Focal translation by frequency shift in free space

Variable focusing in range from a transmit array can be accomplished by a frequency shift in an acoustic waveguide. In this paper, a general algorithm is derived in free space that can move the focal spot of a linear transmit array both transversely and horizontally. In particular, for variable range focusing, the prescribed frequency shift is the same for all elements of the array, whereas, for transverse focal shifts, the frequency shift varies with element location in the array. The method described in this paper is especially suitable for varying the location of the focal spot of a time-reversal mirror in the presence of an aberrating layer in that no knowledge of the medium properties is necessary. Simulation results demonstrating the proposed method are presented in comparison with those from a conventional steering method.