以疊代演算法設計整型高斯光束為強度及相位均勻分佈之純相位繞射元件

Abstract

在許多的雷射應用中，均勻強度的光束是常被利用，甚至在某些應用中這樣的特性是被要求必有的特質。然而一般的雷射光束並沒有提供均勻強度的光場，其強度為高斯分佈；當入射雷射光被擴大，僅使用部分近似均勻強度光場時，將會造成大量的能量損失，這是在許多應用時所不樂見的情況。因此，有效的將高斯光束轉化成強度均勻及相位均勻之光場將是雷射光束整型典型的重要問題。 在本論文中，我們設計一片繞射元件將高斯光束轉換成均勻分布的光束，並且利用另外一片繞射相位元件去補償相位差，在重建場得到相位均勻的效果。根據Fresnel 繞射理論，我們利用複立葉轉換疊代演算法(Iterative Fourier Transform Algorithm)計算設計，以得到繞射元件的相位分佈。在模擬過程中，我們透過統計化參數測試的模擬情形，提出如何得到較佳光束品質的設計規則；我們使用不同的相位量化方法模擬設計，進一步提昇均勻度及效率較好的結果。對於二階元件而言，傳統相位量化方法與步階量化方法的均勻度值(Uniformity)各別為6.04及4.16；對於四階元件而言，其均勻度值各別為2.46及2.36；與前人的模擬結果比較，其八階相位量化的誤差平方和(sum-squared error)為19.5%。根據步階量化的結果可改善至13.5%。最後，針對元件之製程深度及刻度誤差，進行容忍度的模擬分析。

In many laser applications, a uniform beam is useful and required. However, common Gaussian beams don’t provide uniform intensity distributions and will have considerable energy loss if it is expanded to obtain a locally uniform illumination. Therefore, to efficiently shape a Gaussian beam into a uniform beam is of significant. Hence, a typical and important beam shaping problem is the transformation of a Gaussian laser beam into a beam with uniform intensity and phase. In this thesis, we design a diffractive optical element to transform a Gaussian beam to an expanded squared uniform profile and use another diffractive phase element which can compensate the phase difference to achieve a uniform phase distribution on the reconstruction plane. According to Fresnel diffraction theory, we use a design method based on the iterative Fourier transform algorithm (IFTA) to compute the phase distributions of an optical system composed of diffractive phase elements. In this thesis, we propose some design rules to get a better beam quality through systematically studying the simulation parameters. We also study the effects of different quantized methods, further improve the beam quality. For L=2, the uniformity values of traditional quantization and progressive quantization are 6.04 and 4.16, respectively. For L=4, the uniformity values of traditional quantization and progressive quantization are 2.46 and 2.36, respectively. Comparing with the previous literature by Xin Tan [10], the value of sum-squared error is 19.5% by the traditional quantization of L=8 in [10] and is 13.5% by progressive quantization of L=4 in our study. After designing the DOEs, we make a tolerance analysis about the fabricated error of depth and pitch.