本論文提出利用幾何光學原理，來設計線性軸長行程六自由度誤差量測方法及裝置。本系統以一額外線性軸拖曳感測器，讓光點在感測器內來回移動，使其能夠突破以往幾何光學量測受到感測器大小的限制，完成長行程六自由度誤差量測。本系統對比昂貴的市售雷射干涉儀，本研究所提出的量測系統的成本更低，架構簡便，還可以同時量測六自由度誤差等優勢。
本論文會先以Zemax光學模擬軟體模擬光路中六自由度誤差與感測器變化量的關係，再利用Matlab數學軟體利用歪斜光線追跡法建構出所有光路的正逆向數學關係，並使用曲線擬合來簡化數學模型，最後實際將系統架設起來，並實際架設到市售工具機進行量測。
本論文也提出一能解決光學量測系統之系統誤差的方法，利用六軸史都華平台給予精確的六自由度運動，並透過數學關係計算得到真實的逆向方程式，最後將二種逆向數學進行實驗比較，確認此方法的可行性。

In this study, a linear stage six-degree-of-freedom error measurement system based on geometry optics is provided. The proposed system utilizes an extra linear stage to drag the sensor on it, makes the light spot projected on the sensor shift back and forth when the moving stage moves. This method successfully makes long range six-degree-of-freedom error measurement become possible. Compared with commercial laser interferometers, the proposed measurement system has the advantage of lower cost, simple structure, and the capability of measuring six-degree-of-freedom error simultaneously.
In the beginning of the study, Zemax is used to simulate the relationship between the six-degree-of-freedom error and the value of the position sensitive detectors (PSDs). After that, utilize Matlab to construct the forward and reverse mathematical kinematics model of all optical paths, and simplify the mathematical model by curve fitting. Last but not least, because of the installation error and the manufacturing error, the real reverse kinematics mathematics is obtained with the six-axis Stewart platform. In the experiment, the proposed system is set up on the commercial linear axis to measure the six-degree-of-freedom error, and verify by the commercial interferometer and electronic level.

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