{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"基于混合镜组模型的变焦镜头设计"}]},{"lang":"en","data":[{"name":"text","data":"Zoom lens design using mixed lens modules"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"张","givenname":"金凯","namestyle":"eastern","prefix":""},{"lang":"en","surname":"ZHANG","givenname":"Jin-kai","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":["corresp","first-author"],"corresp":[{"rid":"cor1","lang":"en","text":"ZHANG Jin-kai, E-mail:youjianer@sohu.com","data":[{"name":"text","data":"ZHANG Jin-kai, E-mail:youjianer@sohu.com"}]}],"bio":[{"lang":"zh","text":["张金凯(1986-), 男, 山东德州人, 博士, 讲师, 2008年于山东大学获得学士学位, 2011年于中国科学院长春光机所获得硕士学位, 2015年于上海交通大学获得博士学位, 主要从事光学设计、光学检测、精密测量以及机器视觉等方面的研究。E-mail:youjianer@sohu.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"张金凯"}]},{"name":"text","data":"(1986-), 男, 山东德州人, 博士, 讲师, 2008年于山东大学获得学士学位, 2011年于中国科学院长春光机所获得硕士学位, 2015年于上海交通大学获得博士学位, 主要从事光学设计、光学检测、精密测量以及机器视觉等方面的研究。E-mail:"},{"name":"text","data":"youjianer@sohu.com"}]]}],"email":"youjianer@sohu.com","deceased":false},{"name":[{"lang":"zh","surname":"陈","givenname":"晓波","namestyle":"eastern","prefix":""},{"lang":"en","surname":"CHEN","givenname":"Xiao-bo","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff2","text":"2"}],"role":[],"bio":[{"lang":"zh","text":["陈晓波(1979-), 男, 博士, 助理研究员, 2001年、2009年于上海交通大学分别获得学士、博士学位, 2002年于上海交通大学获得工商管理第二学士学位, 2003年于美国密西根大学获得硕士学位, 2012年于上海交通大学师资博后出站, 主要从事三维视觉测量等方面的研究。E-mail:xiaoboc@sjtu.edu.cn"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"陈晓波"}]},{"name":"text","data":"(1979-), 男, 博士, 助理研究员, 2001年、2009年于上海交通大学分别获得学士、博士学位, 2002年于上海交通大学获得工商管理第二学士学位, 2003年于美国密西根大学获得硕士学位, 2012年于上海交通大学师资博后出站, 主要从事三维视觉测量等方面的研究。E-mail:"},{"name":"text","data":"xiaoboc@sjtu.edu.cn"}]]}],"email":"xiaoboc@sjtu.edu.cn","deceased":false},{"name":[{"lang":"zh","surname":"邵","givenname":"海燕","namestyle":"eastern","prefix":""},{"lang":"en","surname":"SHAO","givenname":"Hai-yan","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"王","givenname":"晓慧","namestyle":"eastern","prefix":""},{"lang":"en","surname":"WANG","givenname":"Xiao-hui","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"孙","givenname":"选","namestyle":"eastern","prefix":""},{"lang":"en","surname":"SUN","givenname":"Xuan","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"济南大学 机械工程学院, 山东 济南 250022","data":[{"name":"text","data":"济南大学 机械工程学院, 山东 济南 250022"}]},{"lang":"en","label":"1","text":"School of Mechanical Engineering, University of Jinan, Jinan 250022, China","data":[{"name":"text","data":"School of Mechanical Engineering, University of Jinan, Jinan 250022, China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"上海交通大学 机械与动力工程学院, 上海 200240","data":[{"name":"text","data":"上海交通大学 机械与动力工程学院, 上海 200240"}]},{"lang":"en","label":"2","text":"School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China","data":[{"name":"text","data":"School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"为了优化变焦镜头的设计过程，本文提出了基于混合镜组模型的变焦镜头设计方法，包括近轴设计，镜组模型确定以及基于混合镜组模型的像差设计。近轴设计阶段采用了高斯括号和矩阵光学，可以很方便地构建镜组间隔和镜组焦距之间的关系。镜组模型确定阶段是根据现有镜头专利训练了一个镜组分类模型，它可以根据镜组近轴数据将镜组分为薄透镜模型或者厚透镜模型。像差设计阶段综合了薄镜组模型像差设计和厚镜组模型像差设计。镜组分类模型成功地将80%以上的镜组进行了分类。最后采用基于混合镜组模型设计方法设计了一个物方远心的变焦镜头。结果表明，该镜头具有良好的设计初值，基于混合镜组模型的变焦镜头设计方法能减少像差变量数量，准确、方便地完成像差设计。