For example, when reducing element spacing d by a factor of 2, it is necessary to double the resulting values of the geometry phase {tilde over (??)}i in order for the initial geometry phase to remain invariant to such change as suggested by the following equation for the real component of the signal received at an arbitrary array element: Re{S}=A 1 cos({tilde over (??)}1)+A 2 cos({tilde over (??)