Time-harmonic far-field source array imaging in a two-dimensional waveguide is analyzed. A low-frequency situation is considered in which the diameter of the waveguide is slightly larger than the wavelength, so that the waveguide supports a limited number of guided modes, and the diameter of the antenna array is smaller than the wavelength, so that the standard resolution formulas in open media predict very poor imaging resolution. A general framework to analyze the resolution and stability performances of such antenna arrays is introduced. It is shown that planar antenna arrays perform better (in terms of resolution and stability with respect to measurement noise) than linear (horizontal or vertical) arrays and that vertical linear arrays perform better than horizontal arrays, for a given diameter. However a fundamental limitation to imaging in waveguides is identified that is due to the form of the dispersion relation. It is intrinsic to scalar waves, whatever the complexity of the medium and the array geometry.

中文翻译：

---

声波导管中的低频源成像

分析了二维波导中的时谐远场源阵列成像。考虑一种低频情况，其中波导的直径略大于波长，使得波导支持有限数量的导模，而天线阵列的直径小于波长，使得标准开放介质中的分辨率公式预测成像分辨率非常差。介绍了分析此类天线阵列的分辨率和稳定性性能的一般框架。结果表明，对于给定的直径，平面天线阵列的性能（在测量噪声的分辨率和稳定性方面）优于线性（水平或垂直）阵列，并且垂直线性阵列的性能优于水平阵列。然而，由于色散关系的形式，确定了波导成像的基本限制。无论介质和阵列几何结构的复杂程度如何，它都是标量波所固有的。