- 學位論文
三維純量繞射光場模擬方法之實現與比較
Implementations and Comparisons of Simulation Methods of Three-Dimensional Scalar Diffraction Fields
摘要
Huygens-Fresnel principle通常用來計算二維繞射光場分佈，根據McCutchen[6]與J. Lin[7]等人所提出的處理方法，可以將Huygens-Fresnel principle修改成一個由任意穿透函數經過孔徑後的三維繞射光場(Three-dimensional diffraction field)分佈函數。這個三維繞射光場分佈函數是以近軸近似為基礎所提出的，其數學形式是一個三維傅立葉轉換(Three-dimensional Fourier transform)。這個三維繞射光場分佈函數與以往的Fresnel diffraction近似、角頻譜(Angular spectrum)近似以及以單次傅立葉轉換為基礎的近似不同，它並不是在傳播方向作(x,y)平面的堆疊，而是用一個三维空間的輸入場來直接計算三維空間的繞射場。 Chirp z-transform是純量繞射上的數值方法，可以用來取代快速傅立葉轉換(Fast Fourier transform)，並用來計算特定的頻譜，例如：縮放全部的頻譜、只取一段頻譜範圍或是縮放任一段頻譜範圍。 本論文實現了以三維繞射光場分佈函數來模擬三維繞射光場分佈，為了證明這個三維繞射光場分佈函數的繞射光場是具有進步性的，我們另外使用Fresnel diffraction近似公式與角頻譜近似公式來模擬繞射光場，然後根據模擬結果來比較在焦平面上的繞射光場分佈各自的優缺點。 Chirp z-transform增加三維繞射光場的計算方式，用來清楚說明焦平面上的繞射光場分佈情形。最後再將這些三維繞射光場加入chirp z-transform的分析，藉此來觀察在焦平面上的繞射光場分佈，是否有更大更明顯的原理現象。
並列摘要
Huygens-Fresnel principle is used to calculate the diffraction field distribution. According to the modification proposed by McCutchen [6] and J. Lin [7] et al., the Huygens-Fresnel principle can be used for any arbitrary transmittance function after the aperture of the three-dimensional diffraction field distribution function. The three-dimensional diffraction field distribution function is proposed on the basis of paraxial approximation, which is in a form of three-dimensional Fourier transform. Therefore, this three-dimensional diffraction field distribution function is different from Fresnel diffraction approximation, the angular spectrum approximation and the single-Fourier-transform-based approximation in which the diffraction field distribution function is stacked with (x,y) plane in the propagation direction. Instead, a three-dimensional space of the input field is directly used to calculate the diffraction field of three-dimensional space. Chirp z-transform is a numerical method in the scalar diffraction which can be used to replace the fast Fourier transform, and to calculate the specific spectrum, for examples, scaling the entire spectrum, specifying some spectral range, or zooming particular any spectral range. In this thesis, we implemental three-dimensional diffraction field distribution function to simulate three-dimensional diffraction field distribution, which shows the progression of three-dimensional diffraction field distribution function of the diffraction field. In addition, we used the Fresnel diffraction approximation formula and the angular spectrum approximation formula to simulate the diffraction field. According to these different simulational results, we compared the advantages and disadvantages of the distribution in the focal plane of the diffraction field. The chirp z-transform was added to the calculation of the three-dimensional diffraction field to clearly illustrate the diffraction field distribution in the focal plane. Finally, these are three-dimensional diffraction fields to by adding the chirp z-transform analysis. To take this observation in the focal plane of the diffraction field distribution, whether there is a greater and more obvious of the phenomenon.