Kirchhoff approximations for the forward-scattering target strength of underwater objects are developed by combining Babinet’s principle and the Kirchhoff integral, where theoretical formulations and a numerical implementation are given in detail. The Kirchhoff approximation is found to be a high-frequency physical acoustic approximation. The forward-scattering target strength versus frequency and the spatial angles for spherical objects, prolate spheroids and the Benchmark Target Strength Simulation Submarine (BeTSSi-Sub) model are obtained by the Kirchhoff approximation and compared with results from theory, the deformed cylinder method (DCM) and the boundary element method (BEM). The Kirchhoff approximation shows considerable agreement with the theoretical and numerical approaches in a region of [Formula: see text] from the rigorous forward-scattering direction. The forward-scattered field contour and the corresponding directivity for the BeTSSi-Sub model are also calculated as a demonstration. Mode coupling caused by the simulated target is clearly revealed. The results indicate that the Kirchhoff approximation can predict the forward-scattering target strength of complex underwater objects.

中文翻译：

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水下物体前向散射目标强度的基尔霍夫近似

结合巴比涅原理和基尔霍夫积分，提出了水下物体前向散射目标强度的基尔霍夫近似，详细给出了理论公式和数值实现。基尔霍夫近似被发现是一种高频物理声学近似。球体、长椭球体和基准目标强度模拟潜艇（BeTSSi-Sub）模型的前向散射目标强度与频率和空间角的关系通过基尔霍夫近似得到，并与变形圆柱法（DCM）理论结果进行了比较。 ) 和边界元法 (BEM)。基尔霍夫近似与 [公式：见正文]从严格的前向散射方向。还计算了 BeTSSi-Sub 模型的前向散射场轮廓和相应的方向性作为演示。清楚地揭示了由模拟目标引起的模式耦合。结果表明，基尔霍夫近似可以预测复杂水下物体的前向散射目标强度。