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.4像差特性参数P，W，C的规化任意物距任意入射高任意焦距保持透镜组的几何形状相似11什么是规化？Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.AA’FF’hEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.(1)P、W对f’的规化AA’FF’Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.AA’FF’（2）保持焦距和物距不变，把入射高放大到1，即Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.AA’F’(3)，对物距的规化Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.(4)C的规化Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.外形尺寸计算根据对系统的像差要求，列出初级像差方程组求解方程组得到系统中每个薄透镜组的像差特性参数P，W，C经过规化，求出,,求出每个透镜组的结构参数薄透镜系统的求解过程Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.5单透镜的、、和结构参数的关系Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.例：有一平凸透镜，焦距f’＝4000mm，玻璃材料为K9（n=1.5163,=64.1）用作平行光管物镜，如下图。通光口径D＝160mm，求该透镜的初级球差、彗差和轴向色差。f’＝4000F’Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.由表3－1用插值法得到n=1.5163时的，值为：由于透镜为平凸形，并且凸面向前，所以，代入公式，得：将，，代入公式，得：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.下面由，求P，W：由于实际物平面位在无限远，不需要对物距进行规化，因此，，只要对规化，由公式得：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.根据公式，得：根据公式，并假定入瞳与透镜重合，有：由公式Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.下面求色差，由公式得：实际的C值为：代入公式得：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.6双胶合透镜组结构参数的求解Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.双胶合透镜表、Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.已知,找出玻璃材料和求出结构参数：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.7平行玻璃板的初级像差公式Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.平行玻璃板的初级像差公式（1）球差（2）彗差（3）像散（4）场曲（5）畸变（6）轴向色差（7）垂轴色差Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.例3、设计一个10×望远镜物镜，要求为：f’=250mm，D=40mm，2w=6°,入瞳与物镜重合。物镜后有1棱镜系统，展开成平行玻璃板的总厚度为150mm，棱镜的玻璃材料为K9。为了补偿目镜的像差，要求物镜系统（包括双胶合物镜和棱镜）的像差为：根据上述光学特性和像差要求，求解双胶合物镜的结构参数。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.物镜棱镜Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.8光学系统消场曲的条件——petzval条件Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.消场曲的条件(petzval条件)上式对薄透镜系统或厚透镜系统都能应用，对薄透镜系统来说就是薄透镜的实际光焦度。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.能够校正场曲的光学系统的结构(1)正、负光焦度远离的薄透镜系统(2)弯月形厚透镜Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.