Phased Array Diffraction Demonstration

This is a rudimentary approximation of phased array behavior based off of the Fraunhofer approximation taking the generated pattern as the Fourier transform of the input signal. What this represents is two simple facts about phased arrays which are easily understood in the Fraunhofer approximation; that is:
-a linearly (spatially) varying phase function results in a spatial shifting of the pattern; this is the primary reason we care about phased arrays as it allows us to steer radiation sheerly by manipulating the phase of our emitters.
-a quadratically varying phase has the effect of a concave mirror. This seems odd maybe at first glance but if one consider the approximation of the height profile of such a lens as corresponding directly to phase changes, then it should be obvious that having such a spatially varying phase achieves this effect