Abstract

We propose that fluctuations of the atmospheric refractive index be modeled by an appropriate band-limited Weierstrass function that has fractal characteristics. In one dimension, the average Weierstrass spectrum approaches the Kolmogorov spectrum when the fractal dimension of the former becomes 5/3. The intermittent characteristic of the atmospheric refractivity fluctuations is also taken into account by modifying this Weierstrass function. Three-dimensional extensions of this model with a fractal dimension of 11/3 are described briefly. This model is particularly attractive for the problem of wave propagation in the atmosphere because it expresses the atmospheric fluctuation in terms of an almost-periodic function or a generalized Fourier series.

© 1988 Optical Society of America

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