Abstract

The fractal concept is useful in describing structures displaying dilation symmetry. Such structures are said to be self-similar. Physical structures, whether naturally occurring or man-made, are at best self-similar over a regime of interest between an appropriate inner and outer scale. Here we model such structures by a bandlimited Weierstrass function which incorporates these scales and possesses an identifiable fractional dimension denoted the fractal dimension. We call such structures bandlimited fractals. Of interest here is the scattering and inverse scattering of waves from 1-D bandlimited fractal slabs. We demonstrate exact and approximate methods for calculating the reflection from such slabs and relate the scattering data to the fractal dimension of the slab. In certain conditions, the solution of this forward problem provides a means for attacking the inverse problem. In the case of the latter, the fractal dimension is desired based on scattering data. Here we find criteria for the approximate solution of this inverse problem and demonstrate the method on bandlimited fractal slabs of varying dimension. This method is useful in the remote probing of turbulent media or in the scattering of optical waves from imperfect optical structures.

© 1987 Optical Society of America