Abstract

The bandlimited Weierstrass function as a fractal function is used to model fluctuations of the atmospheric refractive index within the inertial subrange. It can be shown that the average Weierstrass spectrum approaches the Kolmogorov spectrum when the fractal dimension of the former becomes 5/3 in one dimension. By appropriately modifying this function, the intermittent characteristic of the atmospheric turbulence can be taken into account. The validity of this fractal model is tested by comparing the bandlimited Weierstrass spectrum and the Kolmogorov spectrum. The extensions of this model for three dimensions are briefly discussed.

© 1987 Optical Society of America