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篇名 幾種不同的簡單幾何孔徑的夫朗和斐繞射
卷期 45
並列篇名 Simulation of Fraunhofer Diffraction Pattern Through an Aperture with Different Simple Geometric Structure
作者 柳銘哲
頁次 031-039
關鍵字 克希荷夫理論矩形孔圓孔三角形孔夫朗和斐繞射圖樣相對繞射強度Kirchhoff theoryrectangular holecircular holetriangular holeFraunhofer diffraction patternrelative diffraction intensity
出刊日期 201406

中文摘要

我們簡短回顧克希荷夫如何透過亥姆霍兹方程和格林定理推導出克希荷夫繞射公式[1,2]。事實上,該公式已在更루時間被菲涅耳猜測出來,只不過菲捏耳無法嚴謹的證明它並留下了幾個未定參數。克希荷夫繞射公式的積分很複雜,必須透過近似的手段將公式化簡才能得到積分結果。還好很多實驗條件是符合近似所需的前提。我們採取的是夫朗和斐近似,基本上它要求開孔的面積<<繞射觀察距離x波長。其實說穿了它有點像傅立葉變換,也就是說,觀察屏看到的是孔徑的傅立葉轉換。我們利用它計算了矩形孔、矩形環、十字形孔、圓形孔、圓形環和三角形孔的夫朗和斐繞射圖樣和強度分布。有點像量子力學中的不確定原理,真實孔徑的尺寸若在某方向縮小,則其在繞射屏上的繞射圖案,就會在相對應的方向上延展。

英文摘要

We review briefly the processes that Kirchhoff derive the Kirchhoffs diffraction formula from Helmholtz equation and Green’s Theorem. In fact, Fresnel have deduced the formula at an earlier time. Unfortunately, Fresnel couldn’t prove it strictly in mathematics, in the meantime, he left some undetermined parameter. The integral of the Kirchhoffs diffraction formula is complex extremely. With the help of approximate means, we could simplify it and get the result of the integral. Fortunately, most of experimental situation fit the premise of making approximation. We adopt the Fraunhofer approximation which require that the area of the hole is much less than the observation distance from the diffraction hole x wave length. To put it bluntly, this is a kind of Fourier Transformation. It means what is observed on the screen exactly is the Fourier Transformation of the diffraction hole. In this paper, using the Kirchhoff diffraction theory, the pattern and the relative diffraction intensity of Fraunhofer diffraction through different shaped holes (rectangular, rectangular ring, cross-shaped, circular, annulus and triangular)have been derived. It resembles the uncertainty principle of the quantum mechanics: the more narrow the size of diffraction hole in certain direction, the more cold-drawn the space in the corresponding direction.

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