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研究生: 蔡宜蓁
Tsai, I-Chen
論文名稱: 基於空間光調變器與回饋控制之雷射多點聚焦能量調控
Laser Multi-focus Energy Manipulation with Feedback-control Algorithm using a Spatial Light Modulator
指導教授: 張家源
Chang, Chia-Yuan
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2025
畢業學年度: 113
語文別: 中文
論文頁數: 129
中文關鍵詞: 空間光調變器Bessel 光束相位切割法多點聚焦能量調控回饋控制演算法
外文關鍵詞: spatial light modulator, Bessel beam, phase segmentation method, multi- focus energy manipulation with feedback-control algorithm
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  • 當前光束整形多採用固定式的繞射元件(diffraction optical element,DOE),雖然設計與操作簡單,卻無法因應不同應用需求進行動態調整,相較之下,空間光調變器(spatial light modulator,SLM)可依需求調整相位圖,靈活產生所需的光型。在本研究主要分為兩個部分,首先,在Bessel 光束的生成方面,實驗發現雷射正入射至 SLM 能有效減少由斜入射所造成的光學像差,進而提升 Bessel 光束的特性,展現 SLM 於高品質光束整形應用中的實用性,第二部分則是著重於多點聚焦系統的優化,採用相位切割法來快速設計多點聚焦的相位圖,免去反覆的相位重建過程,然而多點聚焦在實際應用中仍受外在擾動影響其能量均勻性。
    為了解決此問題,提出一種多點聚焦能量調控回饋控制演算法(multi-focus energy manipulation with feedback-control algorithm,MEMFA),透過多點聚焦的影像回饋資訊,動態調整相位圖中各區的角度比例,進而控制能量分佈,並加入 Zernike 進行像差補償,提升多點聚焦的聚焦品質。最終實驗結果顯示,使用 MEMFA 後,3×3 聚焦點的均勻性大幅提升,RMSD 從 46.1%降至 1.06%,提升約 43.5 倍,且僅需 4 次迭代即可收斂,此外 MEMFA 也能實現不同能量比例的多點聚焦,3×3 與 5×5 聚焦點 RMSD 分別為 1.85%與 1.35%,透過掃描 5×5 的聚焦點,能達成大規模的聚焦控制,總計 2500 個雷射點的 RMSD 從 11.6%降至 1.99%,結果證實,MEMFA 有效控制多點能量品質,適用於平行雷射加工應用。

    Fixed diffraction optical elements (DOEs) are commonly used for beam shaping due to their simple design, but they lack flexibility for dynamic adjustment. In contrast, spatial light modulators (SLMs) allow real-time phase pattern modulation to generate various beam shapes. This study is divided into two main parts. First, in the generation of Bessel beams, experiments show that using normal incidence on the SLM reduces optical aberrations compared to oblique incidence, improving beam quality. This demonstrates the practical utility of SLMs in high-quality beam shaping applications. The second part focuses on the optimization of multi-point focusing systems. In this study adopts the phase segmentation method to design multi-focus phase patterns efficiently, avoiding iterative phase reconstruction. However, the energy uniformity of multi-focus is still affected by system imperfections and external disturbances. To address this, we propose a multi-focus energy manipulation with feedback-control algorithm (MEMFA), which dynamically adjusts the angular proportions of phase segments based on feedback from the multi-focus image. Zernike polynomials are also incorporated for aberration compensation. Experimental results demonstrate that MEMFA improves the RMSD of a 3×3 multi-focus from 46.1% to 1.06%, converging in just four iterations. It also enables generation of beams with varied energy distributions, achieving RMSDs of 1.85%(3×3) and 1.35% (5×5). Scanning the 5×5 pattern further achieves large-scale control with 2,500 laser points, reducing RMSD from 11.6% to 1.99%. These results confirm MEMFA’s effectiveness in enhancing and maintaining energy uniformity in multi-focus, making it well-suited for parallel laser processing applications.

    摘要 i Extended Abstract ii 誌謝 vii 目錄 viii 表目錄 xi 圖目錄 xii 第一章 緒論 1 1-1 前言 1 1-2 文獻回顧 2 1-3 研究動機 4 1-4 論文架構 6 第二章 空間相位調變原理 7 2-1 SLM工作原理 7 2-1-1 液晶起源與特性 7 2-1-2 液晶分子排列種類 9 2-1-3 SLM原理介紹 11 2-2 SLM規格介紹 12 2-3 SLM校正 16 2-3-1 SLM校正光路系統 17 2-3-2 SLM校正公式推導 19 2-3-3 SLM校正結果 21 第三章 Bessel光束設計 23 3-1 Bessel光束原理 23 3-1-1 穿透式錐形透鏡 25 3-1-2 反射式錐形透鏡 29 3-2 Bessel光束之SLM相位分析 30 3-3 系統架設 34 3-4 實驗與理論驗證 36 3-4-1 HOLOEYE內建相位圖結果比較 36 3-4-2 HT-BPM演算法模擬與實驗結果比較 42 第四章 多點聚焦優化系統 46 4-1 系統架設 47 4-2 扇形相位切割法 48 4-3 多點聚焦品質優化 50 4-3-1 多點聚焦能量調控演算法 52 4-4 多點聚焦系統自動化流程 54 4-4-1 流程架構 55 4-4-2 影像分析與重心演算法 57 4-4-3 光束分析儀參數設定 58 4-4-4 雷射與SLM穩定性測試 62 4-5 像差補償 64 4-5-1 SLM相位設計 64 4-5-2 靜態干擾補償 66 4-6 多點聚焦速度優化 71 4-6-1 控制器優化 71 4-6-2 相位切割法程式優化 73 4-7 實驗結果 75 4-7-1 不同位置聚焦點均勻性變化與均勻化 75 4-7-2 不同聚焦點數強度均勻化 83 4-7-3 光強比例調整 87 4-7-4 大範圍多點聚焦能量均勻性優化 89 第五章 結論與未來展望 93 5-1 結果與討論 93 5-2 未來展望 94 參考文獻 97 附錄 106

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