本研究旨在開發一套完整的 3D-DIC 變形量測系統，並驗證其量測準確度。系統實作涵蓋雙相機校正、立體匹配、三維重建以及應變場計算等完整流程。雙相機校正部分使用棋盤格校正板，透過雙相機系統獲取相機的內部參數（焦距、影像中心與透鏡畸變係數）與外部參數（兩相機之間的相對旋轉與平移關係）。匹配演算法以零均值正規化平方差和（Zero-mean Normalized Sum of Squared Difference, ZNSSD）作為相關性準則，並採用 Newton-Raphson Method迭代法和雙立方樣條內插法達到次像素級的匹配精度。三維重建則藉由已知的相機內外參數與匹配所得的影像對應點，先以線性方程式Ax=b求得初始解，再透過 Levenberg-Marquardt 非線性最佳化演算法，以最小化重投影誤差求解出最佳的三維座標。應變場計算採用逐點最小二乘法（Pointwise Least Squares, PLS），透過對每個追蹤點周圍進行多項式擬合，可以從擬合出的多項式係數得到位移梯度，再代入Lagrangian 應變公式，求得應變。
本研究進行了六組位移實驗以驗證本系統的量測準確度，將試件沿 X、Y、Z 三個方向同時平移相同量，分別為0.1mm、0.2mm、0.5mm、1 mm、2 mm 與 3 mm。首先比較三種不同相關性準則平均誤差，接著和商業軟體 VIC-3D 比較六組的位移實驗。最後實驗驗證為懸臂樑彎曲實驗，量測樑的撓度，並與 VIC-3D 軟體的量測結果進行比較。在位移實驗中，三種相關性準則的比較結果顯示，在 X 方向，ZNSSD 的平均誤差為 0.001~0.002 mm，遠小於 SSD 與 NSSD 的 0.02~0.05 mm；在 Y 方向，ZNSSD 的平均誤差為 0.002~0.012 mm，亦小於 SSD 與 NSSD 的 0.01~0.03 mm；在 Z 方向，ZNSSD 的平均誤差為 0.014~0.047 mm，同樣優於 SSD 與 NSSD 的 0.02~0.08 mm。此結果驗證了 ZNSSD 優於SSD 與 NSSD。進一步將本系統與商業軟體 VIC-3D 進行比較，在 X 方向，本系統的平均誤差為 0.001~0.002 mm，優於 VIC-3D 的 0.007~0.025 mm；在 Y 方向，本系統的平均誤差為 0.002~0.012 mm，相較於 VIC-3D 的 0.002~0.003 mm 略高約 0.009 mm，但相對誤差仍小於 0.4%；在 Z 方向，本系統的平均誤差為 0.014~0.047 mm，相較於 VIC-3D 的 0.001~0.018 mm 略高約 0.029 mm，相對誤差仍小於 1.4%。整體而言，本系統在 X 方向的位移量測表現最佳，在 Y 與 Z 方向的量測精度雖略低於 VIC-3D，但相對誤差皆控制在 2% 以內，證實本系統具有良好的量測準確度。在懸臂樑彎曲實驗中，將本系統與 VIC-3D 的位移結果進行比較，以 VIC-3D 的數據作為標準值、本系統的數據作為實際值，針對126個位移點進行誤差分析。結果顯示平均誤差為 0.007 mm，標準差為0.007mm，最大誤差為 0.012 mm。

This study aims to develop a complete 3D-DIC deformation measurement system and to validate its measurement accuracy. The system implementation covers the entire process, including stereo camera calibration, stereo matching, three-dimensional reconstruction, and strain field computation. For stereo camera cali-bration, a checkerboard calibration board was used to obtain, through the stereo camera system, the intrinsic parameters (focal length, principal point, and lens distortion coefficients) and the extrinsic parameters (the relative rotation and translation between the two cameras). In the matching algorithm, the zero-mean normalized sum of squared difference (ZNSSD) was adopted as the correlation criterion, and the Newton-Raphson iterative method combined with bicubic spline interpolation was employed to achieve sub-pixel matching accuracy. For three-dimensional reconstruction, based on the known intrinsic and extrinsic camera parameters and the corresponding image points obtained from matching, an initial solution was first computed using the linear equation Ax = b, and the optimal three-dimensional coordinates were then obtained by minimizing the reprojection error through the Levenberg-Marquardt nonlinear optimization algorithm. For strain field computation, the pointwise least squares (PLS) method was employed; by performing polynomial fitting around each tracking point, the displacement gradients were obtained from the fitted polynomial coefficients and substituted into the Lagrangian strain formula to determine the strain.
Six sets of displacement experiments were conducted to validate the measurement accuracy of the developed system, in which the specimen was translated simulta-neously along the X, Y, and Z directions by the same amount of 0.1, 0.2, 0.5, 1, 2, and 3 mm, respectively. First, the mean errors of three different correlation crite-ria were compared; the six sets of displacement experiments were then compared with the commercial software VIC-3D. Finally, a cantilever beam bending exper-iment was performed to measure the deflection of the beam, and the results were compared with those measured by VIC-3D. In the displacement experiments, the comparison of the three correlation criteria showed that, in the X direction, the mean error of ZNSSD was 0.001–0.002 mm, far smaller than the 0.02–0.05 mm of SSD and NSSD; in the Y direction, the mean error of ZNSSD was 0.002–0.012 mm, also smaller than the 0.01–0.03 mm of SSD and NSSD; and in the Z direc-tion, the mean error of ZNSSD was 0.014–0.047 mm, likewise superior to the 0.02–0.08 mm of SSD and NSSD. These results confirmed that ZNSSD outper-forms SSD and NSSD. The developed system was further compared with the commercial software VIC-3D. In the X direction, the mean error of the developed system was 0.001–0.002 mm, superior to the 0.007–0.025 mm of VIC-3D; in the Y direction, the mean error of the developed system was 0.002–0.012 mm, approxi-mately 0.009 mm higher than the 0.002–0.003 mm of VIC-3D, but with a relative error still below 0.4%; in the Z direction, the mean error of the developed system was 0.014–0.047 mm, approximately 0.029 mm higher than the 0.001–0.018 mm of VIC-3D, with a relative error still below 1.4%. Overall, the developed system performed best in displacement measurement along the X direction; although its measurement accuracy in the Y and Z directions was slightly lower than that of VIC-3D, the relative errors were all controlled within 2%, confirming that the de-veloped system possesses good measurement accuracy. In the cantilever beam bending experiment, the displacement results of the developed system were com-pared with those of VIC-3D, taking the VIC-3D data as the reference values and the developed system data as the measured values; an error analysis was per-formed on 126 displacement points. The results showed a mean error of 0.007 mm, a standard deviation of 0.007 mm, and a maximum error of 0.012 mm.

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