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標題: | 設計多階式繞射光學元件於雷射光束整形之研究 Study of Designing Multi-Level Diffractive Optical Elements for Laser Beam Shaping |
作者: | Ku-Hui Hsu 許顧輝 |
指導教授: | 林晃巖 |
關鍵字: | 繞射光學元件,雷射光束整形,模擬退火演算法,基因演算法, diffractive optical element,laser beam shaping,simulated annealing algorithm,genetic algorithm, |
出版年 : | 2013 |
學位: | 博士 |
摘要: | 伴隨著製程技術的進展,繞射光學元件日漸受到重視。它們具有體積小、重量輕、以及光學功能整合性的優點,尤其是多階式繞射光學元件,它們在大量生產上具有很大的優勢,其中,二位元元件更是製程上成本最低的選擇。我們研究的目的是計設出性能比較好的元件。
首先我們針對設計方法做研究。我們提出一個遞迴設計方法,希望能設計出較好性能的元件。我們比較由遞迴傅立葉演算法、直接搜尋法,模擬退火法、以及我們所提出的演算法所設計出的元件性能。在這方面的研究,我們著重於遞迴式的設計方法,因為遞迴式的設計方法能夠設計任何的目標圖形,是比較通用的設計方法。我們設計一個一般常見的範例,即將入射高斯分佈的光束於成像面上整形成均勻的方形強度分佈。 雖然所提出的演算法在平行化的處理上是具有相當的優勢,但在使用個人電腦為設計的前提下,我們選擇模擬退火演算法為後續研究的設計方法。在一般的設計中,可以設計的參數為入射高斯光束的直徑大小、元件的周期、元件的量化階數、以及目標圖形的性質。然而,元件的周期受到許多的限制,包含製程技術以及計算量。此外,元件的量化階數也因成本考量與製程技術受到限制。我們建立數學模型來研究設計參數對於設計元件的性能有什麼樣的影響,研究的參數包含入射高斯光束的直徑大小、元件的量化階數、以及目標圖形的組成頻率。 研究完設計參數後,我們著手於設計二位元的元件。不幸地,二位元的元件在多階式繞射光學元件設計中是比較特殊的例子,設計出來的元件性能也往往不如預期。於此,我們提出各種的價值函數並將其應用在模擬退火法中以求能設計出性能較好之元件。更進一步地,我們歸納所設計的二位元元件之性能隨著設計參數變化的趨勢。接著,我們設計一個實際比較大尺寸的二位元元件,並且簡單分析其在製程上的公差。 最後,我們對於近軸近似假設在繞射強度分佈計算上所造成的誤差提出另一種看法與觀點,更進一步地提出一個計算方法以獲得較精準的繞射場強度分佈計算。在這方面,我們以數值模擬以及一個簡單的實驗來驗證我們的推論與計算方法。 The diffractive optical elements become important as accompanied with the development of the lithographic technology. They have the advantages of slim size, light weight, and the combination of optical functions. The multi-level elements, especially the binary elements, have the advantages for mass production. First, we studied the accuracy of the general method for the computation of diffraction fields. We proposed the different aspect for the error of the diffractive intensity distribution which computed by the Fraunhofer diffraction. We proposed a computation method to obtain the accuracy intensity distribution of the diffraction field. In this study, we verified the accuracy of the proposed method by the numerical simulation and a simple experiment. Many methods for the design diffractive optical elements have been proposed and applied. We proposed a design method to obtain the element with good performance. In our study, the iterative Fourier algorithms, the direct search, the simulated annealing algorithm, and the proposed algorithm were performed and compared. Note that we focus on the iterative methods of the designing because they can be used to design arbitrary target patterns. We designed a diffractive beam shaper to transform an incident Gaussian beam into a uniform squared intensity distribution at the image plane. The proposed algorithm has advantage of parallelization; however, we selected the simulated annealing algorithm to design elements in the following research when only the personal computer can be used. In the design, the incident Gaussian beam diameter, the pitch, the quantization level, and the property of the target pattern are the designing parameters. Unfortunately, the pitch is constrained by the manufacturing technology and the computational resource. Besides, the quantization level is constrained by the cost and also the manufacturing technology. We derived a mathematical model to study the performance of the designed element when the incident Gaussian beam diameter, the quantization level, or the composition frequency of the target pattern varies. After the study of the design parameters, we designed the binary element by the same way. Unfortunately, the binary element is the special case of the designing owing to its solution space is greatly constrained. Thus, the performance of designed elements is always bad. We proposed and applied various cost functions in the simulated annealing to obtain the element with good performance. Moreover, we studied the trends on the performance when the designing parameters varied. Finally, we designed a practical binary element with large incident Gaussian beam diameter. We studied the tolerance of the designed binary element when the pitch or the depth error occurs in the manufacture. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60679 |
全文授權: | 有償授權 |
顯示於系所單位: | 光電工程學研究所 |
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