Multiple time-reversal focusing with a virtual source array

Abstract

Time reversal (TR) is the process of generating a spatio-temporal focus at a probe source (PS) location by backpropagating a time-reversed version of a received signal. While TR focusing requires the PS for a coherent acoustic focus at its origin, the requirement of the PS has been partially relaxed by the concept of a virtual source array (VSA) [J. Acoust. Soc. Am. 125, 3828–3834 (2009)]. A VSA can serve as a remote platform or lens and redirect a focused field to a selected location beyond the VSA for which the field is assumed as a homogeneous medium with constant sound speed. The objective of this study is to extend VSA-based single TR focusing to simultaneous multiple focusing. This is achieved using the optimization theory by employing the multiple constraints method derived from a constraint matrix, which consists of appropriately synchronized transfer functions. It is found that simultaneous multiple focusing can be achieved with distortionless response at selected multiple locations, and its performance degrades in the presence of sound speed mismatch. Possible applications for the VSA-based TR focusing are discussed, and numerical simulation results are presentedTime reversal (TR) is the process of generating a spatio-temporal focus at a probe source (PS) location by backpropagating a time-reversed version of a received signal. While TR focusing requires the PS for a coherent acoustic focus at its origin, the requirement of the PS has been partially relaxed by the concept of a virtual source array (VSA) [J. Acoust. Soc. Am. 125, 3828–3834 (2009)]. A VSA can serve as a remote platform or lens and redirect a focused field to a selected location beyond the VSA for which the field is assumed as a homogeneous medium with constant sound speed. The objective of this study is to extend VSA-based single TR focusing to simultaneous multiple focusing. This is achieved using the optimization theory by employing the multiple constraints method derived from a constraint matrix, which consists of appropriately synchronized transfer functions. It is found that simultaneous multiple focusing can be achieved with distortionless response at selected multiple locations, and its perf...