高精度光電式動作/位置量測系統，大都是利用光線在兩個光學組件間進行多次折反射，以提高精確度。但是要精確求得感測器讀值與待測位置/角度的關係函數並不容易，本文即是在解決此問題。本文以一個量測系統作為範例，並用歪斜光線追蹤法配合有限差分法，推導出感測器讀值的關係函數，驗證本文所提出之方法，結果顯示本文之方法可精確地提供位置感測器函數。此外，本文另外建立光電式水平儀、高精度角度量測系統及六自由度量測系統等三個光電式多自由度量測系統。
本研究之光電式水平儀由一個單擺、兩個平面反射鏡、一個二維位置感測器及一個雷射二極體所組成，其可用於同時量測兩個垂直方向之傾斜角度。為驗證系統建模結果，本文實際架構此系統，並完成系統校正及穩定度測試等實驗。
本研究之高精度角度量測系統利用一個雷射二極體、一個二維位置感測器及兩面平面反射鏡之間的連續反射達成高精度角度量測。本文已完成系統校正及穩定度測試已完成，系統的精度及量測範圍分別為0.05 arc sec及±250 arc sec。
本研究之六自由度量測系統由一個錐形多面反射鏡、三個雷射二極體及三個二維位置感測器所組成。為驗證系統建模結果，本文實際建構此系統，並完成系統驗證及穩定度測試等實驗。穩定度測試結果顯示本系統之位移量測穩定度約為±1 μm，旋轉量測穩定度約為±1.5 arc sec。

High-accuracy laser-based optoelectronic motion and position measuring systems typically utilize light rays that travel from one optical assembly to another to perform motion and/or position measurements. It is not a simple task to accurately determine the equations of these sensor readings in terms of positional/angular motions. This problem is addressed in this paper by application of the analytic skew-ray tracing methodology as computed by finite difference methodology. An illustrative example of a motion measurement system and comparison of the Position Sensing Detector (PSD) readings are given to validate the proposed methodology. It is shown that the proposed methodology can provide accurate expressions of PSD readings. Based on the proposed methodology, the following three optoelectronic multi-degree-of-freedom measurement systems are established: an optoelectronic inclinometer, a high angular accuracy measurement system and a six Degree-Of-Freedom (DOF) motion measurement system.
The optoelectronic inclinometer which can measure inclination angles along two orthogonal directions simultaneously by using a simple pendulum, two mirrors, a 2-axis PSD, and a laser diode. To validate the proposed methodology, an actual prototype system is built, and its calibration and stability experiments are performed.
The high accuracy angle measurement system performs angle measurement by use of laser-diodes, 2-axis PSDs and a series of reflections between two first-surface-mirrors. Calibration and stability experiments are performed. Experimental results show the accuracy and measurement range are, respectively, 0.05 arc sec and ±250 arc sec.
The six-DOF measurement system comprises a pyramid-polygon- mirror, three laser diodes and three 2-axis PSDs. To validate the proposed methodology, a laboratory prototype system is built. System verification and stability tests are conducted to evaluate its performance. Stability test results show that measurement errors and maximum crosstalk are within ±1 μm in translation and ±1.5 arc sec in rotation.

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