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作者应用微扰理论首先导出了顶角接近π的平面扇形导体衍射场与θ接近π/2的橢锥导体衍射场的微扰项之表达式,因此,对其相应的简单问题——导体半平面屏的衍射与导体平面的反射,也得到了相应的微扰项之表达式。然后,按照文献[10]中所提出的原理,以内接多边形代替一般形状的导体薄片,以许多内接小橢锥面组成的曲面代替一般形状的导体表面,分别将上述微扰对多边形各顶点及曲面各内接锥顶求和。在极限情况下,求和变为积分,从而分别导出了任意形状的导体薄片(因而导体平面屏上的开孔)与导体表面衍射的一级衍射场,它们是对几何光学场的一Applying the perturbation theory to Helmholtz's equations of spherical and sphero-conal systems of coordinates, the author deduces the expressions for the perturbation terms of diffraction due to a plane angular sector with its angle nearly equal to π and those due to an elliptic cone with θ nearly equal to π/2 respectively. Then, following the principle in [10], substituting the diffracting plane disk of arbitrary form by its inscribed polygonal disk and the diffracting surface of arbitrary form by a surface which consists of many small inscribed elliptic cones of the original surface, we make the summations of the perturbation terms for the sectors of the polygon and those of the tops of the small cones respectively. In the limiting case these two summations become integrals, hence the diffraction fields of first-order due to the disk (thereof, the complementary plane screen with a hole) and the surface of arbitrary forms are derived respectively.
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