利用CCD之moiré與小波函數檢驗變焦鏡頭之焦距研究

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陳鴻良(Hung-Liang Chen) 查詢紙本館藏

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光電科學研究所碩士在職專班

論文名稱

利用CCD之moiré與小波函數檢驗變焦鏡頭之焦距研究
(A Measurement in the Focal Length of Zoom Digital Camera by CCD Moiré Pattern and Wavelet Transformation)

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摘要(中)

摘要
本文的研究主要是利用疊紋(moiré)圖案的產生來量測變焦鏡頭或變焦數位相機的焦距長，並使用影像處理的技術來處理對比度不高的疊紋(moiré)圖案。這個方法基本上是利用以參考的光柵(grating)影像和一個CCD像素陣列(或CMOS像素陣列)疊加在一起，因而產生疊紋(moiré)圖案(如圖1-1-0)，並經由移動微小距離得到第二疊紋(moiré)圖案，利用分析這兩個疊紋(moiré)圖案的間距值及移動微小距離、參考的光柵(grating)間距值三個參數，來運算出一個變焦鏡頭或變焦數位相機的焦距長。
當光線穿過直線的光柵(grating)，直線光柵(grating)的影像經過被測試的變焦鏡頭到達CCD(或CMOS) 影像感測器，然後移動被測試透鏡的位置使參考光柵(grating)影像的格子間隔和CCD影像感測器的像素間距相似時，就會產生疊紋(moiré )干涉影像。因透鏡位置不同會產生不同的放大率，因此光柵(grating)影像格子間隔會隨放大率的不同而變化，此變化則和CCD像素不同方向之間格相對應而產生不同的干涉圖案。由此圖案之大小、形狀、方向可判定放大率值，因而可測變焦系統之不同位置之放大率。
透過我們的方法，可以很快的找到產生疊紋(moiré)圖案的數位相機鏡頭移動的位置，進而知道這光柵和變焦數位相機產生moiré後的相關特性。我們採用微調轉鈕(Micro-stages)可以精確地測量被測試透鏡的位移量，而影像處理在增加影像的對比及減少雜訊，並將R、G、B的G層取出，一維的Daubenchies Wavelet轉換演算法在此被應用於估算疊紋(moiré)圖案的間距值。
本方法可用來量測變焦鏡頭各位置的焦距值及放大倍率。經由疊紋(moiré)方法量測變焦鏡頭的各焦距長度，價格便宜，且容易安裝，而量測的結果也能達到4%的誤差內。

摘要(英)

ABSTRACT
The research is to measure the focal lengths of optical zoom lens modules and digital optical zoom cameras by utilizing the appearance of moiré images. In addition, the digital image processing technology is implemented to digitize those low contrast moiré images.
By superposing the reference grating image and a CCD Pixel Array (or CMOS Pixel Array) together, a moiré pattern is formed . A following moiré pattern is formed when the CCD Pixel Array (or CMOS Pixel Array) shifts a slight distance. The focal length of a zoom lens of zoom digital camera can be measured by analyzing the intervals of the two moiré patterns, the shift value of the lens, and the grating intervals.
While the image of straight-line grating went through the under-testing zoom lens to reach CCD (or CMOS) Image Sensor, if the grid interval of the reference grating image is similar to the pixel interval of the CCD Image Sensor; as a result, it will appear the moiré interferometry image. Different magnifications came from different positions of zoom lens, thus the changes of grating image’s intervals caused by the different magnifications varies the moiré interferometry images. In the other hand, the value of magnifications can be measured by means of the size, shape and direction of those moiré images.
Though our method, we are easy to find the camera relative shift positions where moiré patterns appear. Then we are able to observe the relevance of the reference grating and digital zoom lens. We adopted the Micro-stages that could precisely measure the shift value of the under-testing lens, as well as the digital image processing technology was used to increase images’ contrast, to filter noises and to extract G value of the images’ (R, G, B) values. One-Dimension Wavelet Transformation Algorithm hereby has been applied to estimate the interval value of moiré images.
This method can be used to measure the focal length value and magnifications of each position for zoom lens. Compare to traditional testing methods for focal length of zoom lens. The method is cost-effective and easily setup. The measured results also can reach the precision of maximum 4% factual error.

關鍵字(中)

★ 小波函數
★ 疊紋

關鍵字(英)

★ Wavelet Transformation
★ Moiré

論文目次

目錄
摘要……………………………………………………………………I
ABSTRACT ……………………………………………………………III
誌謝辭…………………………………………………………………V
目錄……………………………………………………………………VI
圖表目錄 ……………………………………………………………..IX
第一章緒論……………………………………………………..1
1–1 研究背景及動機…………………………………………….1
第二章原理……………………………………………………..5
2–1 疊紋(moiré)原理……………………………………………..5
2–2 多分辨分析(Multi-resolution)與正交小波變換(Orthogonal Wavelet Transform) …………………………………………10
2–2–1 多分辨分析(Multi-resolution) ………………………..11
2–2–2 尺度函數(Scale Function)與尺度空間 ……………...12
2–2–3 多分辨分析(Multi-resolution)概念的引入…………...14
2–2–4 正交小波變換(Orthogonal Wavelet Transform)與多分辨率分析(Multi-resolution) ………………………………17
2–2–5 尺度函數(scale function) 和小波函數(wavelet function) 的一些重要性質…………………………20
2–2–6 二尺度方程…………………………………………...22
2–3 正交小波變換的快速演算法……………………………….24
2–3–1系數分解的快速算法 ………………………………..24
2–4 正交小波基的構造………………………………………….27
2–4–1由尺度函數構造正交小波基 ………………………..27
2–4–2 緊支集正交小波基的性質和構造 ………………….28
2–4–3緊支集正交小波基的構造 …………………………...30
2–5 利用Moiré原理測鏡頭焦距長理論………………………..44
2–6 CCD sensor與光柵產生moiré的光學原理 ………………..47
第三章實驗步驟及實驗結果 ………………………………....51
3–1 實驗架設……………………………………………………51
3–2 實驗流程……………………………………………………52
3–3 結果分析……………………………………………………57
3–3–1 分析一倍光學焦距長………………………………..58
3–3–2 分析二倍光學焦距長………………………………..58
3–3–3 分析三倍光學焦距長………………………………..59
3–3–4 分析四倍光學焦距長………………………………..60
3–3–5 分析五倍光學焦距長………………………………..61
第四章討論及結果……………………………………………62
第五章未來展望………………………………………………64
參考文獻………………………………………………………..65
附錄A………(Moiré的旋轉及間距的變化)……………………...101
附錄B………(使用Matlab求moiré間距值的過程)………………..127

參考文獻

參考文獻
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指導教授

張榮森(Rong-Seng Chang)

審核日期

2005-7-22

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