Expansions for infinite or finite plane circular time-reversal mirrors and acoustic curtains for wave-field-synthesis.

An acoustic curtain is an array of microphones used for recording sound which is subsequently reproduced through an array of loudspeakers in which each loudspeaker reproduces the signal from its corresponding microphone. Here the sound originates from a point source on the axis of symmetry of the circular array. The Kirchhoff-Helmholtz integral for a plane circular curtain is solved analytically as fast-converging expansions, assuming an ideal continuous array, to speed up computations and provide insight. By reversing the time sequence of the recording (or reversing the direction of propagation of the incident wave so that the point source becomes an "ideal" point sink), the curtain becomes a time reversal mirror and the analytical solution for this is given simultaneously. In the case of an infinite planar array, it is demonstrated that either a monopole or dipole curtain will reproduce the diverging sound field of the point source on the far side. However, although the real part of the sound field of the infinite time-reversal mirror is reproduced, the imaginary part is an approximation due to the missing singularity. It is shown that the approximation may be improved by using the appropriate combination of monopole and dipole sources in the mirror.