本博士論文主要的研究方向是著重在「數位影像處理演算法技術應用在BGA檢測的研究」。隨著工業時代的演進及進步，工業製程檢測自動化是這幾十年來全世界努力的目標。製品尺寸在「輕、薄、短、小」概念的驅使下，各種元件無可避免的必須朝向毫米、微米、奈米的尺度發展，才能滿足整體產品的需求。同時，近半世紀來人工費用昂貴，加上線上大量量產及製程自動化的趨勢，因此單靠人工檢查是不夠的，也迫使檢查技術不得不改弦更張，作出革命性技術的突破。為了達到這個目標，必須檢查機器配合演算法才能完成。但是在檢查機器配合演算法的比重上，大略可分為兩大主流：(1)以檢查機器為設計主體及 (2)以演算法為設計主體。前者大體來說是光學儀器，諸如：Ｘ光機、超音波、雷射視覺系統，…等等，設備費用較為昂貴，校正需要較高的技術；後者通常以數位照相機及精緻的演算法為主，設備費用較便宜，著重在演算法的技巧設計，形式方面就比較多樣，依需求而有所不同。因設備費用較低，近年來成為爭相研究的主題。因此本論文也試圖以『演算法為設計主體』的新方向來進行BGA封裝前，自動化品質保證的檢查及量測技術之研究。
本文所提出的解決方案包括：建立以「解析幾何橢球體模型」為主的測試模型，針對這個模型，作者應用具有傾斜角的CCD捕捉到的影像，可以準確的計算出檢查錫球的高度，直徑。利用這個模型，在可完全辨識下，作者可以預估CCD的最小有效測試傾斜角限制，同時可以分析實際CCD傾斜角誤差的影響。
在數位影像處理的「前處理工程」中，作者提出本文作者自行發展的邊跡截取前的「影像自動化分割使用新的混合取門檻值方法(a New Mixed Thresholding Approach)」，此方法是一個「三分之一半經驗公式的法則（The rule of a one third semi- experience formula）」，它可以改良現有影像自動化分割演算法無法達成的目標；其次在圖形邊跡截取上，作者提出圖形邊跡截取演算法，此法也是本文作者自行發展的，它可以有效的、強健的截取圖形的邊跡；圓-橢圓（或類似圓，類似橢圓，渦旋）辨識演算法，此法也是本文作者自行發展的，它可以有效的、強健的辨識出影像中具有圓形、橢圓形、及近似圓形或近似橢圓形的目標物件。結合上述前處理工程的相關演算法，作者對目的物件與背景可以成功的適度分割，完整的截取，有效的辨識。
另外，本文作者在作實際BGA封裝前，自動化品質保證的量測及檢查中，也提出一系列的處理程序及方法，包括：實際測量中，實物與影像間之尺寸轉換函數；由CCD捕捉到的BGA正視圖與斜視照射圖對照之技巧；利用形心法找尋物體中心座標之技巧；結合本文自行發展的所有演算法，成功的完成本文所有演算法及程序技巧實際量測之驗證。證明所有構想是可行的，達到本文的目標，所謂：可以不用傳統尺規，只要利用影像處理及解析幾何的方法，就可以精確的量測出BGA個別錫球橢圓體的長軸、短軸的長度，並且可以間接量測出錫球的高度，並自動化檢查BGA基板共面問題。同時利用形心搜尋技術，成功的檢查出BGA個別錫球與原設計值的偏移量（off set）問題。另外，利用SMS演算法找出錫球的輪廓（contour）後，再利用形心法求出BGA個別錫球橢圓體的長軸、短軸的長度後，與預估標準值比較後，就能斷定整體BGA 植球佈局（Layout）中，錫球大小是否合乎標準值或過大、過小，甚至檢驗出錫球缺失狀況。
雖然在實際測試工程中，本論文的辨識率只達到98.72%，但是這種異常現象到底是出在整體處理過程的某一個環節（包括：前處理工程，相關系列的演算法），或是因為原先作者假設測試件的BGA基板上的錫球皆合乎標準的，但是事實上其中某些並沒有合乎標準所致。這些都不是單靠人眼或經驗可以達成的，它必須靠精密儀器及高級校正技術才能達成的。同時必需準備一套「校正過的BGA基板標準測試件」，如此才可以確實驗證。目前臺灣還沒有提供「校正過的BGA基板標準測試件」的單位，因此詳細探討留待後續再繼續研究。
雖然本文涉及的相關演算法複雜，但是它是精煉可行的。最重要的是，它不必用高貴的儀器，它不需專精純熟的技術人員。更重要的，它可以一次、即時的、迅速的檢查目前BGA基板的缺失。因此未來的工作，作者將此發展出來的模型（SMS BGA MODEL），實際應用於BGA基板的量測。

The main research of this doctorate thesis is focused on “the algorithms of digital image processing applied to the research of BGA measurement”. With the evolution and progress of the industrial era, the inspection and measurement automation of the industrial manufacturing procedure, is a desired goal worldwide in this decade. The products under the drive of “light, thin, short, small” concept, various kinds of components must be moved towards the dimension of millimeter, micron, and nano-scale development, such that they could meet the requirement of high density integration. Meanwhile, manpower is expensive in the near half century, and a tendency to a large amount of on-line quantity producing and the automation of manufacturing procedure, it is not enough by labor checking only. It also forced the inspection technology with no choice but to make revolutionary break-through. To achieve this goal, inspection machines must cooperate with performing algorithms. But in the rate of the inspection machine to cooperate with the performing algorithm, it can be divided into two mainstreams: (1) The inspection machine as design subject and (2) The performing algorithms as design subject. The former is an optical instrument, such as: X-ray, the ultrasonic wave, laser vision system, etc. Its equipment is comparatively expensive; it needs higher technology of calibration. The latter usually relies mainly on the digital cameras and the exquisite performing algorithms. Because the equipment expenses are relatively cheap, it focuses on the skill of the performing algorithm designing; the form is more variable and depends on different requirements to a certain extent. Because the equipment expenses are relatively low, it becomes a competing theme to study in recent years. So this thesis attempted to carry on the BGA before-encapsulation as a technology research new direction of “The performing algorithms as design subject” for inspection and measurement of automatic quality assurance.
