本文使用逆向歪斜光線追蹤方法，建立雙照相機座標量測系統，由照相機所得影像求得待測物位置，並以歪斜光線追蹤對照相機做參數校正，以提高量測系統之精確度。
歪斜光線追蹤是以幾何光學Snell定理，分析光線行經介質邊界時，其折（反）射光線行進方向及入射點（折射點）位置，藉此便可追蹤由光源發出經過光學系統到達影像平面之光線。但在實際量測時，吾人所得到的資料為照相機所取得之影像，光源才是我們要求的物點位置。基於幾何光學的可逆性，吾人以逆向歪斜光線追蹤方法，以像點為光源，以相反方向與順序，追蹤經過光學系統到達物點之光線，因此可由所得之影像達到座標量測之目的。
照相機之參數校正為座標量測系統中一重要環節，參數校正準確與否影響量測系統精確度甚大。目前現有之照相機參數校正方法甚多，但所有方法都是以針孔成像模型為發展基礎，而針孔成像模型只是一種以透視投影法的近似方法，並不符合幾何光學Snell定理，因此使用現有參數校正方法是不可能使量測系統的精確度更臻完美。本文中使用了歪斜光線追蹤的方法，校正照相機的五個內部參數與六個外部參數，以得到影像平面與物點世界座標系之間正確的幾何關係，使逆向歪斜光線追蹤結果更準確，以提高量測系統之精確度。

This paper presents a new method of coordinate measurement system by using two cameras. Instead of pinhole model, the parameters of this system are calibrated by using skew ray tracing method based on Snell’s law, and the model of coordinate measurement is built utilizing reversal skew ray tracing to trace light rays from image plane to 3-D world.
Skew ray tracing is a theory derived from a 4×4 homogeneous coordinate transformation matrix and the Snell’s law of the geometrical optics. It offers a mathematical model of the direction of refracted (reflected) ray and the position of incident point of light rays while crossing medium boundary surfaces. Therefore, the light rays can be traced from the light source crossing optical elements to the image plane. And because of the reversibility of geometrical optics, the light rays can be also traced from image plane to 3-D world. Thus, the coordinates in 3-D world can be measured by two images took from two cameras using reversal skew ray tracing method.
Camera calibration is a crucial problem for coordinate measurement. However, all existing methods of camera calibration are developed based on pinhole model, an approximation algorithm against to Snell’s law. Thus, it is impossible to obtain an accurate method of camera calibration by using a mathematical pinhole model. This paper models the geometric relationship between 2-D images and 3-D world by using skew ray tracing theory to calibrate five intrinsic parameters and six extrinsic parameters. It is not an abstract approximation algorithm but an absolutely physically correct calibration method. Experimental results have shown the accuracy of the proposed system.

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