Virtual Source Array-Based Multiple Time-Reversal Focusing

Time reversal (TR) is the process of generating a spatio-temporal focus at a probe source (PS) location by transmitting 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 introduction of the concept of a virtual source array (VSA) (J. Acoust. Soc. Am. 2009, 125, 3828–3834). 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. Through numerical simulations, 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. For achieving robust multiple focusing in the mismatch environment, singular value decomposition is applied to obtain the weight vector (i.e., backpropagation vector) that best approximates the column vectors of the constraint matrix. Numerical simulation results show that VSA-based multiple TR focusing using SVD is not a method to simultaneously focus on multiple locations, but a method of constructing a field which robustly passes through multiple locations in sound speed mismatch environment.