Fraunhofer diffraction patterns from uniformly illuminated square output apertures with noncentered square obscurations

Theoretical Fraunhofer diffraction patterns are presented for uniformly illuminated square apertures with noncentered square obscurations. The energy within a given subtended solid angle in the far field is calculated. It is shown that the cornered-off-axis obscuration provides much more far-field energy in a given spot size than the centered obscuration for the same clear aperture area and total energy, for example, 82% more far-field energy in the first Airy square for 50% obscuration, thus providing superior performance for practical systems.