Multifrequency transcranial ultrasound holography with acoustic lenses

Focusing ultrasound through the skull requires the accurate correction of skull-induced aberrations. Acoustic lenses provide an inexpensive and effective measure for correcting these distortions. This study explores a phase unwrapping technique for designing multifrequency acoustic lenses coupled with geometrically focused transducers. Here, we demonstrate numerically and theoretically that, in a homogeneous medium and for a single target steered from the natural focus of the transducer, a wrapped lens can only work at its design frequency, while a phase unwrapped lens is broadband. This concept is further explored in experiments where three human skulls are inserted between a transducer and its natural focus. Unwrapped lenses are used to correct for the skull aberrations at multiple frequencies and are compared with their wrapped counterparts. Such experiments demonstrate that only the unwrapped lenses are capable of correcting for skull aberrations in a broad range of frequencies. At the design frequency of the lenses, the unwrapped lenses perform quantitatively better than their wrapped counterparts since the average intensity behind the three skulls is found to be 49% lower with a phase wrapped lens compared with a phase unwrapped lens, even if both allow the qualitative refocusing of the wave at the desired targets. In addition, such results confirm the necessity of correcting for skull aberrations, since the field may be highly distorted in the absence of aberration correction.