融合主成分分析與不確定理論之雷射干涉儀全域誤差辨識於控制器應用發展

在精密量測領域中，雷射干涉儀是確保工具機與半導體製程中位移平台達到高精度定位的重要量測設備，其量測不確定度之評估對控制器的位置補償具有關鍵影響。然而，由於機台架構差異與工廠溫控環境不一致，傳統不確定度分析方法往往僅針對各影響參數逐一分析，難以全面揭示量測數據中所隱含的「整體變異」（Structural Variability），尤其是在多變量量測情境中，各不確定度來源於不同操作條件下的交互影響亦難以被充分辨識。為突破上述限制，本研究提出一套基於主成分分析 （Principal Component Analysis, PCA）的不確定度診斷方法。相較於僅分析單一參數變異的傳統做法，PCA 能整合多項量測因子，解析其對系統所造成的整體變異模式，並辨識主導不確定度的關鍵因素。此方法可更全面掌握量測系統的變動來源，為精密量測設備的最佳化設計與誤差補償策略提供科學性的決策基礎。

In the field of precision metrology, laser interferometers serve as indispensable instruments for achieving high-accuracy positioning in machine tools and semiconductor motion stages. The proper estimation of measurement uncertainty is crucial, as it directly affects system calibration, error compensation, and overall equipment performance. Conventional uncertainty analysis methods typically evaluate each contributing factor independently, which often fails to reveal the underlying structural variability embedded within multivariate measurement data—particularly the coupled interactions among different uncertainty sources under varying measurement conditions. To address this limitation, this study proposes a principal component analysis (PCA)-based diagnostic technique for uncertainty evaluation. Unlike traditional approaches that focus on the variation of individual parameters, PCA enables the extraction and visualization of system-level variability patterns, thereby providing deeper insights into dominant uncertainty contributors. This method offers a more comprehensive understanding of the behavior of laser interferometer measurement systems and provides a data-driven foundation for improving precision positioning performance.