本文以齊次座標轉換和平面邊界的歪斜光線第一與第二階微分，對三維複合稜鏡作分析與設計。稜鏡作分析方面，本研究探討了由Hagen與Tkaczyk提出之複合稜鏡，其複合稜鏡類型皆為直視稜鏡。直視稜鏡有幾個重要參數，如波長與偏向角，本文比較其微分之後的結果，藉此了解不同複合稜鏡的性質。
目前文獻只有二維複合稜鏡的設計方法，三維複合稜鏡的設計方法還沒有被提出，因此本文就三維稜鏡的設計提出一套數學方法，利用光波長與偏向角當成最佳化函數，再計算其第一與第二階微分，用最佳化程式得到稜鏡的頂角，並且舉了四個例子，分別為：消色差稜鏡，直視稜鏡，無偏移直視稜鏡，以證明其可行性。我們發現三維稜鏡可以用更少的元件就達到二維稜鏡的功能，而且效能並沒有輸給二維稜鏡，除此之外，利用柯西方程式取代阿貝數的計算，在光譜色散與非線性度的結果上也可以使誤差更小更精確。

SUMMARY

Compound prism is very common in the optical instrument. Therefore it is important to know the property of the compound prism. In order to analyze such prisms, in this thesis we use skew-ray tracing method to determine the derivatives of the deviation angle with respect to wave length. Furthermore, we design a 3-D dispersion prism using the first-order and second-order derivatives matrices of a skew ray. It is found that a single 3-D dispersion prism can achieve the function of a 2-D compound dispersion prism without sacrifice its performance.

Key words: skew-ray tracing;compound dispersion prism;dispersion prism;deviation angle

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