Heterodyne and Time-gated Time-delay Spectrometry for Amplitude and Phase Calibration of Hydrophones

The determination of amplitude and phase of the hydrophone sensitivity using two techniques based on time-delay spectrometry is presented. The frequency range in which the technique can be applied is from 1 MHz to 50 MHz. The agreement with the results obtained by alternative calibration techniques is excellent, which emphasises the correct working of this coherent technique. Introduction Calibrated hydrophones form the basis of the precise and reliable measurement of medical and technical ultrasonic fields. To date, primary and secondary calibration methods provide the amplitude of the hydrophone frequency response. The result of an ultrasound measurement is always determined by the transfer characteristic of the detection line with the hydrophone as the most important unit. In the case of a broad-band measurement, for example of highfrequency or nonlinear distorted waveforms, a nonideal hydrophone characteristic may seriously influence the measurement. Correct results can be obtained by deconvolution of the measured waveforms using the complex transfer function of the detection line. This procedure requires determining the phase response of the hydrophone. Recently a calibration method based on timedelay spectrometry (TDS) has been presented that provides both, amplitude and phase response of hydrophones [1]. In the present paper additional measurement examples are given so that a comparison with other calibration techniques can be made. To validate the phase measurement capabilities, a calibration method using short pulses from a focussing transducer was applied [2] and good agreement was found in a wide frequency range. Since TDS is a secondary calibration technique, a standard hydrophone having undergone a primary calibration is necessary for absolute values to be obtained. Unlike for the amplitude, a standard for the phase is not available to date and in the present work an optical multilayer hydrophone [3] was used for this purpose. It has an extremely flat amplitude frequency response [4], and keeping in mind the KramersKronig relations, it can be assumed that the phase is just as constant over a wide frequency range as the amplitude. With the aid of this standard, ‘absolute’ phase responses could be obtained and they were compared to the results of a theoretical model. Calibration techniques and set-up Time-delay spectrometry exploits the finite propagation time of ultrasound in a medium to ensure freefield conditions during calibration [5-8]. The pressure wave emitted by the transducer takes some time to reach the hydrophone and the instantaneous frequency of the received signal is shifted by