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"To facilitate zoom lens design, a systematic zoom lens design approach, based on mixed lens modules, is proposed in this paper, which consists of paraxial lens design, lens type determination, and aberration design. During paraxial lens design, Gaussian brackets and matrix optics are adopted, with which the relationship between component interval distances and component focal lengths can be easily determined. A lens module classification model is trained, with which the lens type can be determined from its thin lens parameters. More than 80% of the lens components have been successfully classified by the classification model. Mixed lens modules, namely thin lens modules and thick lens modules, are applied for aberration design of lens components, with which the component aberrations can be easily balanced and some practical considerations, such as interval distances between lens elements and components collisions, can be handled simultaneously. At last, an example is provided, which shows the detailed procedure of zoom lens design using mixed lens modules."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"光学设计"}],[{"name":"text","data":"薄透镜模型"}],[{"name":"text","data":"厚透镜模型"}],[{"name":"text","data":"像差设计"}],[{"name":"text","data":"变焦镜头"}],[{"name":"text","data":"远心镜头"}]]},{"lang":"en","data":[[{"name":"text","data":"optical design"}],[{"name":"text","data":"thin lens module"}],[{"name":"text","data":"thick lens module"}],[{"name":"text","data":"aberration design"}],[{"name":"text","data":"zoom lens"}],[{"name":"text","data":"telecentric lens"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"变焦镜头能连续改变自身焦距和放大倍率，获取被测物不同尺度的清晰图像，所以在工业测量、机器视觉、光刻"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"等领域获得了广泛应用。变焦镜头设计首先从近轴设计开始，确定镜组的焦距、镜头视场、物高、像高、变焦倍率和焦距范围等。虽然现在有很多文章关注变焦镜头的近轴设计"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"2","type":"bibr","rid":"b2","data":[{"name":"text","data":"2"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"6","type":"bibr","rid":"b6","data":[{"name":"text","data":"6"}]}}],"rid":["b2","b3","b4","b5","b6"],"text":"2-6","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"，但是有关变焦镜头的像差设计，尤其是近距离、小视场远心镜头的像差设计比较少"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"7","type":"bibr","rid":"b7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"8","type":"bibr","rid":"b8","data":[{"name":"text","data":"8"}]}}],"rid":["b7","b8"],"text":"7-8","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。像差设计方面，大部分文章采用薄透镜模型进行像差设计"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"9","type":"bibr","rid":"b9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"14","type":"bibr","rid":"b14","data":[{"name":"text","data":"14"}]}}],"rid":["b9","b10","b11","b12","b13","b14"],"text":"9-14","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"，也有少部分文章关注了厚透镜模型设计方法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"16","type":"bibr","rid":"b16","data":[{"name":"text","data":"16"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"17","type":"bibr","rid":"b17","data":[{"name":"text","data":"17"}]}}],"rid":["b16","b17"],"text":"16-17","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。基于薄透镜模型设计像差的优点是变量数量非常少，仅需中心球差、中心彗差以及中心轴向色差就可以模拟出每个薄透镜模型在不同变焦位置的所有三阶像差。但是采用薄透镜模型的缺点也非常明显：很多实际问题考虑不到，比如镜片厚度、镜片边缘厚度、镜片间隔、镜组间隔等；薄透镜模型中镜组场曲"},{"name":"italic","data":[{"name":"text","data":"S"}]},{"name":"sub","data":[{"name":"text","data":"Ⅳ"}]},{"name":"text","data":"计算时采用了平均镜片材料折射率，因此会降低每个镜组场曲"},{"name":"italic","data":[{"name":"text","data":"S"}]},{"name":"sub","data":[{"name":"text","data":"Ⅳ"}]},{"name":"text","data":"的计算准确性；薄透镜模型中畸变"},{"name":"italic","data":[{"name":"text","data":"S"}]},{"name":"sub","data":[{"name":"text","data":"Ⅴ"}]},{"name":"text","data":"和垂轴色差"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"Ⅱ"}]},{"name":"text","data":"为零，但实际镜组中对应的像差一般不为零；薄透镜设计完成之后需要逐步增加镜片厚度，在这个过程中可能会改变已经平衡的像差。采用厚透镜模型设计方法可以对每个镜组进行精确的像差估计，并且可以考虑镜片厚度、镜片间隔及镜组间隔等实际问题。但是在厚透镜模型中每个镜组需要9个变量来模拟镜组的所有三阶像差，这9个变量分别为球差、彗差、像散、场曲、畸变、光阑球差、轴向色差、垂轴色差以及光阑轴向色差。过多的变量使得后期的全局优化不易找到最优的极值点，并且会加大计算量。