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<p>With the continuous improvement in semiconductor manufacturing precision, the impact of 6-degree-of-freedom (6-DOF) geometric errors in wafer fabrication equipment on process accuracy has become increasingly significant. This study proposes a compact optical measurement system based on geometric optics principles for measuring 5-DOF geometric errors of a linear axis. First, the proposed method combines laser collimation, laser autocollimation, and dual-laser beam techniques to measure geometric errors. A mathematical model is then established using skew ray tracing. Subsequently, the system’s average accuracy and repeatability are evaluated by comparison with a commercially available high-precision measurement instrument. Furthermore, this study develops a thermal error compensation technique for improving the positioning accuracy of the feed system of a single-axis platform based on multi-point temperature monitoring. Ten temperature sensors are employed for distributed monitoring, and a multiple linear regression analysis is used to establish the mathematical relationship between temperature variations and positioning thermal errors. To achieve precise compensation, two complementary strategies are further developed: the direct compensation method and the linear interpolation/extrapolation compensation method. Experimental results demonstrate that the overall mean absolute error is reduced from 0.35&#xa0;μm to 0.145&#xa0;μm, corresponding to an improvement of 58.6%. The compensation performance exhibits clear position dependency, with particularly significant improvements observed in the mid-to-long travel range, thereby confirming the effectiveness of the proposed approach. The proposed method provides a feasible and compact approach for geometric-error monitoring and thermal-error compensation in precision linear-motion systems.</p>

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Miniaturized Optical Measurement System for Five-Degree-of-Freedom Geometric Errors of Linear Axes and Compensating Thermal Deformation in Linear Positioning Axes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Hsin-Hua Chiang,
  • Chien-Sheng Liu,
  • Wei-Jen Chen,
  • Zhi-Kun Chen,
  • Chih-Chun Cheng

摘要

With the continuous improvement in semiconductor manufacturing precision, the impact of 6-degree-of-freedom (6-DOF) geometric errors in wafer fabrication equipment on process accuracy has become increasingly significant. This study proposes a compact optical measurement system based on geometric optics principles for measuring 5-DOF geometric errors of a linear axis. First, the proposed method combines laser collimation, laser autocollimation, and dual-laser beam techniques to measure geometric errors. A mathematical model is then established using skew ray tracing. Subsequently, the system’s average accuracy and repeatability are evaluated by comparison with a commercially available high-precision measurement instrument. Furthermore, this study develops a thermal error compensation technique for improving the positioning accuracy of the feed system of a single-axis platform based on multi-point temperature monitoring. Ten temperature sensors are employed for distributed monitoring, and a multiple linear regression analysis is used to establish the mathematical relationship between temperature variations and positioning thermal errors. To achieve precise compensation, two complementary strategies are further developed: the direct compensation method and the linear interpolation/extrapolation compensation method. Experimental results demonstrate that the overall mean absolute error is reduced from 0.35 μm to 0.145 μm, corresponding to an improvement of 58.6%. The compensation performance exhibits clear position dependency, with particularly significant improvements observed in the mid-to-long travel range, thereby confirming the effectiveness of the proposed approach. The proposed method provides a feasible and compact approach for geometric-error monitoring and thermal-error compensation in precision linear-motion systems.