PAR-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 vibrati ng circular cylindrical shell using the far-field pressure measured al ong a meridional semicircle. The method is examined and some new resul ts are obtained. The procedure is generalized to handle cylindrical su rfaces of noncircular but convex cross section. It is demonstrated tha t Williams' formula predicts a supersonic surface intensity which give s the same meridional energy flux as the exact radiated far-field pres sure. A modification of Williams' formula is suggested which uses pres sure data from several neighboring semicircles, although complete sphe rical coverage is not required. The modified imaging formula is based upon the first two terms in an asymptotic expansion in the dimensionle ss wave number. The leading-order term yields the original formula, an d the second term results in a boundary layer type of correction in th e circumferential direction. Numerical examples are presented which co mpare the exact supersonic acoustic intensity on a cylinder with that from the original and the modified formula. These indicate that the ci rcumferential on-surface resolution is significantly enhanced by combi ning data from neighboring semicircles, even when the total far-field spherical coverage is small. (C) 1997 Acoustical Society of America. [ S0001-4966(97)05110-2] PACS numbers: 43.30.Jx, 43.20.Rz, 43.40.Rj, 43. 35.Sx [SAC-B].