Far-field acoustic holography onto cylindrical surfaces using pressure measured on semicircles

Abstract

A simple formula was recently proposed by Williams [J. Acoust. Soc. Am. 99, 2022–2032 (1996)] for imaging pressure and velocity on a vibrating circular cylindrical shell using the far-field pressure measured along a meridional semicircle. The method is examined and some new results are obtained. The procedure is generalized to handle cylindrical surfaces of noncircular but convex cross section. It is demonstrated that Williams’ formula predicts a supersonic surface intensity which gives the same meridional energy flux as the exact radiated far-field pressure. A modification of Williams’ formula is suggested which uses pressure data from several neighboring semicircles, although complete spherical coverage is not required. The modified imaging formula is based upon the first two terms in an asymptotic expansion in the dimensionless wave number. The leading-order term yields the original formula, and the second term results in a boundary layer type of correction in the circumferential direction. Numerical examples are presented which compare the exact supersonic acoustic intensity on a cylinder with that from the original and the modified formula. These indicate that the circumferential on-surface resolution is significantly enhanced by combining data from neighboring semicircles, even when the total far-field spherical coverage is small.