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导出局部矢量平面波三维复射线平行波束展开的完整表达式，并得到了展开截断误差与离散化展开误差的计算公式．在给定展开误差与最大展开距离的前提下，定出局部矢量平面波，包括复原点参量与展开间距在内的三维复源展开参量与展开半径，使从展开面到最大展开距离之间的规定半径范围内；空间各处的合成场均满足给定误差要求．这种展开方法特别适合于应用复射线法来研究波的传播与分析目标的散射特性．
The complete expressions of the parallel beams of three-dimensional complex radiations of local vector plane waves are deduced and the formulas for calculating the truncation errors and discretization errors are obtained. Given the expansion error and the maximum expansion distance under the premise of local vector plane wave set, including the restoration point parameters and the expansion of the distance, including three-dimensional complex source expansion parameters and the expansion radius, so that the expansion from the surface to the maximum distance between the provisions Within the radius of the space; synthetic field around the meet the given error requirements. This method of expansion is particularly suitable for the application of complex ray method to study the wave propagation and analysis of the scattering characteristics of the target.