Acoustic reciprocity in the spherical harmonic domain: A formulation for directional sources and receivers

Acoustic reciprocity states that the transfer function between a source and a receiver remains unchanged if the two are interchanged. An extension of acoustic reciprocity to the spherical harmonic domain has been derived in the literature between a directional source and a directional receiver. The present letter derives a reciprocal relation between source and receiver directivity coefficients, which facilitates the derivation of a transfer function in the spherical harmonic domain using directivity coefficients obtained via reciprocity. Additionally, reciprocity between transfer functions is extended for more general source and receiver directivities, which include acoustic scattering effects.