The normalized transfer function of an elliptical annular aperture for incoherent illumination is derived. The relationship between the formulation developed here and a problem occurring in the diffraction from apertures illuminated with partially coherent radiation is shown. Results are discussed in terms of spatial-filtering concepts, with emphasis on the behavior of the cutoff frequency and the passband characteristics in the spatial-frequency plane.
The effect of the aperture ellipticity for arbitrary annulus width is to introduce an asymmetry in the behavior of the cutoff frequency. The presence of a central obstruction, for arbitrary ellipticity, emphasizes the high-frequency transmission, with the region of emphasis dependent upon the angular orientation in the frequency plane.
J. V. CORNACCHIO, "Transfer Function of an Elliptical Annular Aperture," J. Opt. Soc. Am. 57, 1325-1327 (1967)