近軸光線之2×2矩陣追蹤法通常被用來做光學系統設計之初步性能評估，但這種方法僅適用於分析光軸為一直線(common straight-line optical axis) 之光學系統，若系統中包含了反射鏡和(或)稜鏡則不再適用，亦即傳統的2×2矩陣追蹤法無法用來分析三維的光學系統。因此本論文進一步擴展實驗室已發展出的6×6矩陣追蹤法，用來分析與設計包含反射鏡、球面鏡或是稜鏡的三維非共軸面(非直線光軸)光學系統，並做初步設計階段的像差分析，且提出一個光學系統設計範例，以本論文所提出的方法來進行分析並以程式與光學設計軟體驗證之。因此本研究旨在延伸了早期以近軸光線矩陣追蹤法對光學系統的設計技巧，使其具有可應用於含有反射鏡和(或)稜鏡的光學系統，並且以焦距來表示光學元件的折(反)射能力矩陣，進而將矩陣推展至適用於三維光學系統，簡化複雜的數學模型。

Paraxial ray tracing using ray matrices is commonly used for first estimates in early design stages of optical systems. However, this technique is suitable only for rays in systems with a common straight-line optical axis, and cannot be used in 3-D systems. This study extends the applications of the ray matrices to analyze the non-coplanar systems containing mirrors and/or reflecting prisms for first estimates in early design stages of 3D optical systems. The primary astigmatism, distortion, chromatic aberrations of a 3-D system can be investigated analytically. An illustrative example is designed and analyzed by the proposed methodology and commercial software for comparison. This study extends earlier Matrix-based paraxial ray-tracing design technique to include non-coplanar systems containing mirrors and/or reflecting prisms. It is also to make the reflection and refraction matrices represented by focal length. Furthermore, these matrix will be extended to 3-D optical systems in order to simplify the complicated mathemtical model.

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