本研究藉由離散差分預測模型與區間二分法設計一自動對焦搜尋演算法。隨著數位相機產業的發展，現今消費市場對數位相機的要求為－「輕、薄、短、小」、「高解析度」且「反應時間快」。就現今對焦技術而言，唯有被動式對焦技術能達到此一要求。被動式對焦技術係利用清晰度尺度來作為移動鏡頭位置的依據，然而高解析度所代表的意義為更大量的數位化資料處理，所以一般的搜尋演算法處理此一對焦問題所花費的時間往往過於冗長，但自動對焦搜尋演算法在使用上的先決條件則是它的「即時性」。
為此，本論文將運用離散差分預測模型的預測特性，提前預測對焦曲線的走勢，用以克服一般搜尋演算法因為過度伸縮鏡頭而造成搜尋時間過於冗長的問題，且由於可事先預知對焦曲線的走勢，更可以減少鏡頭在反轉時因鏡頭馬達齒輪間隙所造成反衝(backlash)的問題，如此可達到加快對焦速度的目的。最後，將離散差分預測模型搭配區間二分法，實際用於數位相機對焦模組的測試以驗證其可行性。

This paper presents a new auto-focus search algorithm based on Discrete Difference Equation Prediction Model (DDEPM) and Bisection Method. Now, mainstream market of digital camera is “light”, “thin”, “small size”, and “mega-pixels level”. To achieving these requests, the passive auto-focus technique should be adopted. In passive auto-focus technique, the lens will move to the highest focus-value position which is calculated by sharpness measure, so that the CCD layer will be in the image plane. In “mega-pixels level” digital camera, it will spend much time to compute a lot of digital image data. The common search algorithm for searching focus point will spend a lot of time, because the lens moves eternally, so that it can limit the focus region.
Actually, the auto-focus search algorithm for digital camera must be “real-time”. For this purpose, we will use DDEPM method to forecast the tendency of focus-curve, so that we can shorten the searching time by reducing the backlash times.
Finally, we will design an auto-focus algorithm based on DDEPM and Bisection Method and we will realize it by coding into digital camera, actually. The final experiment result can show the performance of this algorithm and it will prove that this algorithm is useful for reducing the backlash times.

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