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| 題名: | 利用初始解析相位函數與澤爾尼克像差多項式優化在空間光調製器產生高效率且平坦聚焦光斑
Efficient and uniform flat-top focus using a spatial light modulator with an initial analytic phase function and optimization by Zernike aberration polynomials |
| 作者: | 張洋瑞
Chang, Yang-Jui |
| 貢獻者: | 陳應誠
林瑜琤
Chen, Ying-Cheng
Lin, Yu-Cheng
張洋瑞
Chang, Yang-Jui |
| 關鍵詞: | 空間光調製器
GS 演算法
平頂光
波前調製
澤爾尼克多項式
模擬退火演算法
Spatial light modulator
Gerchberg-Saxton algorithm
Flat top beam
Wavefront modulation
Zernike polynomials
Simulated annealing |
| 日期: | 2025 |
| 上傳時間: | 2025-09-01 16:52:22 (UTC+8) |
| 摘要: | 在量子光學實驗中，產生具有高度均勻的聚焦平頂光非常重要。特別是在原子陣列的實驗，為了實現多個量子位元間的平行操作，像是利用受激輻射拉曼躍遷實現單量子位元邏輯閘，或是透過雷德堡躍遷實現雙量子位元邏輯閘，必須確保聚焦平頂光在原子陣列前後保持強度均勻。否則，原子陣列中的各個量子閘的保真度無法維持一致。因此，如何產生具有強度均勻聚焦平頂光成為實驗上重要的課題。
在過去的五十年間，光學領域發展出多種透過繞射與折射元件將波前轉換的方法，這些方法可大致分為迭代式與非迭代式兩大類。第一類是 Gerchberg-Saxton 演算法及其改良版本是最常用於生成電腦相位全息圖，此方法是最早被研究的，而其他演算法如共軛梯度最小化也可以達到此目的。第二類則包含中間角頻譜法、誤差擴散法與解析解等等。
電腦生成相位圖在重建影像時常伴隨斑點雜訊，這源自於像素之間相位差異所造成的干涉。為了過濾掉這些雜訊，有人提出在焦平面上引入訊號區域與雜訊區域的方式過濾高頻訊號，有效降低雜訊，但此種方式必須在雷射效率以及平整度之間做權衡。因此，此論文式採用 Harald Aagedal 的團隊提出的解析方法，當超高斯函數的指數趨近於無限大的情況下可直接將轉換高斯光束為平頂光束的公式變為解析解。
在生成聚焦平頂光束前，需對空間光調變器進行初始最佳化，包括校準空間光調製器的電壓、確認第一級繞射效率，以及準確輸入光束尺寸。此外，光學系統不完美也會造成像差問題，像是平頂光沒有聚焦在焦平面或是選擇的透鏡並非理想球面。為補償這些誤差，本文使用澤爾尼克多項式修正波前，並結合模擬退火演算法自動搜尋最佳係數，以達到更準確的相位補償與波前調整。
In quantum optics experiments, the focused flattop beam with uniform intensity profile is crucial. In particular, atom array systems rely on uniform illumination to perform parallel quantum operations. For instant, single-qubit gate using stimulated Raman transitions and two-qubit gates using Rydberg transitions require consistent laser intensity across all the qubits and qubit pairs. Any non-uniformity intensity will lead to variations in gate fidelity. As a result, generating uniform focused flattop beam become a key technical requirement.
Over the past five decades, a variety of methods have been developed for transforming optical wavefronts using diffractive and refractive elements. These methods can be broadly classified into iterative and non-iterative methods. Among iterative methods, the Gerchberg-Saxton algorithm and its modified version are widely used for phase-only computer-generated holograms, while alternatives such as conjugate gradient minimization also work. Non-iterative techniques include the intermediate angular-spectrum method, error diffusion, and analytical solutions.
A common issue in phase-only computer-generated hologram systems is the occurrence of speckle noise in the reconstructed plane, which is caused by interference resulting from phase differences between adjacent pixels. To minimize this noise, the reconstructed plane divided into signal region and noise region, effectively reducing speckle at the cost of a trade-off between efficiency and uniformity. In this study, we adopt the method proposed by Harald Aagedal \textit{et al.}, which provides an analytical solution for converting a Gaussian beam into a flat-top beam with high efficiency.
Before generating the flat-top beam, optimization of the spatial light modulator is necessary. This includes calibrating the driving voltage, verifying the first-order diffraction efficiency, and accurately determining the input beam size, which is critical for applying the analytical solution. To correct optical aberrations such as lens defocus or spherical distortion, we employ Zernike polynomials due to their orthogonality and correlation with classical Seidel aberrations. Furthermore, we utilize the simulated annealing to automatically search for the optimal Zernike coefficients, enabling effective wavefront error compensation. |
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| 描述: | 碩士
國立政治大學
應用物理研究所
112755003 |
| 資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0112755003 |
| 資料類型: | thesis |
| 顯示於類別: | [應用物理研究所 ] 學位論文
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