The traditional method for calculating acoustic pressure amplitude is to divide a hydrophone output voltage measurement by the hydrophone sensitivity at the acoustic working frequency, but this approach neglects frequency dependence of hydrophone sensitivity. Another method is to perform a complex deconvolution between the hydrophone output waveform and the hydrophone impulse response (the inverse Fourier transform of the sensitivity). In this paper, the effects of deconvolution on measurements of peak compressional pressure (p+), peak rarefactional pressure (p_), and pulse intensity integral (PII) are studied. Time-delay spectrometry (TDS) was used to measure complex sensitivities from 1 to 40 MHz for 8 hydrophones used in medical ultrasound exposimetry. These included polyvinylidene fluoride (PVDF) spot-poled membrane, needle, capsule, and fiber-optic designs. Subsequently, the 8 hydrophones were used to measure a 4-cycle, 3 MHz pressure waveform mimicking a pulsed Doppler waveform. Acoustic parameters were measured for the 8 hydrophones using the traditional approach and deconvolution. Average measurements (across all 8 hydrophones) of acoustic parameters from deconvolved waveforms were 4.8 MPa (p+), 2.4 MPa (p_), and 0.21 mJ/cm(2) (PII). Compared with the traditional method, deconvolution reduced the coefficient of variation (ratio of standard deviation to mean across all 8 hydrophones) from 29% to 8% (p+), 39% to 13% (p_), and 58% to 10% (PII).

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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 minimumphase model is a relatively simple and practical alternative to direct measurement of phase.

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