目前使用的光學系統，大部分是球邊界面，但球邊界面會有像差的存在，進而造成品質下降。非球邊界面可以改善球面邊界的缺點，但因為製作困難，價格上也較為昂貴，但在幾何光學中，仍佔有重要地位，值得深入探討，而圓柱體透鏡就是其中一種非球邊界面。
本文藉由歪斜光線追蹤法，來求得圓柱體透鏡的結構參數，由其折(反)射光線方向及入射點位置，導出光線經過圓柱體的成像方程式，並利用這些參數，對元件作出光源變化量以及元件位姿偏移量所產生的靈敏度分析，再利用FORTRAN電腦程式分析出，期待圓柱體面鏡能產生更好的成像品質。
文中也提到圓柱體透鏡於眼睛散光矯正的應用，由於患有散光者，在不同角度會有不同的聚焦情況，所以可利用圓柱體透鏡於一軸度的放置，使光線都能有相同的聚焦能力，最後會根據散光的五種情況，來做矯正情況的模擬。

The majority of optical systems are based on spherical components because they are easy to manufacture and low in costs. But the aberration from a spherical boundary is inevitable and may degrade the quality of image. Aspherical boundary surfaces are more difficult and expensive to make. However, there are cases where components with aspherical boundary surfaces have a significant advantage over spherical ones. Thus the aspherical boundary surfaces are worthful for study.
In this thesis, we used skew-ray-tracing method to obtain parameters of cylindrical lens structure. We can derive the image-forming equation according to refracted/reflected vector and incident point. We obtained the sensitivity analysis that determine by direct mathematical analysis based on differential changes in incident light source or orientation of optical element.
We also wrote the application of cylindrical lens that used in astigmatism. Because astigmatism have five cases, we must use cylindrical lens and spherical lens to improve these cases.

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