  Knowledge of the diffuse-field coherence between array sensors is a basic
assumption for a wide range of array processing applications. Explicit
relations previously existed only for omnidirectional and first-order
directional sensors, or a restricted arrangement of differential patterns. We
present a closed-form formulation of the theoretical coherence function between
arbitrary directionally band-limited sensors for the general cases that a) the
responses of the individual sensors are known or estimated, and the coherence
needs to be known for an arbitrary arrangement, and b) that no information on
the sensor directionality or on array geometry exists, but calibration
measurements around the array are available.