综合薄透镜模型像差设计方法和厚透镜模型像差设计方法的优缺点，本文提出了基于混合镜组的设计方法："}]},{"name":"p","data":[{"name":"text","data":"对于由一片或者两片镜片组成的镜组，镜片厚度对像差影响较小，因此采用薄透镜模型对其进行估计，这样可以减少变量数量；对于由三片或者以上镜片组成的镜组，镜片厚度对镜组像差的影响较大，因此采用厚透镜模型对其进行像差估计。由两片镜片组成的镜组总共有9个变量，分别为四个镜面曲率、两个镜片厚度、一个镜片间隔和两个镜片材料。一般近轴设计完成之后，每个镜组都有固定的焦距，因此实际上两镜片镜组有8个独立变量。同理，由三个镜片组成的镜组共有13个独立变量。厚透镜模型需要9个独立变量，两镜片镜组的独立变量数小于9，而由三镜片及以上镜片组成的镜组中独立变量数目大于9。这从另一方面解释了为什么对于由一片或者两片镜片组成的镜组，采用薄透镜模型；而对于由三片或者以上镜片组成的镜组，则采用厚透镜镜组。但是采用混合镜组模型设计需要在像差设计之前就要确定每个镜组是采用薄透镜模型还是厚透镜模型，从而能用尽量少的变量比较精确地估计镜头像差。然而，这对于光学设计初学者来说，有点本末倒置。有经验的设计者往往能够在设计之初就能大体确定每个镜组的镜组类型。为了能够有效地区分薄镜组和厚镜组，本文根据现有的大量镜头专利数据，从镜组的近轴数据和已知的镜组类型出发，训练了一个镜组近轴数据和镜组类型之间的分类模型。基于此分类模型，可以根据镜组的近轴数据估计出镜组类型。镜组分类模型采用Matlab的Classification Learner App，可以很容易地求解出镜组焦距和镜组间隔之间的关系。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"变焦镜头近轴设计"}],"level":"1","id":"s2"}},{"name":"p","data":[{"name":"text","data":"本文以物方远心镜头为例，首先对其进行近轴设计。如"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示，我们采用三镜组结构，从左到右依次为物面、镜组1、镜组2、镜组3和像面4。镜组"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3的焦距为"},{"name":"italic","data":[{"name":"text","data":"φ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，镜组"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"和镜组"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"+1之间的距离为"},{"name":"italic","data":[{"name":"text","data":"e"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，镜组的总长度为常数"},{"name":"italic","data":[{"name":"text","data":"L"}]},{"name":"text","data":"。"}]},{"name":"fig","data":{"id":"Figure1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"三镜组结构物方远心变焦镜头的近轴模型"}]},{"lang":"en","label":[{"name":"text","data":"Fig 1"}],"title":[{"name":"text","data":"Principal configuration of three-component object-sided telecentric zoom lenses"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757251&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757251&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757251&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"采用高斯括号和矩阵光学表示变焦镜头，则有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"1"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757255&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757255&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757255&type=middle"}}}],"id":"gxjmgc-26-1-38-E1"}}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"2"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757258&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757258&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757258&type=middle"}}}],"id":"gxjmgc-26-1-38-E2"}}]},{"name":"p","data":[{"name":"text","data":"式中：1和0指的是近轴主光线在镜组1上的入射高度和入射角度，"},{"name":"italic","data":[{"name":"text","data":"h"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"θ"}]},{"name":"text","data":"指的是此光线经镜组3之后的出射高度和出射角度，"},{"name":"italic","data":[{"name":"text","data":"φ"}]},{"name":"text","data":"指的是边缘光线在镜组1上的入射角度，"},{"name":"italic","data":[{"name":"text","data":"H"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"Φ"}]},{"name":"text","data":"指的是此边缘光线经过镜组3之后的出射高度和出射角度，"},{"name":"sup","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"，"},{"name":"sup","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"，"},{"name":"sup","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"，"},{"name":"sup","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"D"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"是高斯常量。