摘要
由於一般球面只有曲率半徑這一項變數，而非球面擁有其他高階項可變動的係數，所以可以提供更多提升光學系統品質的自由度。近來非球面製作技術的進步，降低了非球面的製作成本，使得非球面可以更廣泛的應用在光學設計上，因此有關非球面特性的研究越來越重要。
當軟體優化結果不如預期時，對於非球面有直接的認識或許可以提供方向自行微調，以達到所需的規格。因此本研究著重在於非球面係數的闡明，與三階像差之間的關聯，並且發掘非球面係數與三片型鏡組映像品質之間的關係。
本研究中提供幾種不同的做法調整非球面係數，達到縮小成像點尺寸的趨勢。並且這些微調的方法是有效的：當軸上物點時，光點的大小可以改善到比原先沒有做非球面改善時，降低兩個尺度(RMS：3.5590.05um)。而離軸時，可以降低一個尺度(RMS：68.325
6.575um)。而且與軟體優化的結果比較，並不遜色。因此，於本文實驗中所得到非球面係數與三階像差之間的關係以及調整之效果，可以作為設計光學系統時調整非球面係數的參考。

Abstract
A sphere has only one parameter, its curvature. But, an aspheric surface can have infinite parameters that will benefit the optimization of optic system design. With the improvement of the manufacturing ability of aspherics, the use of aspherics is becoming more and more common now a day, which makes the study aspherics more important.
In order to have a direct understanding about aspherics, which may offer some fine-tuning to reach the necessary specification when the optimization results of the software is not as good as expected. Therefore, our study focused on the coefficients interpretation, correlated to the third order aberrations, to dig out its relationships with respect to the image quality of a cooke triplet.
Several different experimental ways of coefficients adjustment have been made to master the reduction trends the image spot-size. We found the tuning method is effective: The on axis spot can be reduced about two orders (RMS: 3.559 to 0.05um) of magnitude; and off axis point can be reduced about one order (RMS: 68.325 to 6.575um) of magnitude. Both are comparable to optimization program, and even a little fine.

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, 1 October 2000