Determination of ultrasound hydrophone phase from Fourier-Hilbert transformed 1 to 40 MHz time delay spectrometry amplitude

A Fourier-Hilbert transform (FHT) algorithm procedure was developed to obtain the complex characteristics of different hydrophones which included the most widely used membrane and capsule types. The theory presented was experimentally verified using magnitude response of the hydrophone probes determined with the time-delay-spectrometry (TDS) technique. The TDS setup implemented was similar to one used by Wear et al. in 2011, with the frequency range being extended to 1 to 40 MHz to ensure consistency with recently published international standards covering the properties, calibration, and performance evaluation of ultrasound hydrophones. The theoretical and experimental limitations of FHT were examined and revealed that extrapolations of the available logarithmic (volts per pascal magnitude) frequency response were needed to carry out acceptable FHT calculations of the phase response. The complex-valued analytic signal Hilbert transform (HT) algorithm was less practical in developing an efficient minimum phase calculation protocol than the equivalent real-valued discrete convolution HT algorithm. Examples of measured transfer function and FHT calculated phase response spectra of representative membrane and capsule ultrasound hydrophones are presented and are shown to obey the simple rule for minimum phase presented by Heyser in 1969.