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An analytical filter design method for guided wave phased arrays

机译：导波相控阵的解析滤波器设计方法

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This paper presents an analytical method for designing a spatial filter that processes the data from an array of two-dimensional guided wave transducers. An inverse problem is defined where the spatial filter coefficients are determined in such a way that a prescribed beam shape, i.e., a desired array output is best approximated in the least-squares sense. Taking advantage of the 2π-periodicity of the generated wave field, Fourier-series representation is used to derive closed-form expressions for the constituting matrix elements. Special cases in which the desired array output is an ideal delta function and a gate function are considered in a more explicit way. Numerical simulations are performed to examine the performance of the filters designed by the proposed method. It is shown that the proposed filters can significantly improve the beam quality in general. Most notable is that the proposed method does not compromise between the main lobe width and the sidelobe levels; i.e. a narrow main lobe and low sidelobes are simultaneously achieved. It is also shown that the proposed filter can compensate the effects of nonuniform directivity and sensitivity of array elements by explicitly taking these into account in the formulation. From an example of detecting two separate targets, how much the angular resolution can be improved as compared to the conventional delay-and-sum filter is quantitatively illustrated. Lamb wave based imaging of localized defects in an elastic plate using a circular array is also presented as an example of practical applications.
机译：本文提出了一种用于设计空间滤波器的分析方法，该滤波器可处理二维导波换能器阵列中的数据。定义了一个反问题，其中以这样的方式确定空间滤波器系数，使得在最小二乘意义上最佳地近似规定的波束形状，即期望的阵列输出。利用所生成波场的2π周期，傅里叶级数表示法可用于得出构成矩阵元素的闭式表达式。期望阵列输出为理想增量函数和门函数的特殊情况将以更明确的方式考虑。进行数值模拟以检查通过所提出的方法设计的滤波器的性能。结果表明，所提出的滤波器总体上可以显着提高光束质量。最值得注意的是，所提出的方法不会在主瓣宽度和旁瓣水平之间做出折衷。即同时实现了狭窄的主瓣和低旁瓣。还表明，所提出的滤波器可以通过在公式中明确考虑到阵列元件的不均匀方向性和灵敏度的影响来补偿这些影响。从检测两个分离的目标的示例，定量地示出了与传统的延迟和求和滤波器相比可以将角度分辨率提高多少。作为实际应用的示例，还提出了使用基于圆形阵列的基于Lamb波的弹性板中局部缺陷成像的方法。

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