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,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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）,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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）。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,2.2 薄透镜系统的初级像差方程组,A,B,y,y,B,A,孔径光阑,O,已知： ， ， ， ， ， 第一辅助光线： ， 第二辅助光线： ，,第二辅助光线,第一辅助光线,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,薄透镜系统的初级像差方程组,(1),(2),(3),(4),(5),(6),(7),Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,(1),(2),(3),(4),(5),(6),(7),Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,(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。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,(6) 单薄透镜的petzval场曲,对单薄透镜组来说， 与结构无关。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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,1,1,什么是规化？,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,A,A,F,F,h,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,(1) P、W对f的规化,A,A,F,F,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,A,A,F,F,（2）保持焦距,和物距,不变，把入射高,放大到1，即,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,A,A,F,(3),，,对物距的规化,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,(4) C的规化,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,2.5 单透镜的 、 、 和结构参数的关系,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,例：有一平凸透镜，焦距f4000mm，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D160mm，求该透镜的初级球差、彗差和轴向色差。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,由表31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：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,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：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,根据公式 ，得：,根据公式 ，并假定入瞳与透镜重合 ，有：,由公式,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,下面求色差，由公式 得：,实际的C值为：,代入公式 得：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,2.6 双胶合透镜组结构参数的求解,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.,双胶合透镜 表,、,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client