臺灣博碩士論文加值系統

在電子計算機及電腦發明前，前人就利用徒手計算出透鏡中的三階像差及多階像差值，實在非常辛苦及要耗費許多時間及精力，但站在二十一世紀，面對如此複雜的公式，實應借重於現在科技----電腦，為使計算簡單化，所以儘可能將像差公式程式化，並借重於三種軟體，分別是matlab、excel及zemax。
本研究主要工作分兩部份：第一部分是藉由探討單片透鏡中，形狀因子對於賽德像差及色像差的影響，以得到形狀因子會影響到賽德像差及色像差中的因子，及形狀因子的最佳值。第二部分，以第一部分得知形狀因子及與賽德像差和色像差的關係為基礎，來探討以三個形狀因子、三個鏡片K值及鏡片之間的二個間距的八個自由度來修正三片型鏡組中的賽德像差(球差、彗差、像散、場曲、畸變)、色像差(縱向色差、橫向色差)與系統焦距的八個參數，以得到最佳化的三片型鏡組。
本文中，由單片鏡推導到第四章的三片鏡的的三階像差，從各項專利及鏡片範例不難發現例子，但很少探究其原因及過程。希望在推導的過程中，本文能對光學研究者有所幫助。

Before the electronic accounting machine and the computer were invented, lens designer calculated the lens' third-order aberration and the multistage likely differential value without any technical instrument. It was really a laborious work. However, in the 21st century, it will be helpful to rely on computer to deal with the lens design formula. To simplify the computation procedure, the aberration formula will be programized with the aids of Matlab, Excel , and Zemax will be used to simulate the performance of the optical system.
This research includes two important parts. Firstly,through the discussion of single lens, it shows the influence of shape factor on the aberration and the chromatic aberration. It is aimed to find the shape factor which will affect the Seidel aberration and the chromatic aberration. The second part, based on the above result ,we will discuss the eight degrees-of-freedom in three shape factors,the K value of three lenses and the two spaces of lens in Cooke triplet. Then, the Siedel aberration (spherical aberration, bright difference, astigmatic aberration, field tune, distortion), and the chromatic aberration (longitudinal chromatic aberration, lateral chromatic aberration) will be corrected to meet the specifications of the designed system. Therefore, the optimal three piece of lenses group can be obtained.
In this paper, it shows the first order lenses structure can be got by fundamental image forming equations in chapter 4 which is often called the start point of lens design. In these days, it is easily to get this point from patents, lens demo, but it lacks the chance to know how it comes from.
Beside, we also show the power of the computer lens design pakage that it gives the advanced design by optimization process. I hope this paper will give the idea how the computer helps to design a lens system.

第一章 緒論……………………………………………1
第二章 像差的種類及意義……………………………3
2-1 像差理論…………………………………………………3
2-2 像差多項式及賽德像差 ……………………………4
2-2-1 球差(Spherical aberration) ……………5
2-2-2 彗差（Coma/Comatic Aberration）…………6
2-2-3 像散(Astigmatism) ………………………6
2-2-4 場曲(Curvature of field) ………………7
2-2-5 失真或畸變(Distortion) …………………8
2-3 色像差…………………………………………………9
2-3-1縱向色差……………………………………9
2-3-2横向色差………………………………………10
2-4 形狀因子……………………………………………11
2-5 光閘不同位置上時，賽德公式的修正……………12
2-5-1單透鏡光閘放置在透鏡上……………………12
2-5-1單透鏡光閘離開透鏡修正公式………………13
第三章 單透鏡賽德像差及色像差計算分析………16
3-1 光閘在單透鏡上的賽德像差及色像差………………16
3-2 光閘不在單透鏡上的賽德像差及色像差……………17
3-3 討論……………………………………………………17
第四章 三片鏡組的像差修正………………………20
4-1 經由薄透鏡的K值與空氣間距的安排來調整像差…20
4-1-1 固定第三片的截高……………………………22
4-1-2 同時調整第二片及第三片的截高……………24
4-2 調整透鏡形狀因子來修正像差………………………25
4-3 薄透鏡的加厚…………………………………………29
4-3-1 加厚的原則…………………………………29
4-3-2 透鏡加厚厚度的範圍值………………………30
第五章 結論與未來工作……………………………33
5-1 三片鏡的討論……………………………………33
5-2 結論……………………………………………………36
5-2 未來工作………………………………………………37
參考文獻………………………………………………39
附錄……………………………………………………41

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