Acoustic holography for piston sound radiation with non-uniform velocity profiles

The theory of orthogonal (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical results for the radiation of sound due to a non-uniformly moving, baffled, circular piston. For this particular case, a scheme for retrieval of the radially symmetric part of the velocity profile from on-axis, nearfield measurements on the level of expansion coefficients of the profile has been developed and demonstrated previously with simulation results and with results obtained from measured pressure data of a loudspeaker. In this contribution, (semi-) analytic expressions for transient responses, valid on the whole half-space in front of the baffle, including the axis, are presented. It thus appears that the radially symmetric part of the velocity profile on the disk is reproduced in warped form at any on-axis point as an impulse response. This offers an alternative method in present holography to estimate the velocity profile from on-axis pressure data.