光線追蹤對於光學系統的設計與分析極為重要，其主要可分為歪斜光線追蹤與近軸光線追蹤方法。本文中所探討的近軸光線追蹤是用於處理光線極為接近光學系統中心軸的光線傳播，在許多光學教科書的特定章節中，都包含有關使用基於2x2 ABCD 矩陣的傳統近軸光線追踪方法，對軸對稱系統進行初始的光學設計。然而，這些傳統的近軸光線追蹤方法僅適用於軸對稱的光學系統。本論文通過使用一階泰勒級數展開來近似歪斜光線追蹤方程式，獲得一組適用於三維非軸對稱系統的近軸光線追蹤矩陣。通過在軸對稱與非軸對光學系統中的數值驗證結果顯示，本文提出的方法能夠準確地追蹤光線位置，為像差分析奠定基礎。

Many optical textbooks include specific chapters on the use of conventional paraxial raytracing techniques based on ABCD matrices to obtain initial estimates of the optical systems in the design stage of axis-symmetrical systems. However, these conventional paraxial raytracing techniques are valid only for systems having a common straight-line optical axis. This thesis circumvents this limitation by using the first-order Taylor series expansion to approximate the skew-ray tracing equations and obtain a set of matrices for paraxial raytracing. The numerical results show that the proposed method can determine the rays accurately, and consequently can lay the foundation of aberration explorations.

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