BGA（Ball Grid Array）是一廣泛使用在晶片製程上成熟的封裝技術。每顆出產晶片的功能與型號是透過其封裝表面的印字符號來辨別。雷射刻印的諸多優點，與影像視覺系統、電腦控制的結合下，提供了速度、恆久和多功能等獨特的優勢，使其成為晶片打印技術的主流。實際應用上，良好刻印結果的呈現，必須仰頼對晶片封裝表面作精確的校準。因此，本論文提出一準確與強健的方法，對三種不同的BGA晶片影像，考量雜訊的干擾下，量測其封裝表面的中心位置與方向角。

　　首先，在檢測的區域內，使用區域投影法產生橫向與縱向的投影曲線。利用一對相差90度的Gabor濾波器與投影曲線作迴旋運算，偵測響應曲線中的最大區域能量所對應的特徵訊號，藉此了解待測物的輪廓，以界定影像感興趣的區域。邊緣偵測方面，使用一針對指數型傾斜邊緣訊號最佳化的平滑濾波器與Sobel運算子得到梯度影像。在梯度影像中有條件地抑制區域非極值，篩選出位於BGA晶片邊界的邊緣像素。此外，提出的邊緣追隨法過濾掉肇因於裂縫瑕疵或短斜邊的邊緣像素。最後，經由最小平方差直線匹配的迴歸演算以及幾何運算，得到校準的中心位置與偏向角。

　　本論文針對所提出的方法，評估其在高斯雜訊干擾下的穩定性，使用人工合成影像量測精確度，以及執行效能。整體上，對於三種不同類型的樣本影像，不同程度高斯雜訊的干擾下（標準差上達30，期望值為零），中心定位維持0.5像素的精確度，正負誤差0.3像素；而偏向角可下達0.1度，正負誤差0.3度。實驗結果顯示，使用較大尺度的影像可保留較多的邊緣資訊點，使得偏向角可達0.01度之更高準確度。執行效能方面，使用可分離的二維濾波器節省可觀的運算時間。在一台備有PentiumM 1.3GHz處理器的電腦上，完成單次運算程序需要時間約105毫秒，平均檢測範圍為360×300像素。

　　BGA (Ball Grid Array), a mature technology of packaging, is widely used in the manufacturing process of integrated circuits. The model name of each BGA chip is identified by recognizing the etched mark on package surface. The combination of laser marking, imaging systems and computer control provides a unique advantage of speed, permanence and versatility. Such a compelling application becomes the main stream in IC marking. In practice, good marking relies on accurate alignment for IC package. In this thesis, a precise and robust method is proposed to measure the central position and orientation angle of a BGA package. Three kinds of BGA images under noise degradation are studied.

　　Firstly, region projection is applied to generate vertical and horizontal profiles within the inspected area. Then the projection profile is convolved with the Gabor quadrature filter. Image features corresponding to maxima of local energy in the response are detected, so as to find the object’s contour and delimit the regions of interest. In edge detection, an optimal smoothing filter for exponential ramp edge is applied with Sobel operators to derive the gradient image. The edge elements around boundary of BGA package are picked out from gradient image by using non-maximum suppression with some additional constraints. Further, the edge elements resulting from flaws or short beveled edges are filtered out by our proposed edge following method. Finally, the central position and orientation angle are obtained by the LSE line fitting algorithm followed geometric computation.

　　Our proposed method is evaluated in terms of the stability under noise degradation, accuracy and running time. For the three kinds of sample images studied under various levels of Gaussian noise corruption (up to σ=30 with zero mean), the accuracies of the central position and the orientation calculated is within 0.5 pixel with error of ±0.3 pixel and 0.1 degree with error of ±0.3 degree respectively. The experiments also show that our method can achieve 0.01 degree in angular accuracy while more edge elements can be preserved by using the images in larger scale. On the other hand, applying a separable 2-D filter in our method can remarkably reduce the computation time. It takes approximate 105 ms to complete the entire process for an inspected area of 360×300 pixels while running on a PC equipped with a processor of PentiumM 1.3GHz.

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