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

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 discussed and some new results are presented. The procedure is generalized to handle cylindrical surfaces of a 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. Numer...