This is a beamforming problem, but since the people who do this work are typically EEs, I thought I'd give this ng a try. I am a mathematician working on some interferometric problems, and I find myself having trouble getting an actual definition of "direction of arrival" (or DOA).
Some older analyses using linear antenna arrays seem to use the inclination angle, theta, (i.e. the angle with the +z-axis or "azimuthal angle") for the DOA, but for a source that is not coplanar with the array, there is a factor of Cos(phi) in the phase portion of the steering vector (where phi is the angle with the +x-axis or polar angle).
Some analyses seem to define a generic phase angle from the inner product of the source orientation with the array position vector. This definition is consistent for a linear array, but it is not for a planar array.
Is there a rigorous definition of what is meant for "direction of arrival" (or angle of arrival) that holds for a general array and source? You can respond directly to this post or via my e-mail address.