Simple method for measuring phase transfer functions of transducers

The impulse response of a transducer can be represented in the frequencydomain by its complex analog, the transfer function. The amplitude transferfunction is measured regularly in contrast to the phase transfer function (PTF).Applications for the PTF range from adjusting the emitted pulse shape forcoding based imaging to the optimization of ultrasound contrast imaging methodsbased on destructive interference. A number of acoustic methods to measure atransducer's PTF exists, but they usually require accurate distance and acousticwave speed measurements. Small discrepancies in these cause large phase errors.We present a pulse-echo method to measure a transducer's PTF without needing ameasurement of the wave travel distance and speed. We generalize it torectangular transducers. In our method the transducer is excited by amonofrequency sine burst with a rectangular envelope. The transducer initiallyvibrates at resonance (transient regime) prior to the forcing frequency (steadystate regime). The PTF value of the system is the difference between the phasesdeduced from the transient and the steady state regimes at different forcingfrequencies. As the PTF is calculated from a relative difference measuring thewave travel distance or speed is unnecessary. The approach assumes linear wavepropagation and uses a pulse-echo setup. The method was tested on a custom builtsingle element transducer (square: 13 13 mm, center frequency 4 MHz, no backingor matching layers). The results were compared with KLM model simulations.Also, we phase calibrated a hydrophone, which was then used to measure the PTFof the square transducer. The simulated and measured resonance frequenciesdiffered by 0.17 MHz. The mean PTF difference between simulation andmeasurements was 7-14. The method's reproducibility was 15. The PTF of thetransducer was measured with good reproducibility, without measuring the wavetravel distance or speed of sound in the medium. Our simple setup requires basiclaboratory ultrasound equipment.

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