它们都是关于镜组焦距"},{"name":"italic","data":[{"name":"text","data":"f"}]},{"name":"text","data":"和镜组间隔"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"text","data":"的量："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"3"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757262&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757262&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757262&type=middle"}}}],"id":"gxjmgc-26-1-38-E3"}}]},{"name":"p","data":[{"name":"text","data":"式中[…]为高斯括号，高斯括号的计算方法如下："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"4"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757266&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757266&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757266&type=middle"}}}],"id":"gxjmgc-26-1-38-E4"}}]},{"name":"p","data":[{"name":"text","data":"从式(1)和式(2)可得："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"5"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757269&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757269&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757269&type=middle"}}}],"id":"gxjmgc-26-1-38-E5"}}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"6"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757273&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757273&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757273&type=middle"}}}],"id":"gxjmgc-26-1-38-E6"}}]},{"name":"p","data":[{"name":"text","data":"根据主光线和边缘光线与像面的交点可得："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"7"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757277&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757277&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757277&type=middle"}}}],"id":"gxjmgc-26-1-38-E7"}}]},{"name":"p","data":[{"name":"text","data":"将式(5)和式(6)带入式(7)可得："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"8"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757280&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757280&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757280&type=middle"}}}],"id":"gxjmgc-26-1-38-E8"}}]},{"name":"p","data":[{"name":"text","data":"通常变焦过程中物面和像面之间距离保持不变，即："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"9"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757287&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757287&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757287&type=middle"}}}],"id":"gxjmgc-26-1-38-E9"}}]},{"name":"p","data":[{"name":"text","data":"如果限定变焦过程中"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"也为常量，则通过式(8)和式(9)，"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，和"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"可以表示为放大倍率m的量。"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，和"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"的具体表达形式非常复杂，但是其相应解析解可以通过Matlab获得"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，和"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"的关系如下："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"10"}],"data":[{"name":"text","data":" 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"},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757296&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757296&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757296&type=middle"}}}],"id":"gxjmgc-26-1-38-E12"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"h"}]},{"name":"text","data":"是边缘光线和薄透镜的交点高度，"},{"name":"italic","data":[{"name":"text","data":"K"}]},{"name":"text","data":"为薄透镜的光焦度，"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"text","data":"分别是镜片玻璃的折射率和阿贝常数，"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"是镜片曲率，"},{"name":"italic","data":[{"name":"text","data":"H"}]},{"name":"text","data":"为拉格朗日常数，"},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"text","data":"是镜片的弯曲变量，"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"text","data":"是镜片的共轭变量。"},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"text","data":"分别为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"13"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757299&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757299&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757299&type=middle"}}}],"id":"gxjmgc-26-1-38-E13"}}]},{"name":"p","data":[{"name":"text","data":"其中"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"分别是近轴边缘光线入射和出射镜片时的会聚角。