几种抛物方程形式的相位误差分析

近轴近似是引起抛物方程（parabolic equation, PE）自身固有相位误差的根本原因. 为选取适合目标场景中的最优PE形式，基于色散分析方法，推导了现有六种PE形式的色散关系，评估出折射率和传播仰角对各PE形式相位误差的影响，进而分析出对流层电波传播、水下声波传播、森林电波传播三种典型场景中各PE形式的精度. 研究发现，对于对流层电波传播场景，Lin-Duda型PE精度最高，Feit-Fleck型PE和Tappert型PE的精度几乎完全相同，紧随其后的是Padé型PE；对于水下声波传播场景，Padé型PE和Lin-Duda型PE最为准确；对于森林电波传播场景，Lin-Duda型PE的精度依旧是最高的. 进一步地，通过固定相位误差限给出了不同PE形式的适用仰角范围.

Phase error analysis of several parabolic equation forms

The intrinsic phase error of the parabolic equation (PE) is mainly caused by the paraxial approximation. In order to select the optimal PE form in the target scenario, we analyze the accuracy of the existing six PE forms in the typical tropospheric electromagnetic wave propagation, underwater acoustic propagation, and forest electromagnetic wave propagation scenarios through studying their phase error properties. The dispersion relation of each PE is derived. It is found that in tropospheric electromagnetic wave propagation scenario, the Lin-Duda PE is the most accurate, the Tappert and Feit-Fleck PEs are almost identical, and the Padé PE is closely followed. In underwater acoustic propagation scenario, the Padé and Lin-Duda PEs get the highest accuracy. For forest electromagnetic wave propagation scenario, Lin-Duda PE still maintains the highest accuracy. Furthermore, the acceptable propagation angle limit of each PE is given for a fixed phase error limit.