Abstract
The Fourier transform relationship between an aperture distribution and its radiation pattern is exact, but its application involves an approximation at once for the field is never known over the entire aperture plane. Usually it is known approximately only within the aperture and is assumed to vanish in the rest of the aperture plane. Suppose a field exists in an aperture S in the plane z = 0 and is negligible outside S. The tangential electric field in S is resolved into appropriate components, usually Cartesian if the aperture shape is rectangular.
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