The Practicalities of Obtaining and Using Hydrophone Calibration Data to Derive Pressure Waveforms

This paper considers the means by which calibration data are used to convert hydrophone output voltage into pressure. Hydrophone frequency responses are complex-valued quantities, and only by correcting for the magnitude and phase variations, is it possible to accurately recover the original pressure waveform. The limitations of current hydrophone calibration techniques are discussed, and a new method of obtaining hydrophone phase data is presented. Magnitude and phase information is measured via both coarse increment (1 MHz) and fine increment (50 kHz) calibration techniques for three exemplar hydrophones (0.5 mm needle, 0.2 mm needle, and 0.4 mm membrane). Frequently hydrophone calibration data are available at frequency increments that do not match that required by the deconvolution process. Therefore, a variety of methods to interpolate the calibrated system response to obtain correctly spaced data are considered, and two spline interpolation methods are found to offer best performance. Data preconditioning and filtering to address artifacts above and below the 1 to 40 MHz bandwidth of the coarse frequency increment calibration are also investigated, and a simple procedure for selecting an appropriate low-pass filter is presented. The revised calibration data are used to deconvolve the hydrophone frequency response for experimentally derived waveforms. Standard ultrasonic output parameters (such as peak compressional and peak rarefactional pressures, pulse intensity integral, and temporal peak and pulse average acoustic intensities) are calculated from these waveforms. Although the three hydrophones used in this paper are of different types and have a range of active element sizes, all output parameters derived from the deconvolved waveforms have <5% variation from their respective population means (with the majority being within <2%).