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 20 MHz. 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 20 MHz planar transmitters with an effective diameter of 12.7 mm 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 = a2/λ) of the transmitter. The results of this study indicate that the spatial averaging effect on the beam directivity pattern is negligible for π(γ2+4γ)s≪1 (where γ = b/a, and s is the normalized distance to the planar transducer).