Designing of sparse 2D arrays for Lamb wave imaging using coarray concept

Abstract

2D ultrasonic arrays have considerable application potential in Lamb wave based SHM systems, since they enable equivocal damage imaging and even in some cases wave-mode selection. Recently, it has been shown that the 2D arrays can be used in SHM applications in a synthetic focusing (SF) mode, which is much more effective than the classical phase array mode commonly used in NDT. The SF mode assumes a single element excitation of subsequent transmitters and off-line processing the acquired data. In the simplest implementation of the technique, only single multiplexed input and output channels are required, which results in significant hardware simplification. Application of the SF mode for 2D arrays creates additional degrees of freedom during the design of the array topology, which complicates the array design process, however, it enables sparse array designs with performance similar to that of the fully populated dense arrays. In this paper we present the coarray concept to facilitate synthesis process of an array’s aperture used in the multistatic synthetic focusing approach in Lamb waves-based imaging systems. In the coherent imaging, performed in the transmit/receive mode, the sum coarray is a morphological convolution of the transmit/receive sub-arrays. It can be calculated as the set of sums of the individual sub-arrays’ elements locations. The coarray framework will be presented here using a an example of a star-shaped array. The approach will be discussed in terms of beampatterns of the resulting imaging systems. Both simulated and experimental results will be included.