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3"}],"title":[{"name":"text","data":"薄透镜中心拉格朗日变化公式"}],"level":"2","id":"s3-3"}},{"name":"p","data":[{"name":"text","data":"薄透镜中心拉格朗日变化是指当光阑位于薄透镜上且物体在无穷远时，改变主光线的入射角度或者改变近轴边缘光线的入射高度所引起的像差变化，如"},{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"和"},{"name":"xref","data":{"text":"2(b)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"2(b)"}]}},{"name":"text","data":"所示。中心拉格朗日变化过程中，拉格朗日常数不一定会发生变化。"}]},{"name":"fig","data":{"id":"Figure2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"薄透镜像差变化图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 2"}],"title":[{"name":"text","data":"Aberration calculation process"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757302&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757302&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757302&type=middle"}]}},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"14"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  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2(c)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(c)"}]}},{"name":"text","data":"所示。此时拉格朗日常数保持不变，这意味着物体尺寸要做相应变化，即："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"15"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757307&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757307&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757307&type=middle"}}}],"id":"gxjmgc-26-1-38-E15"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"g"}]},{"name":"text","data":"表示中心物像共轭；"},{"name":"overline","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"指的是每一个镜面偏心率："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"16"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757309&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757309&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757309&type=middle"}}}],"id":"gxjmgc-26-1-38-E16"}}]},{"name":"p","data":[{"name":"text","data":"当物体由无穷远移动到有限远位置时，"},{"name":"overline","data":[{"name":"text","data":"ε"}]},{"name":"text","data":"可按下式计算："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"17"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757311&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757311&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757311&type=middle"}}}],"id":"gxjmgc-26-1-38-E17"}}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.5"}],"title":[{"name":"text","data":"薄透镜中心光阑变化公式"}],"level":"2","id":"s3-5"}},{"name":"p","data":[{"name":"text","data":"薄透镜中心光阑变化是指光阑位置从薄透镜上移开后引起的像差系数变化量，如"},{"name":"xref","data":{"text":"图 2(d)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(d)"}]}},{"name":"text","data":"所示。"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"18"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757314&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757314&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757314&type=middle"}}}],"id":"gxjmgc-26-1-38-E18"}}]},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"italic","data":[{"name":"text","data":"w"}]},{"name":"text","data":"表示中心光阑变化；ε为光阑变化系数："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"19"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757317&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757317&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757317&type=middle"}}}],"id":"gxjmgc-26-1-38-E19"}}]},{"name":"p","data":[{"name":"text","data":"综上，采用薄透镜模型进行像差设计时先选择一个变焦位置，假设此时每个镜组有3个独立的中心像差：中心球差、中心彗差和中心色差。