雷射於目前工業發展佔有重要地位，常應用在訊息傳送、成像、切削、量測、定位等技術上。提高雷射的效率，減少能量的散失是重要的課題。為達到減少能量散失的目的，現今常利用二維光線追蹤法推導不使光線偏離雷射震盪腔的限制條件。然而二維光線追蹤法設計的前提皆為光線通過震盪腔之光軸，在現實的雷射震盪腔為三維空間的情形下，腔內存在著不通過光軸的光線，二維光線追蹤法推導的限制條件是否一樣能限制其路徑，使得不經光軸光線不偏離雷射震盪腔，需要進一步的探討。
本文藉由三維近軸光線追蹤法建立三維雷射震盪腔的光學系統傳播反射矩陣。利用Matlab電腦程式，運算得到在三維雷射震盪腔內不經過光軸之近軸光線路徑，並使用歪斜光線追蹤法進行數據驗證確保模擬的精確度。更進一步利用歪斜光線法追蹤三維雷射震盪腔內非近軸光線在不經過光軸的情形下，是否會發生偏離震盪腔之情形。

Laser has taken up important roles in modern industry, it is commonly used in communication, imaging, milling, measurement and positioning techniques. To improve the efficiency of laser is a key aspect to lower energy dissipation. For this reason, recent techniques often involve two dimensional ray tracing derivation to satisfy the requirement of not diverting the rays from their resonator. However, two dimensional ray tracing techniques are designed under the assumption of rays passing through the resonator ray axis, but since realistic resonator are of three dimension, there exists rays that does not pass through the ray axis of the chamber. In this sense, whether two dimensional ray tracing derivation can restrain the rays not aligned with the ray axis within the resonator should be looked into.
This paper establishes a three dimensional optical system transfer reflection matrix by three dimensional near axis ray tracing. By Matlab programming, the path of near-axis rays within a three dimensional resonator is computed, and the result is compared with the data of skew axis tracing techniques to confirm the accuracy of the simulation. Skew axis tracing is further used to verify the off set of non-near-axis rays from the resonator.

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