This article presents the exact evaluation of the physical optics (PO) integral in time-domain. The surface of a perfect electrically conducting (PEC) scatterer is modeled by quadratic triangles. Using the Radon transform interpretation, the PO integral is reduced to a line integral, which is formed by the intersection of the quadratic surface and the plane defined by the Dirac delta function. It is shown that the resulting line is a quadratic curve, e.g., an ellipse, in barycentric coordinates of the quadratic triangle, since the incident wave is a plane wave and the scattered fields are observed at the far-field. To evaluate the PO integral: 1) the PO integral is represented in barycentric coordinates and the type of the intersecting curve is determined; 2) an appropriate coordinate transformation is applied, e.g., elliptic coordinates for the ellipse; and then 3) the Gauss–Legendre quadrature rule (GLQR) is applied. It is shown that a suitable GLQR order yields the PO integral exactly. The validity and accuracy of the proposed method are demonstrated via numerical examples.

中文翻译：

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二次三角面上时域物理光学积分的精确计算

本文介绍了时域中物理光学 (PO) 积分的准确评估。完美导电 (PEC) 散射体的表面由二次三角形建模。使用 Radon 变换解释，PO 积分简化为线积分，由二次曲面与狄拉克 delta 函数定义的平面相交形成。结果表明，由于入射波是平面波并且在远场观察到散射场，因此结果线是二次曲线，例如椭圆，在二次三角形的重心坐标中。PO 积分的计算： 1) PO 积分用重心坐标表示，并确定相交曲线的类型；2）应用适当的坐标变换，例如，椭圆的椭圆坐标；然后 3) 应用高斯-勒让德求积法则 (GLQR)。结果表明，合适的 GLQR 阶可以精确地产生 PO 积分。通过数值例子证明了所提出方法的有效性和准确性。