The theory of recording and reproduction of three-dimensional sound fields based on spherical harmonics is reviewed and extended. Free-field, sphere, and general recording arrays are reviewed, and the mode-matching and simple source approaches to sound reproduction in anechoic environments are discussed. Both methods avoid the need for both monopole and dipole loudspeakers—as required by the Kirchhoff–Helmholtz integral. An error analysis is presented and simulation examples are given. It is also shown that the theory can be extended to sound reproduction in reverberant environments.
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