Theoretical derivation and numerical analysis for droplet's boundary diffraction
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摘要: 为了研究云和降水的微物理特性,根据杨氏边界衍射理论,结合MATHEMATICA和MATLAB两种数学软件,采取理论推导和数值模拟的方法,针对球形和椭球形云雨滴建立了在夫琅和费近似条件下,光轴上的单色点光源照射情况以及单色平行光照射情况的边沿衍射场分布;对单色平行光照射下云雨滴的边沿衍射进行了数值摸拟;并针对边沿衍射在雨滴探测中会引起的问题进行了分析,提出了变动阈值解决办法。结果表明,孔径衍射图样是几何投影光波和边界衍射光波的叠加;边界衍射是粒子边沿的不均匀性散射的结果,同等条件下随粒子大小和形状的差异而不同。这对云雨粒子的探测具有指导意义。Abstract: To study the microphysical characteristics of clouds and precipitation, theoretical boundary diffraction field was derived according to Young's boundary diffraction theory and diffraction field distributions were established under exposure of point light source on the optical axis and parallel monochromatic light with the Fraunhofer approximation, the boundary diffraction field of droplet under exposure of monochromatic parallel light was simulated with MATHEMATICA and MATLAB. Furthermore, the effect of boundary diffraction on droplet detection was analyzed and accordingly a threshold change solution was put forward. It is concluded that diffraction by an aperture is addition of geometric projection and boundary diffraction, boundary diffraction is caused by non-uniformity of particles'edge, varying with size and shape. It is meaningful for the detection of droplets.
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