基於平面參考波的子孔徑拼接干涉術於球面檢測的應用

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徐浚宸(Hsu, Chun-Chen) 查詢紙本館藏

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光電科學與工程學系

論文名稱

基於平面參考波的子孔徑拼接干涉術於球面檢測的應用
(Application of Sub-aperture Stitching Interferometry Based on Plane Reference Wave in Spherical Surface Testing)

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至系統瀏覽論文 (2026-11-30以後開放)

摘要(中)

干涉儀在光學元件測量扮演著不可或缺的角色，其在檢測表面平整度中
功不可沒。現今許多大型光學元件應用於國防、天文等行業，子孔徑干涉術
儼然成為未來趨勢。若檢測技術能夠提升，在光學元件製作工藝上就能繪出
嶄新的篇章。
相較於以往使用球面標準鏡進行曲面量測，在本研究中，將會提出了全
新的量測方法，既是以平面標準鏡作為干涉儀架構來檢測球面樣品。通過將
樣品劃分為多個子孔徑進行拼接，能夠減少干涉條紋擷取時引入的像差，同
時也能突破量測範圍的限制。
本文將會從使用到的五步相移干涉術及子孔徑拼接干涉術等基礎理論，
延伸至後續實驗的進行。為了確保實驗量測的準確性，在實際量測前，會將
相位模擬引入該演算法中進行分析與討論。根據實驗結果顯示，目前可量測
範圍可達總面積70%。在平面量測中，方均根誤差能達到0.0139wave。球
面樣品的曲率半徑誤差可達到約2%，系統架構可量測樣品極限為±833mm。
驗證了本實驗的可行性。
總言之，本實驗架構以平面標準鏡頭取代球面標準鏡頭，不但能有效的
降低標準鏡頭購置的成本，對於操作人員的專業度要求也降低了許多。在光
學檢測中提出嶄新的做法，唯有在誤差校正及量測範圍中仍有可持續進步
的空間。

摘要(英)

Interferometers play an indispensable role in measuring optical components,
particularly in assessing surface flatness. Today, many large optical components
are utilized in industries such as defense and astronomy, making sub-aperture
interferometry a rising trend. If detection technology can be improved, it will pave
the way for new advancements in the manufacturing process of optical
components.
Compared to the traditional method of using Transmission Spheres for curved
surface measurement, this study introduces a novel approach by utilizing a
Transmission Flat within the interferometer setup to measure spherical samples.
By dividing the sample into multiple sub-apertures for stitching, this method
minimizes aberrations introduced during the capture of interference fringes and
overcomes limitations in the measurement range.
This paper will extend from the foundational theories of the five-step phase
shifting interferometry and sub-aperture stitching interferometry to the execution
of subsequent experiments.
vi
To ensure the accuracy of the experimental measurements, phase simulations
will be incorporated into the algorithm for analysis and discussion before actual
measurements. According to the experimental results, the current measurable
range reaches up to 70% of the total area. In flat surface measurements, the root
mean square error achieves 0.0139 waves, while the curvature radius error for
spherical samples reaches approximately 2%. The system is capable of measuring
samples up to a limit of ±833mm, verifying the feasibility of this experiment.
In summary, this experimental setup replaces the Transmission Spheres with
Transmission Flats, effectively reducing the cost of acquiring standard mirrors
while also lowering the expertise required for operators. Although the method
introduces an innovative approach to optical detection, there is still room for
improvement in terms of error correction and measurement range.

關鍵字(中)

★ 子孔徑拼接

關鍵字(英)

論文目次

第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 2
1-3 研究動機與目的 4
1-4 論文架構 6
第二章基礎理論 7
2-1 相移干涉術 7
2-1-1 相移干涉術-五步相移法 8
2-2 Zernike多項式 10
2-3 相位解纏繞 12
2-4 子孔徑拼接干涉術 13
第三章實驗架構與方法 17
3-1 實驗設備與架構 17
3-2 實驗流程與方法 19
3-2-1 拼接設計 19
3-2-2 重疊面積與誤差 20
3-2-3 相位擷取 23
3-2-4 相位拼接 25
第四章實驗結果與討論 28
4-1 平面拼接 28
4-1-1 拼接模擬 28
4-1-2 平面樣品拼接結果 31
4-2 球面拼接 35
4-2-1 拼接模擬 35
4-2-2 球面樣品拼接－曲率半徑10000mm凸面樣品 39
4-2-3 球面樣品拼接－曲率半徑5000mm凸面樣品 46
4-2-4 球面樣品拼接－曲率半徑4000mm凸面樣品 52
4-3 量測極限分析 58
第五章結論與未來展望 60
參考文獻 62

參考文獻

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指導教授

郭倩丞(Kuo, Chien-Cheng)

審核日期

2024-11-14

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