A Numerical Optimization Method for Transducer Transfer Functions by the Linearity of the Phase Spectrum.

New ultrasound imaging and therapeutic modalities may require transducer designs that are not readily facilitated by conventional design guidelines and analytical expressions. This motivates the investigation of numerical methods for complex transducer structures. Based on a mathematical theorem, we propose a new numerical design and optimization method for ultrasound transducers by linearizing the phase spectrum of transducer transfer functions. A gradient-based algorithm obtains the optimal transducer by varying a selected set of transducer parameters. To demonstrate the linear phase method, a simulated air-backed 4-MHz single-element imaging transducer with two matching layers, bondlines, and electrodes is optimized by varying the impedances and thicknesses of the matching layers. The magnitude spectrum resembles that of a Gaussian and, compared to a conventional transducer, the time-sidelobe level is reduced by more than 15-dB. Moreover, we apply the linear phase method to analyze and compensate for bondlines that resonate within the passband. Finally, we address the challenge of obtaining materials for the matching layers with the optimized impedance values by calculating alternative material pairs.