Plane-wave Fresnel diffraction by elliptic apertures: a Fourier-based approach

A simple theoretical approach to evaluate the scalar wavefield, produced, within paraxial approximation, by the diffraction of monochromatic plane waves impinging on elliptic apertures or obstacles is presented. We find that the diffracted field can be mathematically described in terms of a Fourier series with respect to an angular variable suitably related to the elliptic parametrization of the observation plane. The convergence features of such Fourier series are analyzed, and a priori truncation criterion is also proposed. Two-dimensional maps of the optical intensity diffraction patterns are then numerically generated and compared, at a visual level, with several experimental pictures produced in the past. The last part of this work is devoted to carrying out an analytical investigation of the diffracted field along the ellipse axis. A uniform approximation is derived on applying a method originally developed by Schwarzschild, and an asymptotic estimate, valid in the limit of small eccentricities, is also obtained via the Maggi-Rubinowicz boundary wave theory. (C) 2014 Optical Society of America