The solution put forward by this text includes: to set up the test model relying mainly on “the ellipse spheroid model based on analytic geometry”, to focus on this model, to utilize images which were captured from CCD with angle of inclination, to be able to calculate the heights and diameters of solder balls accurately. Utilizing this model, under totally distinguishing, the author can pre-estimate the minimum limited angle of CCD inclination, and can analyze the influence of the angle error of real CCD inclination.
In the preprocessing engineering of digital image processing, the author proposed an algorithm that image before the intercepting boundary, of “a New Mixed Thresholding Approach” which is a “The rule of a one third semi-experience formula” method. It can improve the goal that the existing image automatic segmented algorithms can't be reached. Next in the boundary intercepting algorithm of objects, the author presented an “image contour intercepting algorithm” which was also developed by the author. It can intercept the boundary of the image effectively and strongly; The round-the ellipse (or the similar round, the similar ellipse, the vortex) distinguishing algorithm which was also developed by the author can be effectively strongly distinguished out the goal objects in the image that has a round, an ellipse, an approximate round or an approximate ellipse. Combined the relevant algorithm of the preprocessing engineering which was mentioned above, to the target objects and background, the author can segmentalize appropriately, intercepte completely, distinguish effectively.
In addition, before making real BGA encapsulation, in the automatic inspection and measurement of quality assurance, the author also proposed a series of treatment procedure and method, including: in actual measurement, the transform function between the actual size and size of image; BGA images contrasted skill between normal view and oblique side view that are captured by the CCD; using the shape center method to seek out the coordinate of object centre; combining all performing algorithms which was developed by the author, the author succeeds to complete the verification of the actual measurement which is relative to all performing algorithms and procedure skill. Proven that all ideas are feasible, and to reach the goal of this text without the use of the traditional ruler and compass. By employing the image processing and analytic geometry method only, the author can accurately measure the semimajor and semiminor lengths and the height of every solder ball on the BGA base plate, such that making BGA base-plate coplanarity automation checking feasible. At the same time, to utilize shape center technology to check “off set” between real solder ball on BGA base plate to the originally design value. In addition, using “SMS Vortices Detecting Algorithm” to seek out contour of every solder ball, and utilize the shape center method in seeking out the semimajor and semiminor lengths of every solder ball, then comparing these values to estimated standard values, the author can conclude the whole BGA layout, whether or not the solder ball size could satisfy the criteria, whether or not it is too large or too small, and even seeking out the solder ball missing state.
Though in real test engineering, the distinguishing rate is only 98.72%, yet the abnormal phenomenon is finally a certain link of lying in the whole course of dealing (including: preprocessing engineering, a series of the relevant performing algorithm), or because suppose the test base-plate of BGA solder ball satisfying the criteria originally, the fact that some of them does not satisfy the criteria to cause them. All of these could not be reached by human eyes or experience alone, it must be reached by the precision type instrument and used the advanced calibration technology. Moreover, one must prepare a set of "a calibrated test standard of BGA base-plate ", such that inspection can be certain and guaranteed. At present, Taiwan does not have one unit that offered the calibrated test standard of BGA base-plate yet. So the detailed studying will be awaited in the succeeding study.
Although complicated algorithm is involved in this text, yet it is a refined and feasible one. More importantly, it does not need expensive instrument and also it does not need skill technical personnel. Even more it can check any solder ball flaw on the BGA base plate at one setting, in real time, and at a high speed. So in the future work, the author will use this development model (SMS BGA MODEL) and apply it to the BGA base plate actual measurement.

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