光學元件量測的精確性與科技的發展息息相關，包括光學機構尺寸微小化，影像品質的細膩度，甚至是近年來的奈米技術也有極大的關連。而本研究針對光學元件量測機構，利用4×4齊次座標轉換矩陣與幾何光學Snell定理，推導歪斜光線追蹤法。利用此法對光學對心機與雷射對心機做機構建模與理論分析，且對其偏心誤差的量測公式做詳盡推導。

　　偏心誤差的量測對光學元件影響十分深遠，本研究使用歪斜光線追蹤法做建模與分析可瞭解其真正的光線路徑，進而推導出真實量測公式。在光學對心機公式推導中，平行光聚焦位置與量測結果有很大的關係，本研究在聚焦平面上作光點分佈情形，以確定聚焦位置，推導出真實公式。而雷射對心機公式推導，視雷射光線為單一光線，採用歪斜光線追蹤法，找出其光線在感測平面落點位置。求得真實公式後，研究發現誤差值極小時，偏心誤差與感測器量測半徑可視為近似線性關係，將真實公式做一階微分近似後，即得精簡的近似公式。

　　Precise measurement of optical unit have led to many technical advances, including making optical mechanism smaller and image quality fine and smooth. Even the recent nanotechnology was related to precise measurement of optical unit. The purpose of this paper is using a skew ray tracing method to modeling and analysis of centering device.

　　This method is derived from 4×4 homogeneous coordinate transformation matrix and geometrical optics Snell’s law. We made a detailed description for the measure theory of decentration error.

　　The measurement of decentration error has important influence for optical unit. We can know the real optical path by using a skew ray tracing method to modeling and analysis of centering device, and further, infer a real measure theory from the modeling. After finding real tilt angle formula, then the formula can be take as approximate linear function when decentration error is very small. We use one order differentiation for the real tilt angle formula. The difference formula can be derived from Taylor's formula. The result of the differentiation produces a easily and precise formula.

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