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本文从理论上较全面地分析了入射瞬态平面波的三维复源脉冲波束展开，出发点是从频域球面波严格的格林函数导出球面复源点表达式，由此得到频域平面波的复源点展开公式，对这一公式作单边付里叶变换，得到瞬态标量平面波三维复源脉冲波束平行射线展开的完整公式，并得到展开截断误差、离散化展开误差与总误差的表达式。这种展开适用于任意脉冲信号。通过选择复源参量、展开间距与展开半径，可使从展开面到最大展开距离之间的给定范围内，空间各处的合成场处处满足规定的误差要求。解决了“快速简捷地对入射瞬态平面波进行复源脉冲波束展开”这一分析瞬态波传播与散射的关键技术。本文具体计算了常用的高斯包络信号瞬态标量平面波的三维复源脉冲波束展开，分析了计算数值并得到了满意的结果。这种展开方法特别适合于应用复源脉冲波未理论来研究瞬态波的传播与目标的散射特性分析。
In this paper, the three-dimensional complex source pulse beam spreading of incident transient plane wave is analyzed in a comprehensive way. The starting point is to derive the spherical complex source expression from the strictly Green’s function of the frequency spherical wave, Expanding the formula, this formula is unilateral Fourier transform, get the complete formula of the parallel rays of three-dimensional complex source pulse beam of transient scalar plane wave, and obtain the expressions of truncation error, discretization expansion error and total error. This expansion applies to any pulse signal. By selecting the complex source parameters, expanding the space and expanding the radius, the prescribed error requirements can be fulfilled in the composite field all over the space within a given range from the expanded surface to the maximum expanded distance. This paper solves the key technique of analyzing the transient wave propagation and scattering in the fast and simple repetitive pulsed beam spreading of incident transient plane wave. In this paper, three-dimensional complex source pulse beam spread of the commonly used transient Gaussian envelope signal of the Gaussian envelope signal is calculated. The numerical results are analyzed and satisfactory results are obtained. This expansion method is particularly suitable for the application of complex source pulse wave theory to study the transient wave propagation and scattering characteristics of the target analysis.