基於聚焦成形技術之藍寶石玻璃孔洞自動化量測系統開發

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姓名

林言叡(Yan-Rui Lin) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

基於聚焦成形技術之藍寶石玻璃孔洞自動化量測系統開發
(Development of an Automated Measurement System for Sapphire Glass Holes Based on Shape-From-Focus Method)

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至系統瀏覽論文 (2027-8-24以後開放)

摘要(中)

本研究開發了一套基於聚焦成形技術的圓孔自動定位與量測系統，解決了機械手
臂難以將藍寶石玻璃圓孔精確對準量測視野的問題，實現全自動化量測。系統通過獲
取不同聚焦位置的影像，使用聚焦度值演算法進行圓孔的三維形貌重建，並以非接觸
式方式量測圓孔的幾何特徵。
系統由硬體和軟體兩部分組成。硬體包括 CCD 相機、工業鏡頭、低失真微距鏡頭、顯
微鏡頭、照明裝置和電控位移平台等，構成高精度成像與定位系統。軟體使用 Python
進行影像分析與三維重建，C++控制硬體實現自動化定位。工作流程分為圓孔自動粗細
定位和三維形貌重建兩部分。
圓孔自動定位包括粗定位和細定位。粗定位通過 X 與 Y 軸電控位移平台將圓孔快
速移至 2.5 倍顯微鏡頭視野內。細定位則進一步優化圓孔位置，使其對準 20 倍顯微鏡
頭視野中心。實驗顯示，粗細定位成功率均為 100 %，圓孔中心距視野中心最大距離僅
8 μm。
三維形貌重建過程中，系統控制電控升降平台逐微米拍攝圓孔影像。利用聚焦度
值演算法分析每張影像，計算像素點聚焦度值，找出最大值對應的影像位置，從而確
定圓孔入口和出口相對位置，重建三維形貌。
本研究比較了 Roberts、Prewitt、Laplacian、Sobel 和 Scharr 等聚焦度值演算法。結
果顯示，Scharr 演算法與商用形狀分析雷射顯微鏡的量測結果相對誤差最小，最大僅
1%，優於其他算法。
系統性能驗證方面，20 倍物鏡量測範圍為 425 μm * 355 μm，橫向解析度 0.871 μm，
縱向解析度 0.8 μm。重複性實驗表明定位成功率 100%，孔徑與深度誤差分別為 1%和
1.4%。量測極限實驗證實當孔壁傾角小於 80 度時，系統可準確建立三維形貌模型，誤
差為 1.25%。

摘要(英)

This study developed an automatic hole positioning and measurement system based on the
shape-from-focus technique, solving the problem of mechanical arms′ inability to accurately
align sapphire glass holes with the measurement field of view, thus achieving fully automated
measurement. The system captures images at different focus positions, uses focus value
algorithms for 3D shape reconstruction of holes, and measures hole geometry non-contactly.
The system comprises hardware and software components. Hardware includes a CCD
camera, industrial lens, low distortion macro lens, microscope lens, illumination device, and
motorized translation stages, forming a high-precision imaging and positioning system.
Software uses Python for image analysis and 3D reconstruction, while C++ controls hardware
for automated positioning. The workflow consists of automatic coarse and fine hole positioning
and 3D shape reconstruction.
Automatic hole positioning includes coarse and fine positioning. Coarse positioning
quickly moves the hole into the 2.5x microscope lens field of view using X and Y-axis
motorized stages. Fine positioning further optimizes the hole position, aligning it with the 20x
microscope lens field center. Experiments show 100% success rates for both coarse and fine
positioning, with a maximum distance of only 8 μm between the hole center and field center.
During 3D shape reconstruction, the system controls a motorized lift platform to capture
hole images at 1 μm intervals. Focus value algorithms analyze each image, calculating pixel
focus values and identifying the image position with the maximum value, determining the
relative positions of the hole entrance and exit for 3D shape reconstruction.
The study compared Roberts, Prewitt, Laplacian, Sobel, and Scharr focus value algorithms.
Results show the Scharr algorithm has the smallest relative error, maximum 1%, compared to
commercial shape analysis laser microscope measurements, outperforming other algorithms.
For system performance verification, the 20x objective measurement range is 425 μm *
III
355 μm, with lateral resolution of 0.871 μm and vertical resolution of 0.8 μm. Repeatability
experiments show 100% positioning success rate, with 1% and 1.4% errors in hole diameter
and depth, respectively. Measurement limit experiments confirm accurate 3D model
construction for hole wall angles less than 80 degrees, with 1.25% error.

