Simple method for measuring phase transfer functions of transducers

Abstract

The impulse response of a transducer can be represented in the frequency domain by its complex analog, the transfer function. The amplitude transfer function is measured regularly in contrast to the phase transfer function (PTF). Applications for the PTF range from adjusting the emitted pulse shape for coding based imaging to the optimization of ultrasound contrast imaging methods based on destructive interference. A number of acoustic methods to measure a transducer's PTF exists, but they usually require accurate distance and acoustic wave speed measurements. Small discrepancies in these cause large phase errors. We present a pulse-echo method to measure a transducer's PTF without needing a measurement of the wave travel distance and speed. We generalize it to rectangular transducers. In our method the transducer is excited by a monofrequency sine burst with a rectangular envelope. The transducer initially vibrates at resonance (transient regime) prior to the forcing frequency (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes at different forcing frequencies. As the PTF is calculated from a relative difference measuring the wave travel distance or speed is unnecessary. The approach assumes linear wave propagation and uses a pulse-echo setup. The method was tested on a custom built single element transducer (square: 13 × 13 mm, center frequency 4 MHz, no backing or matching layers). The results were compared with KLM model simulations. Also, we phase calibrated a hydrophone, which was then used to measure the PTF of the square transducer. The simulated and measured resonance frequencies differed by 0.17 MHz. The mean PTF difference between simulation and measurements was 7°–14°. The method's reproducibility was ±15°. The PTF of the transducer was measured with good reproducibility, without measuring the wave travel distance or speed of sound in the medium. Our simple setup requires basic laboratory ultrasound equipment.