Spatial averaging in the beam of a piston transducer

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%).

Spatial averaging effects of hydrophone on field characterization of planar transducer using Fresnel approximation

The purpose of this work was to improve the existing models that allow spatial averaging effects of piezoelectric hydrophones to be accounted for. The model derived in the present study is valid for a planar source and was verified using transducers operating at 5 and 20MHz. It is based on Fresnel approximation and enables corrections for both on-axis and off-axis measurements. A single-integral approximate formula for the axial acoustic pressure was derived, and the validity of the Fresnel approximation in the near field of the planar transducer was examined. The numerical results obtained using 5 and 20MHz planar transmitters with an effective diameter of 12.7mm showed that the derived model could account for spatial averaging effects to within 0.2% with Beissner's exact integral (Beissner, 1981), for k(a+b)2≫π (where k is the circular wavenumber, and a and b are the effective radii of the transmitter and hydrophone, respectively). The field distributions along the acoustic axis and the beam directivity patterns are also included in the model. The spatial averaging effects of the hydrophone were generally observed to cause underestimation of the absolute pressure amplitudes of the acoustic beam, and overestimation of the cross-sectional size of the beam directivity pattern. However, the cross-sectional size of the directivity pattern was also found to be underestimated in the "far zone" (beyond Y0=a(2)/λ) of the transmitter. The results of this study indicate that the spatial averaging effect on the beam directivity pattern is negligible for π(γ(2)+4γ)s≪1 (where γ=b/a, and s is the normalized distance to the planar transducer).

An accurate analysis of the radiation characteristics of a plane piston transducer with phase apodization for focusing

A plane piston transducer can be focused by a continuous variation of the excitation signal phase (or time delay) over the transducer surface. Prior analyses of this scheme used the Fresnel approximation, thereby limiting the validity. Using the angular spectrum method, an accurate radiation model of such a transducer has been developed that includes amplitude and phase apodization. The derivation includes the effects of diffraction and evanescent waves without using the Fresnel approximation. Moreover, this model develops insights into radiated field characteristics, including: (a) the spatial frequency bandwidth is constant over axial depth, suggesting that spatial resolution can be improved away from the focus; (b) the phase of the angular spectrum determines the spatial resolution for a given transducer configuration-a constant phase is optimal on any observation plane; (c) focusing can significantly increase the spatial frequency bandwidth; (d) the velocity potential on a plane parallel to the transducer is the Hankel convolution of the transducer surface velocity with the Green's function; and (e) evanescent waves decay both with increasing spatial frequency and axial depth. The analytical model and associated insights enhance understanding of the radiated field characteristics, which can be of value in the development of signal processing techniques for image enhancement.