由式(12)可以确定此镜组在此变焦位置的所用中心像差。此镜组在其他变焦位置的中心像差可由薄透镜中心拉格朗日变化公式(14)确定。再经过薄透镜中心物像共轭变化公式(15)和薄透镜中心光阑变化公式(18)就可以确定镜组在不同变焦位置处的工作像差。将所有镜组的工作像差相加，即可得到变焦系统总的像差。然后通过全局优化算法，以最小化变焦系统总的像差为目标函数即可确定出每个镜组最优的3个中心像差。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"厚透镜模型像差设计"}],"level":"1","id":"s4"}},{"name":"p","data":[{"name":"text","data":"相比于薄透镜模型像差设计，厚透镜模型像差设计方法在像差估计上更为准确，且综合考虑了镜片厚度、镜片及镜组间隔等实际问题。然而厚透镜模型比较复杂，需要9个独立变量来表示所有的三阶像差。变量数目增多必然会增加后期优化计算的计算量，加大最优目标的寻找难度。"}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4.1"}],"title":[{"name":"text","data":"基于镜组结构的厚透镜像差计算"}],"level":"2","id":"s4-1"}},{"name":"p","data":[{"name":"text","data":"在采用厚镜组像差设计之前，这里首先给出镜组像差和镜组结构之间的关系式。如公式(11)所示，已知主光线和边缘光线在每个镜面上的折射不变量"},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"text","data":"、入射高度"},{"name":"italic","data":[{"name":"text","data":"h"}]},{"name":"text","data":"和会聚角"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"text","data":"，就可以计算出全部的三阶像差。"}]},{"name":"p","data":[{"name":"text","data":"如"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"所示，如果追迹的光线平行于光轴入射，则此光线在每个镜面上的"},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"h"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"text","data":"的计算公式为："}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"厚透镜镜组中追迹近轴主光线和近轴边缘光线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"Ray tracing of paraxial principle ray and paraxial marginal ray for a thick lens component"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757319&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757319&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1757319&type=middle"}]}},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"20"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  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Classification Learner App对镜组进行分类，分类器为Subspace KNN classifier，学习类型是nearest neighbors，maximum number of split是20，number of learners是30，the learning rate是0.1，subspace dimension是6，cross-validation是5。"}]},{"name":"p","data":[{"name":"text","data":"训练之后的分类模型见"},{"name":"xref","data":{"text":"图 4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"，其中0代表薄透镜镜组，1代表厚透镜镜组。训练得出的分类模型成功地将86%的薄透镜镜组和81.5%的厚透镜镜组进行了分类。此分类模型的准确率不是特别高，主要是因为决定实际镜组结构的因素非常多，存在很多不确定性。此分类的意义在于可以根据近轴数据给出一个镜组结构的指导方案。此分类对于后面的像差设计非常有意义，但是镜组的具体结构还需经后期优化才能最终确定。"}]},{"name":"fig","data":{"id":"Figure4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"Subspace KNN分类器的混合矩阵图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 4"}],"title":[{"name":"text","data":"Confusion matrix for trained Subspace KNN 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2"}]}},{"name":"text","data":"和"},{"name":"xref","data":{"text":"表 3","type":"table","rid":"Table3","data":[{"name":"text","data":"表 3"}]}},{"name":"text","data":"，其变焦位置如"},{"name":"xref","data":{"text":"图 5","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5"}]}},{"name":"text","data":"所示。"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"给出了不同变焦位置时镜组间距及相应的放大倍率，"},{"name":"xref","data":{"text":"表 2","type":"table","rid":"Table2","data":[{"name":"text","data":"表 2"}]}},{"name":"text","data":"给出了每个镜组的焦距，"},{"name":"xref","data":{"text":"表 3","type":"table","rid":"Table3","data":[{"name":"text","data":"表 3"}]}},{"name":"text","data":"给出了不同变焦位置处系统的拉格朗日不变量数值。由公式可见，每一个镜组间距"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"e"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"都有两个解。为了使变焦镜头连续变焦，所有解都要保证变焦镜组在变焦过程中均位于同一变焦轨迹上。"}]},{"name":"table","data":{"id":"Table1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"镜组间距及相应放大倍率"}]},{"lang":"en","label":[{"name":"text","data":"Table 1"}],"title":[{"name":"text","data":"Interval distances between components and corresponding 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10"}]}},{"name":"text","data":"稍有不同，因为除了三阶像差对镜组结构有影响外，高阶像差也会影响到镜组的最终结构。