本文主要利用歪斜光線追蹤法，探討如何分析及設計一稜鏡，使之能用以來導引物所發出的光線，在經稜鏡多次反射後，其最後看到的虛像與物之間能達到指定的方位變化（在此簡稱為成像位姿變化），並成功地發展出完整且純解析的稜鏡設計理論。
　　傳統的稜鏡設計方法，乃是以幾何圖解法或數值近似的方法，利用試誤方式一步一步慢慢地尋找解答。但此粗略的設計方法，除了曠日費時且無法提供解析的結果外，在光學分析上也有一定的難度。因此，本論文深入探討歪斜光線追踪與靈敏度分析，並推導出單一平坦邊界折(反)射矩陣的數學模式，並以此為像位變化的數學模式基礎，進而建構出優化函數矩陣之理論。其中，優化函數矩陣可以非常完整且明確地描述物在經過一連串任意的平坦邊界成像後其像位變化。接著由優化函數矩陣與反射矩陣出發，發展出不同以往的稜鏡設計理論。
　　本文針對不同的設計需求，發展了二種不同的稜鏡設計方法：矩陣分解法與輔助向量法。其中，矩陣分解法較適用於簡單的系統，方便且直接；而輔助向量法，乃是引進了一套輔助旋轉軸與輔助旋轉角，設計出最少反射面的稜鏡，並找出其解析解。而其中所有參與稜鏡設計的數學建模過程，完全利用代數解析的方法來推導及求出解答，而完全不用數值逼近求解法，可見其本文設計理論之精確度與便利性。

This paper presents an exactly analytical methodology of prism analysis　and design base on an image with a required orientation change with respect to the object (referred to as Image Orientation Change for short) by using the methods of skew-ray tracing and sensitivity analysis.
Traditional prism design of this kind is a trial-and-error with the aid of geometrical drawing and difficultly provides analytical results. By using skew ray tracing sensitivity analysis, a reflector matrix is addressed. In addition, a merit function matrix is presented which can specify image orientation change after the image is reflected by an arbitrary number of flat boundary surfaces. Base on the applications of reflector matrix and merit function matrix, we develop the diffenent design method from traditional method.
Two design approaches are proposed in this paper. One can obtain many different configurations of prisms by matrix decomposition method which is sutalbe for simple system design. The other can design a prism with a minimum number of flat boundary surfaces by the aid of an auxiliary unit vector, and the exact analytical solutions are addressed and then find our the analytical solutions. In particular, the methemetical modeling of this prisms design method is exactly algebraic analytical instead of numerical approsimation. Consequently, compared with traditional trail-and-error methods, the propose approaches are more systematic, efficient, and accurate.

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