Reflector-based phase calibration of ultrasound transducers

Recently, the measurement of phase transfer functions (PTFs) of piezoelectric transducers has received more attention. These PTFs are useful for e.g. coding and interference based imaging methods, and ultrasound contrast microbubble research. Several optical and acoustic methods to measure a transducer's PTF have been reported in literature. The optical methods require a setup to which not all ultrasound laboratories have access to. The acoustic methods require accurate distance and acoustic wave speed measurements. A small error in these leads to a large error in phase, e.g. an accuracy of 0.1% on an axial distance of 10cm leads to an uncertainty in the PTF measurement of ±97° at 4MHz. In this paper we present an acoustic pulse-echo method to measure the PTF of a transducer, which is based on linear wave propagation and only requires an estimate of the wave travel distance and the acoustic wave speed. 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 response (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes. Good agreement, to within 7°, was obtained between KLM simulations and measurements on two transducers in a 1-8MHz frequency range. The reproducibility of the method was ±10°, with a systematic error of 2° at 1MHz increasing to 16° at 8MHz. This work demonstrates that the PTF of a transducer can be measured in a simple laboratory setting.