An analysis of Fresnel zone and diffraction fields near the boresight of practical acoustic radar antennas

Abstract

Based upon a generalized theory of an analytic model of a practical acoustic radar (echosonde) antenna [S. A. Adekola, J. Acoust. Soc. Am. 60, 230–239 (1976)] whose potential has been exploited to measure atmospheric turbulent velocity fields and temperature fluctuations, we present an analysis of the Fresnel zone and diffraction fields near the boresight of a typical antenna. Invoking the Fresnel zone approximation and employing a tapered parabolic source excitation, the Fresnel zone field at the antenna boresight is evaluated in closed forms in terms of a highly convergent Lommel series function of the form Ω0m (ν,n) that is expedient for practical computations. A generalized diffraction integral equation at the boresight region, which can be used for both circularly symmetric and asymmetric echosonde apertures, is formulated whereby the existing integral, previously derived in the reference above, is split into a sum of zeroth‐order Hankel and Lommel transforms that describe the field in the two principal planes of the aperture. The results clearly demonstrate that circular symmetry still leads to zeroth‐order Hankel transform, while antisymmetry produces an additional Lommel transform. Analytical examples presented include closed form pattern evaluations for some commonly used source excitations, in terms of tabulated Anger–Weber and Struve functions, while illustrative numerical pattern characteristics discussed comprise beam patterns arising from Hamming—cos2 on a pedestal—and doublet‐source distributions. A realization of the echosonde antenna described by the integral equations is discussed. Raw, experimentally measured, beam patterns in the acoustic frequency band 1750–3000 Hz are redrafted, statistically averaged, and presented, using standard error bars. We also discuss a facsimile recording that describes the measurements of turbulence components in the lower marine boundary layer, using an echosonde antenna. An attempt is made towards a rigorous treatment of the echosonde synthesis, based on the synthesis integral equations deduced from the results of the diffraction fields.