但是若在像差设计阶段引入高阶像差，则会大幅增加像差设计的计算量和计算难度。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"7"}],"title":[{"name":"text","data":"结论"}],"level":"1","id":"s7"}},{"name":"p","data":[{"name":"text","data":"本文提出了变焦镜头系统的设计方法，包括近轴设计、像差设计、镜组模型分类以及最终优化计算。近轴设计阶段采用高斯括号和矩阵光学，这样能非常方便地构建变焦镜头的数学模型。镜组间隔的解析解可以通过Matlab编程获得。像差设计阶段给出了基于薄透镜模型的像差设计方法和基于厚透镜模型的像差设计方法。每种模型的设计方法大体包含三组像差变化公式：中心拉格朗日变化公式、中心物像共轭变化公式和中心光阑变化公式。薄透镜模型设计方法相对简单，对于每个镜组只需要三个中心像差就可以估算出镜组在每个变焦位置下的工作像差。但其像差估计近似度不如厚透镜模型，并且薄透镜模型必然要经过一个镜片加厚的过程，此过程会改变之前设计好的镜头总的工作像差。厚透镜模型像差近似度高，而且镜片厚度、镜片及镜组间隔等实际问题可以在设计阶段解决，但需要9个独立变量来表示全部三阶像差，因此厚透镜模型较薄透镜模型要复杂很多。鉴于薄透镜模型和厚透镜模型像差设计的优缺点，本文提出了基于混合模型的像差设计方法。此方法需要在像差设计之前确定镜组是薄透镜模型还是厚透镜模型。为确定镜组类型，采用Matlab中Classification Learner App训练了一个镜组分类模型。输入预测量为镜组近轴数据，预测输出量为镜组类型：薄透镜镜组或者厚透镜镜组。虽然此分类模型的分类精度不是很高，不足90%，但是其对像差设计来说意义重大。最后以一个物方远心镜头设计为例展示了变焦镜头像差设计的全过程。像差设计的意义在于为镜头设计提供了一个良好的初始值，镜头最终的结构还需采用光学设计软件经过优化计算确定。镜头的最终结构和像差设计阶段的结构存在一定差异，主要是因为像差设计阶段只考虑了三阶像差而没有考虑高阶像差。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"b1","label":"1","citation":[{"lang":"zh","text":[{"name":"text","data":"徐明飞, 黄玮.高数值孔径投影光刻物镜波像差的自动平衡优化[J].光学 精密工程, 2015, 23(8):2143-2148."}]},{"lang":"en","text":[{"name":"text","data":"XU M F, HUANG W. Automatic balancing of wavefront aberrations in high-numerical aperture lithographic lenses[J]."},{"name":"italic","data":[{"name":"text","data":"Opt. Precision Eng"}]},{"name":"text","data":"., 2015, 23(8):2143-2148. (in Chinese)"}]}]},{"id":"b2","label":"2","citation":[{"lang":"en","text":[{"name":"text","data":"TANAKA K. Recent development of zoom lenses[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 1997, 3129:13-22."}]}]},{"id":"b3","label":"3","citation":[{"lang":"en","text":[{"name":"text","data":"KAZUO T. Zooming-component loci of mechanically compensated zoom lenses[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 1999, 3729:452-457."}]}]},{"id":"b4","label":"4","citation":[{"lang":"en","text":[{"name":"text","data":"TANAKA K. Zooming components loci of a generally constructed mechanically compensated zoom lens[J]."},{"name":"italic","data":[{"name":"text","data":"Optik-International Journal for Light and Electron Optics"}]},{"name":"text","data":", 2001, 112(6):232-238."}]}]},{"id":"b5","label":"5","citation":[{"lang":"en","text":[{"name":"text","data":"MIKS A, NOVAK J. Paraxial analysis of four-component zoom lens with fixed distance between focal points[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2012, 51(21):5231-5235."}]}]},{"id":"b6","label":"6","citation":[{"lang":"en","text":[{"name":"text","data":"YOUNGWORTH R N, BETENSKY E I. Fundamental considerations for zoom lens design[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 2012, 8488:848806."}]}]},{"id":"b7","label":"7","citation":[{"lang":"en","text":[{"name":"text","data":"KRYSZCZY ŃSKI T. Development of the double-sided telecentric three-component zoom systems by means of matrix optics[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 2008, 7141:71411Y."}]}]},{"id":"b8","label":"8","citation":[{"lang":"en","text":[{"name":"text","data":"MIKŠ A, NOVÁK J. Design of a double-sided telecentric zoom lens[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2012, 51(24):5928-5935."}]}]},{"id":"b9","label":"9","citation":[{"lang":"en","text":[{"name":"text","data":"HOPKINS H H. An analytical technique for stable aberration correction in zoom systems[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 1983, 399:100-135."}]}]},{"id":"b10","label":"10","citation":[{"lang":"en","text":[{"name":"text","data":"SALTER M J. Zoom lens aberration correction algorithm[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 2001, 4487:76-82."