Time-delay spectrometry measurement of magnitude and phase of hydrophone response

A method based on time-delay spectrometry (TDS) was developed for measuring both magnitude and phase response of a hydrophone. The method was tested on several types of hydrophones used in medical ultrasound exposimetry over the range from 5 to 18 MHz. These included polyvinylidene fluoride (PVDF) spot-poled membrane, needle, and capsule designs. One needle hydrophone was designed for high-intensity focused ultrasound (HIFU) applications. The average reproducibility (after repositioning the hydrophone) of the phase measurement was 2.4°. The minimum-phase model, which implies that the phase response is equal to the inverse Hilbert transform of the natural logarithm of the magnitude response, was tested with TDS hydrophone data. Direct TDS-based measurements of hydrophone phase responses agreed well with calculations based on the minimum-phase model, with rms differences of 1.76° (PVDF spot-poled membrane hydrophone), 3.10° (PVDF capsule hydrophone), 3.43° (PVDF needle hydrophone), and 3.36° (ceramic needle hydrophone) over the range from 5 to 18 MHz. Therefore, phase responses for several types of hydrophones may be inferred from measurements of their magnitude responses. Calculation of phase response based on magnitude response using the minimum-phase model is a relatively simple and practical alternative to direct measurement of phase.