An antenna array's actual response to a point source , not to be confused with a "CLEAN beam" or "
dirty beam." Let the beam have angular response pattern , where is the angle from the
peak response. Let the beam be at an angle to the zenith. The observed response to a collection of point
sources at angles to the zenith (in the plane of ) with specific brightnesses is then
where the finite receiver bandwidth, phase errors, and other errors have been ignored. Defining
gives
This can be solved explicitly using the convolution theorem, Eric Weisstein's World of Math
© 1996-2007 Eric W. Weisstein
