現今的光學量測方法只有部分技術能量測厚度與折射率，通常僅適用於極薄物質或單層特性的個別量測，少部分研究雖然能夠同時量測球面透明物質的曲率半徑、中心厚度和折射率，但這些方法往往成本高昂，限制了其廣泛應用。本論文以光學基本定律為基礎，提出一套新穎的光學量測方法，透過簡易的光路架構搭配歪斜光追跡，將量測目標從平面待測物延伸至球面待測物，不僅能同時量測出厚度與折射率，也能量測球面之曲率半徑，以提升其應用範圍。
首先，本量測系統透過齊次座標轉換矩陣定義每個介面座標，再搭配歪斜光線追跡建立數學模型，接著，利用 Z 軸電動位移平台上下移動球面待測物，使得量測光線接觸至待測物表面的入射角發生變化，產生兩個入射點的不同光路，由感測器擷取從待測物各邊界表面反射與折射的光斑影像，透過結合最大值法與灰度重心法的影像處理技術計算光點座標，再將此座標資訊代回數學模型中以計算所求未知數。
本論文使用MATLAB建立量測系統之數學模型並驗證正、逆向數學模型，利用ZEMAX光學模擬軟體建立系統架構，初步驗證系統以及影像處理方法之可行性，並透過SOLIDWORK繪圖軟體確立各元件的架設位置。系統之量測範圍為 100 mm ≤ 曲率半徑 R ≤ 940 mm 、1 mm ≤ 中心厚度 t ≤ 10 mm 以及 1 ≤ 折射率 n ≤ 3.6，且本系統在量測範圍內的曲率半徑、中心厚度以及折射率之最佳精度分別為 0.01 mm、0.0001 mm 與 0.001。
經模擬結果證實，本量測系統可在設定的量測範圍內，達到同時量測曲率半徑、中心厚度及折射率，也藉由模擬驗證系統的正確性與穩定性。最後將量測系統實際架設於光學桌，並藉由校正方法補償系統安裝誤差後，進行實際實驗與分析，以此驗證本系統實際的量測精度與重複性。

In contemporary optical measurement techniques, only a few methods could measure both thickness and refractive index of spherical transparent materials simultaneously, such methods are often prohibitively expensive. This paper proposes an innovative optical measurement method based on fundamental optical principles. A simple optical path setup combined with skew ray tracing achieves the simultaneous measurement of the radius of curvature, central thickness, and refractive index of spherical transparent materials.
Firstly, the measurement system establishes a mathematical model using homogeneous transformation matrices combined with skew ray tracing. The spherical object to be measured is moved up and down along the Z-axis using a motorized displacement platform, creating different optical paths from two incident points. The sensor captures the light spot images, and by employing image processing techniques that combine the maximum method and the grayscale centroid method, the coordinates of the light spots are calculated. These coordinates are then substituted back into the mathematical model to determine the unknown parameters.
In this paper, MATLAB is used to establish and verify the mathematical model of the measurement system in both forward and reverse directions. ZEMAX optical simulation software is utilized to construct the system architecture, preliminarily confirming the feasibility of the system and the image processing method. Additionally, SOLIDWORKS drawing software is employed to determine the installation positions of various components. Simulation results confirm that within the designated measurement range, the system can simultaneously measure the radius of curvature, central thickness, and refractive index of the spherical object. The accuracy and stability of the system are also validated through simulations. Finally, a calibration method is implemented to compensate for installation errors, followed by actual experiments and analysis to validate the practical measurement accuracy and repeatability of the system.

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