摘 要

　　雷射追蹤技術的運用領域十分廣泛，例如:醫療上對病人的姿勢校準、雷射近視手術時的眼球追蹤定位、軍事上對飛行物體目標的追蹤以獲得軌道的資料、特殊車輛的追蹤、與工程上對構件的3-D座標量測等。利用雷射追蹤技術所發展而成的雷射追蹤器可以克服大型物件量測的限制，並在大型的工作範圍內做三度空間座標量測。然而目前此儀器的量測精度，尚無法與三次元量床媲美，因為此系統的反射鏡尺寸誤差及回射器的對準誤差會降低系統的精度。
　　由於雷射追蹤器有潛力成為精密量測的重要儀器，因而激起本研究之動機。本文首先利用4×4齊次座標轉換矩陣為數學工具，就光線行經介質邊界時，其折(反)射光線行進方向及入射點位置進行回顧。並以靈敏度分析矩陣組成光學系統評價函數，設計雷射追蹤器的回射器，經分析其性能較以近軸光學法設計之回射器有更好的回射性質。
經由儀器的誤差分析，可提高應用儀器的量測精度。因此本文將運用歪斜光線追蹤法，對雷射追蹤器進行數學建模，進而推導該儀器的位置感測器讀數、干涉器讀數，及分析雷射追蹤器的運作方式，並利用軟體模擬，以驗證方程式的正確性並進一步實施誤差分析。
　　雷射追蹤器會因製造精度不足而有誤差，本文考慮三種主要的誤差: (1)反射鏡機構的尺寸誤差；(2)量測操作時的回射器對準誤差；(3) 位置感測器的誤差讀數與伺服馬達編碼器讀數的關係。由誤差分析的結果得知：(1)反射鏡機構的尺寸誤差，對雷射追蹤器精度影響很大；(2)用實心玻璃直角回射器量測，只能透過細心謹慎的量測，才能提高雷射追蹤器的精度。若用垂直角鏡回射器，則無對準誤差，此亦為雷射追蹤器均使用垂直角鏡回射器的緣故。
　　本文最後以實際量測進行驗證。利用CMM的量測值與雷射追蹤器的實際量測值做比較，發現雷射追蹤器的精度尚有改善的空間，未來將發展可行的校正理論，做為提高雷射追蹤器精度的有效方法之一。

ABSTRACT

　　Laser tracking techniques are widely used in many fields, for example patient alignment in CT scanning, eye movement tracking for laser eye surgery, target tracking for military applications and 3-D coordinates measurement for engineering purposes. Coordinate measurement laser trackers (CMLT) such as the Leica Smart 310 have two major advantages: (1) the ability to track a target retroreflector automatically; (2) the ability to measure large objects.
　　CMLT have great potential as precision measuring instruments, but its precision is compromised by errors during manufacture and operation. Therefore this study presents a skew ray tracing method for modeling and sensitivity analysis of CMLT. In order to achieve this, revolution geometry, homogeneous coordinate transformation matrices and Snell’s laws are used to determine: 1) the direction of refracted (reflected) rays based on Snell’s laws; 2) sensitivity analysis expressing differential changes of refracted (reflected) rays in terms of differential changes of incident rays. These are then applied to the optimum design of a cat’s eye retro-reflector. Finally, the skew ray tracing method is employed to build a mathematical model of the CMLT and to study the effects of possible errors to CMLT measurement results. Three major errors are considered in this study: 1) dimension errors of the mirror mechanism; 2) retroreflector alignment errors; 3) relations between PSD reading and retroreflector position. Error analysis results indicate that: 1) mirror-mechanism link dimension errors have great influence on laser tracker precision; 2) extra caution is needed to avoid alignment errors when measuring with a solid corner cube retroreflector.
　　Comparing the measurement precision of CMLT with CMM indicates that CMLT technology is still not optimized, and the development of practical CMLT alignment theory and methodology is the best way to achieve this goal.

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