Directional reverberation time and the image source method for rectangular parallelepipedal rooms

The image source (IS) method is a commonly used geometrical acoustics simulation technique in room and virtual acoustics. In particular, it has been used in the analysis of room reverberation under different choices of geometry and wall conditions. Under a simple rectangular parallelepipedal geometry, reverberation time is known to be dependent on the direction of arrival of reflections relative to the room axes. In this article, a closed-form expression for the directional energy decay and reverberation time is derived, which is valid in the late response, and may be used in the case of either angle-independent or angle-dependent reflection. The expression reduces to an easily evaluated formula in the case of an omnidirectional energy decay curve (EDC). Various numerical results are presented, including the validation of the closed-form expression against EDCs and late reverberation times drawn directly from the IS method.