Predicting hydrophone phase and evaluating its uncertainty using magnitude data and minimum phase approach

Hydrophones are commonly used to measure the acoustic output of ultrasound transducers and devices. Commonly, only the magnitude response of a hydrophone is quantified, since the direct measurement of phase response requires a complicated calibration procedure, and phase is extremely sensitive to small variations in experimental conditions such as alignment of hydrophone in the ultrasound field, signal-to-noise ratio, and temperature of water. However, for linear, time-invariant systems, phase can be predicted from the magnitude spectrum using the minimum phase approach. Here, a procedure was established to estimate the phase and evaluate the phase uncertainty of a hydrophone. The phase response was calculated using the minimum phase approach and the preconditioned magnitude spectrum. By using the uncertainty in the magnitude spectrum and the propagation of uncertainty, the uncertainty in the subsequently derived phase was calculated. A machine learning model was used to determine the phase uncertainty arising from applying the minimum phase approach to band-limited magnitude spectrum. After the performances of the calculation methods for phase and phase uncertainty were evaluated, the proposed procedure was implemented and assessed using a hydrophone model and two hydrophones with characterised magnitude and phase responses with their associated uncertainties. The predicted phase responses and evaluated uncertainties were comparable to the reference values. The results indicated that the procedure presented in this study could be used in practice to predict the phases and evaluate the phase uncertainties of various hydrophones.