一般的光學干涉術通常都會獲得干涉條紋圖像，然而這些圖像往往都會摻有雜訊，造成分析時的不便。中值濾波是以選取區域範圍內的訊息做小至大的排序，然後取其中間值取代範圍中心值的處理方式，所以此方式能夠找出選取區域的中心傾向，且較不會受到少數特異雜訊點的影響。因此，經常可看到中值濾波會被應用在許多光學圖像的影像處理中。
雖然中值濾波能有效濾除高頻雜訊，可是若在選取範圍較大，會出現將峰端訊息平滑化的錯誤傾向。所以許多爲考量不同訊號特性的改良方式便因應而生；其改良方式有以不同的權重搭配或不同的選取範圍大小做探討等等，然而其目的都是為了能更加精確的獲得真正的訊息。基於上述的觀點，本論文將於處理過程中，運用最小平方差的觀念在二維的干涉圖像，藉此找尋此面域的趨勢，然後避免不必要訊息考量，以達到更精準的處理效果。
由於要更明顯觀看出其改良效果的差異性，本論文也也檢視了兩組由相移斑點干涉術得到之干涉圖形，結果顯示本文所提方法對平滑化現象之改良效果較其他傳統方法為佳。

In most of the optical interferometry techniques, one often get interferometric fringe patterns which include noises, and these noises will cause analysis difficulty. The method of median filter is used to sort the data in the region, and use median value to replace the center value of the region. Therefore, the median filter technique can find central tendency of the region, and less affected by the presence of a minority of aberrant value. So the median filter technique is used frequently in image processing of many optical fringe patterns
The median filter technique is effective in removing noise with high frequency, but tends to smooth out details such as summits if the window size is large. So there are many improved methods developed corresponding to different properties of signal. Even though each of the improved methods has different considerations, such as to consider different integer weights, or different window size etc., their purposes are all the same, that is to make results more accurately. On the basis of these viewpoints, this thesis will use concept of least–squares fitting on 2-D interferometric fringe patterns. By finding the trend of the region, and avoid unnecessary signal consideration, make the results more accurately.
In order to study the effect of the proposed technique, two sets of fringe patterns obtained from the phase-shifting speckle interferometry will be used as examples. They showed that the proposed technique presents a better result than traditional technique.

目錄

謝誌……………………………………………. ……………………….I
論文摘要…………………………………………… ………………….II
目錄…………………………………………………………………….IV
圖目錄………………………………………………………………….VI
表目錄…………………………………………………………………. X
符號說明……………………………………………………………….XI

第一章 緒論……………………………………………………………1
1-1 前言…………………………………………………………….1
1-2 文獻回顧……………………………………………………….3
1-3 本文架構……………………………………………………….8

第二章 基礎原理與濾波技術…...…………………………………...9
2-1 條紋成像原理……………………………………………….…9
2-2 相移與相位重建原理………………………………………...11
2-2-1 相移法基本概念………………………………………...11
2-2-2 四影像法原理…………………………………………...12
2-2-3 相位展開法基本概念…………………………………...14
2-2-4 相位展開技術…………………………………………...16
2-3 雜訊濾除技術………………………………………………...18
2-3-1 相位展開前濾波技術概述……………………………...18
2-3-2 最小平方差濾波………………………………………...19
2-3-3 可適應中值濾波………………………………………...24
2-3-4 於濾波加入趨勢判斷考量……………………………...28

第三章 程式模擬架構………………………………………………32

第四章 數值模擬與分析……………………………………………33
4-1 影像模擬說明………………………………………………...33
4-2 濾波效果比較………………………………………………...38
4-2-1 可適應中值濾波與最小平方差濾波應用效果………...38
4-2-2 標準正方形中值濾波與改良濾波應用效果…………...43
4-2-3 標準正方形中值濾波與改良濾波應用效果…………...61

第五章 結論與展望…………………………………………………65

參考文獻………………………………………………………………..67

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