關鍵字(中)

★ 自動化定位
★ 聚焦成形技術
★ 三維形貌重建
★ 形貌量測技術
★ 藍寶石玻璃

關鍵字(英)

★ Automated position
★ Shape-From-Focus
★ Three-dimensional displays
★ Shape measurement
★ Sapphire glass

論文目次

摘要........................................................................................................................................I
Abstract ................................................................................................................................ II
致謝.....................................................................................................................................IV
目錄.....................................................................................................................................VI
圖目錄.................................................................................................................................IX
表目錄................................................................................................................................XII
第一章緒論......................................................................................................................... 1
1-1 研究背景 ................................................................................................................ 1
1-2 文獻回顧 ................................................................................................................ 3
1-2-1 藍寶石玻璃材料的基本性質與應用........................................................... 3
1-2-2 自動化定位 ................................................................................................. 3
1-2-3 聚焦成形 Shape From Focus (SFF).............................................................. 4
1-3 研究動機、目的與方法......................................................................................... 6
1-4 論文架構 ................................................................................................................ 7
第二章實驗原理 ................................................................................................................. 8
2-1 自動定位原理 ........................................................................................................ 8
2-1-1 機器視覺定位.............................................................................................. 8
2-1-2 步進馬達控制.............................................................................................. 9
2-2 光學鏡頭原理 ...................................................................................................... 10
2-2-1 成像........................................................................................................... 10
2-2-2 對焦........................................................................................................... 11
2-2-3 景深........................................................................................................... 12
2-2-4 影像畸變 ................................................................................................... 13
2-3 聚焦成形原理 ...................................................................................................... 14
VII
2-3-1 系統基本架構............................................................................................ 15
2-3-2 聚焦度值的定義和計算 ............................................................................ 15
2-3-3 三維形貌重建流程.................................................................................... 16
2-4 聚焦度值演算法................................................................................................... 16
2-4-1 Roberts........................................................................................................ 18
2-4-2 Prewitt......................................................................................................... 19
2-4-3 Laplacian .................................................................................................... 20
2-4-4 Sobel........................................................................................................... 22
2-4-5 Scharr.......................................................................................................... 23
2-5 小結...................................................................................................................... 25
第三章系統架構 ............................................................................................................... 26
3-1 量測樣本 .............................................................................................................. 26
3-2 量測系統設計 ...................................................................................................... 27
3-2-1 硬體設備 ................................................................................................... 28
3-2-2 軟體設備 ................................................................................................... 41
3-3 量測系統運作流程............................................................................................... 42
3-3-1 自動定位 ................................................................................................... 43
3-3-2 三維形貌重建............................................................................................ 44
3-4 小結...................................................................................................................... 45
第四章實驗結果與討論.................................................................................................... 46
4-1 自動定位 ............................................................................................................... 46
4-1-1 粗定位 ....................................................................................................... 46
4-1-2 細定位 ....................................................................................................... 49
4-2 三維形貌重建與量測........................................................................................... 50
4-2-1 Roberts 演算法 ........................................................................................... 51
4-2-2 Prewitt 演算法............................................................................................ 52
VIII
4-2-3 Laplacian 演算法........................................................................................ 54
4-2-4 Sobel 演算法 .............................................................................................. 55
4-2-5 Scharr 演算法............................................................................................. 57
4-3 系統性能驗證 ...................................................................................................... 59
4-3-1 系統解析度 ............................................................................................... 59
4-3-2 量測範圍 ................................................................................................... 60
4-3-3 重複性量測 ............................................................................................... 63
4-3-4 量測極限 ................................................................................................... 64
4-4 商用機台量測 ...................................................................................................... 65
4-4-1 圓孔孔徑量測............................................................................................ 65
4-4-2 圓孔孔徑驗證............................................................................................ 66
4-5 小結...................................................................................................................... 67
第五章誤差分析 ............................................................................................................... 68
5-1 系統誤差 .............................................................................................................. 68
5-1-1 X、Y 軸電控位移平台之位移誤差 ........................................................... 68
5-2 隨機誤差 .............................................................................................................. 69
5-2-1 環境干擾 ................................................................................................... 70
5-2-2 機械震動 ................................................................................................... 70
5-3 小結...................................................................................................................... 71
第六章結論與未來展望.................................................................................................... 72
6-1 結論...................................................................................................................... 72
6-2 未來展望 .............................................................................................................. 73
參考文獻............................................................................................................................. 74

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指導教授

李朱育(Ju-Yi Lee)

審核日期

2024-8-20

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