Spatial channels for communicating with waves between volumes

I show that there is an exact, complete method for finding the orthogonal spatial channels, or communications modes, between two arbitrary volumes, and the associated connection strengths, for the case of scalar waves. I also show that the sum of the squared connection strengths is given exactly by a simple volume integral. The method is illustrated by a calculation for a particular extreme pair of volumes, and the communications modes are interpreted physically as the modes of a double phase-conjugate resonator.