本文主要利用幾何光學原理與齊次座標轉換法推導歪斜光線追蹤法，進而探討光學系統之成像光斑與立體角大小。

文中藉由歪斜光線追蹤法，配合各透鏡組的特性參數及光源與透鏡間的幾何關係建構出匹茲堡透鏡系統模型，應用
此光學系統模型透過「不同入射方式」及「光源位置變化」的方式，進行光斑大小的計算分析與實際模擬的成像分
析，以期能使光學系統的成像品質有較佳的效果。

由於模擬過程中發現，不同位置的光源所能入射至光學元件邊界面的光束大小不同，若光線無法射至成像光屏，便
會在入射過程中發散掉，此一結果使得各種光源位置所能追蹤光線的數目不同。因此在本文中我們提出「尋找光束
大小」的方法，使得我們可知各光源能入射至成像光屏的光束大小，進而決定欲追蹤的光線數目。

在設計光學系統時，立體角大小是可影響光學系統性能的重要參數之一，因此在本文的最後，我們將藉由近距離光
軸上的光源可射入第一光學邊界面的光束大小，透過不同的角度增值量，計算該邊界面上的立體角大小，並對其結
果進行分析。

In this thesis, we derived skew ray tracing method to analysis the spot size and solid angle of an optical system.
The method is derived from the Snell’s Law and a homogeneous coordinate transformation matrix.

We applied the well-known skew ray tracing method and developed a model of a Petzval Lens System by combining the
parameters of each lens and the geometrical relationship between the source and the lens. We expected the way of
better image quality can be achieved through spot size computation and image simulation by using different
“shooting methods” and “source locations” on the model to analysis the spot size.

During the simulation progress, we found that different locations of sources will induce the different cone-sizes
on the boundary surfaces. If any light can not shoot to the screen, it will diverge from the optical path. This
results that different source locations trace different ray quantities. For this reason, we developed a method,
finding cone-size, so that we can determine the cone size on the screen and decide how many rays we want to trace.

Solid angle is one of the important parameters for designing optical systems. Therefore, we also computed the
solid angle from a on-optical-axis-source to the first boundary surface which has a small distance between them
through changing the number of βin the end of this thesis.

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