二自由度平面移動平台在3D列印、雷射切割、CNC機械加工與視覺量測等領域都被廣泛使用，為了提升精度，必須量測二自由度平面移動平台的誤差。為了能夠實現多自由度的精密量測，本論文提出一個光學量測系統來量測二自由度平台的二自由度定位誤差。本系統基於幾何光學、歪斜光線追跡與齊次座標轉換，並以上述理論建立數學模型並與光學模擬軟體 ZEMAX 進行比較，此方法可減少數學運算量，提升量測效率。
除此之外，本論文也提出雷射源四自由度擾動的補償方法與解耦矩陣校正，首先，本論文使用被動式補償雷射源四自由度擾動誤差，並使用均化功能使雷射源擾動的影響降低，再將量測到的雷射源四自由度擾動誤差放入數學模型進行解析，可以在數學上扣掉雷射源擾動誤差的影響，進而提升精度；解耦矩陣校正方面，本論文使用更精細的解耦矩陣校正法，透過市售干涉儀量測出準確數據，並使用最小平方法進行線性擬合後，可進一步校正解耦矩陣，相較於過去修正工程參數的校正方法，此方法可以更精確的擬合出符合真實實驗情況的解耦矩陣，且可以在一定程度上降低安裝誤差所造成的影響。

A two-degree-of-freedom planar motion platform is widely used in various fields such as 3D printing, laser cutting, and CNC machining. In order to enhance accuracy, it is necessary to measure the errors of the two-degree-of-freedom platform. To achieve multi-degree-of-freedom precision measurement, this paper proposes an optical measurement system for measuring the two-degree-of-freedom positioning errors of the platform. This system is based on geometric optics, skew ray tracing, and homogeneous coordinate transformation. A mathematical model is established based on the above theory and compared with the optical simulation software ZEMAX. This method can reduce the computational workload and improve measurement efficiency.

In addition, this paper presents a compensation method for the four-degree-of-freedom laser drift and a correction method for the decoupling matrix. Firstly, passive compensation is used to compensate for the four-degree-of-freedom laser drift errors, and the influence of laser drift is reduced by averaging. The measured laser drift errors are then analyzed by the mathematical model, so as to solve the laser drift errors and improve accuracy. As for the decoupling matrix correction, a more precise decoupling matrix correction method is used. Accurate data is obtained through commercial interferometers for linear fitting using the least squares method, enabling further correction of the decoupling matrix. This method can more accurately fit the decoupling matrix to the experimental conditions, and to some extent, mitigate the effects of installation errors.

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