Abstract

We investigate far-field diffraction from fractally serrated circular apertures. This investigation has potential use in pattern recognition, remote sensing, and radiation pattern synthesis. Fraunhofer diffraction patterns from these serrated circular apertures are exactly calculated. Then the bandlimited Weierstrass function, which possesses fractal characteristics within limited ranges, is used to model the rough boundaries along a circular aperture. Subsequently, the Fraunhofer diffraction pattern from this fractally serrated aperture is evaluated, and the effects on the diffraction pattern due to each scale size of the bandlimited Weierstrass function are examined. The diffraction effects due to each scale size are explained using the conservation of momentum. We also relate fractal descriptors such as the fundamental spatial frequency and fractal dimension to the diffraction patterns. In particular, the fundamental spatial frequency determines the angular distribution of the diffraction pattern. On the other hand, the radial distribution of the diffraction pattern is characterized by fractal dimension. Results of computer simulations and optical demonstrations are presented.

© 1988 Optical Society of America