本論文是以齊次座標轉換矩陣，將光學系統模型以矩陣方式，建構完整的光線追蹤理論。在一般情況下，光學系統邊界面的光程長和光線可以使用歪斜光線追蹤方法計算，而光程長和光線的導數可用有限差分的近似方法或差分方法求得。然而光學系統的折、反射方程具有高次非線性，從而推導計算系統變數時，總是繁瑣且相當費時，因此以實驗室發展的方法，從推算平面邊界的光路徑幾何長度改變量，進而以求得光源與系統變數的改變對光程差所造成的變化量，且以此方法對菲涅爾雙面鏡與雙稜鏡波前分割干涉儀進行靈敏度分析，並以程式驗證以及評估每個變數的變化對系統所造成的影響。

This study constructs a new method for skew ray tracing by using homogeneous coordinate transformation matrix. The optical systems model matrix to construct a complete theory of ray tracing. In general, the optical path length and ray at the boundary surface in an optical system can be computed using a skew-ray tracing approach. The derivatives of Optical Path Length and ray can be obtained using either Finite Difference approximation methods or differential methods. However, the refraction and reflection equations in optical systems have a high degree of nonlinearity, and thus computing the derivative quantities is time-consuming and cumbersome. Therefore, a mathematical method developed by determining the Jacobin matrix of OPL with respect to system variable such that the change of OPL due to the changes of system variables. The proposed method applied in some wavefront-splitting interferometers, examples include the Fresnel double mirror and Fresnel’s prism.

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