}]}]},{"id":"b11","label":"11","citation":[{"lang":"en","text":[{"name":"text","data":"MIKŠ A. Modification of the formulas for third-order aberration coefficients[J]."},{"name":"italic","data":[{"name":"text","data":"Journal of the Optical Society of America A"}]},{"name":"text","data":", 2002, 19(9):1867-1871."}]}]},{"id":"b12","label":"12","citation":[{"lang":"en","text":[{"name":"text","data":"MIKS A, NOVAK J, NOVAK P. Zoom lens design[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 2005, 5962:596233."}]}]},{"id":"b13","label":"13","citation":[{"lang":"en","text":[{"name":"text","data":"MIKŠ, NOVÁK J, NOVÁK P, Method of zoom lens design[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2008, 47(32):6088-6098."}]}]},{"id":"b14","label":"14","citation":[{"lang":"en","text":[{"name":"text","data":"PAL S. Aberration correction of zoom lenses using evolutionary progra mming[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2013, 52(23):5724-5732."}]}]},{"id":"b15","label":"15","citation":[{"lang":"en","text":[{"name":"text","data":"ZHANG J K, CHEN X B, XI J T, "},{"name":"italic","data":[{"name":"text","data":"et al"}]},{"name":"text","data":".. Aberration correction of double-sided telecentric zoom lenses using lens modules[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2014, 53(27):6123-6132."}]}]},{"id":"b16","label":"16","citation":[{"lang":"en","text":[{"name":"text","data":"PARK S C, SHANNON R R. Zoom lens design using lens modules[J]."},{"name":"italic","data":[{"name":"text","data":"Optical Engineering"}]},{"name":"text","data":", 1996, 35(6):1668-1676."}]}]},{"id":"b17","label":"17","citation":[{"lang":"en","text":[{"name":"text","data":"PARK S C. Zoom system design of 14X using optimized lens modules[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 1997, 3129:60-67."}]}]},{"id":"b18","label":"18","citation":[{"lang":"en","text":[{"name":"text","data":"BANERJEE S, HAZRA L. Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets[J]."},{"name":"italic","data":[{"name":"text","data":"Applied Optics"}]},{"name":"text","data":", 2001, 40(34):6265-6273."}]}]},{"id":"b19","label":"19","citation":[{"lang":"en","text":[{"name":"text","data":"CHATTERJEE S, HAZRA L N. Structural design of cemented triplets by genetic algorithm[J]."},{"name":"italic","data":[{"name":"text","data":"Optical Engineering"}]},{"name":"text","data":", 2004, 43(2):432-440."}]}]},{"id":"b20","label":"20","citation":[{"lang":"en","text":[{"name":"text","data":"CHATTERJEE S, HAZRA L N. Structural design of a lens component with prespecified aberration targets by evolutionary algorithm[J]."},{"name":"italic","data":[{"name":"text","data":"SPIE"}]},{"name":"text","data":", 2007, 6668:66680S."}]}]}]},"response":[],"contributions":[],"acknowledgements":[],"conflict":[],"supportedby":[],"articlemeta":{"doi":"10.3788/OPE.20182601.0038","clc":[[{"name":"text","data":"TH74"}]],"dc":[],"publisherid":"gxjmgc-26-1-38","citeme":[],"fundinggroup":[{"lang":"zh","text":[{"name":"text","data":"国家973重点基础研究发展计划资助项目（No.2014CB046604）；国家重大科技专项资助项目（No.2014ZX04015-021）；国家自然科学基金资助项目（No.51105255，No.51205251）；济南大学博士科研基金资助项目（No.XBS1641，No.XBS1640）；山东省联合专项资助项目（No.ZR2016EL14）"}]}],"history":{"received":"2017-04-21","accepted":"2017-06-01","ppub":"2018-01-25","opub":"2020-06-16"},"copyright":{"data":[{"lang":"zh","data":[{"name":"text","data":"版权所有©《光学 精密工程》编辑部2018"}],"type":"copyright"},{"lang":"en","data":[{"name":"text","data":"Copyright ©2018 Optics and Precision Engineering. All rights reserved."}],"type":"copyright"}],"year":"2018"}},"appendix":[],"type":"research-article","ethics":[],"backSec":[],"supplementary":[],"journalTitle":"光学 精密工程","issue":"1","volume":"26","originalSource":[]}