Characterization of Laser Propagation Through Turbulent Media by Quantifiers Based on the Wavelet Transform

1 The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent motion, with different strength, are analyzed by the wavelet theory. Two quantifiers are calculated, the Hurst exponent, H, and the mean Normalized Total Wavelet Entropy, ˜ S WT. It is verified that both quantifiers give complementary information about the turbulence state. Wavelets-based tools have been shown to be well-suited to fractal processes and their analysis. This is mainly due to the fact that the wavelet transform incorporates in its definition two basic features, time and scale, which are of primary importance for fractal processes. Another remarks concerns the structure of the wavelet transform which, by construction, builds a signal by successive refinements, starting from a coarse approximation and adding finer and finer details at each step. Such a procedure is of course reminiscent of basic fractal constructions, thus suggesting we should make use of wavelets to synthesize a fractal process. Since the earlier leading work of Mandelbrot 4, 5 there is a lot of evidence that several facets of fully developed turbulent flows are fractals. Most of the applications of fractals to turbulence have been devoted to the study of subsets of the region occupied by turbulent flow where a given property is satisfied. For example, the turbulent/non-turbulent interface, some constant property surfaces (such as the iso-velocity and iso-concentration surfaces) and the structure of spatial distribution of dissipation 2 rates have been characterized as fractals or multifractals and the dimension has been measured. 6, 7, 8 Then, it is natural to apply wavelet tools for analyzing atmospheric turbulence. The fractional Brownian motion (fBm) was introduced by Mandelbrot and Van Ness 13 as an example of a process which contains an infinite domain of dependence with the intention of explaining the results reported by Hurst in 1951. 14 fBm as a model for turbulence is not new. 12, 11, 15 In particular, the fBm can be introduced as an alternative model for the turbulent index of refraction, and it can be shown that these processes allow to reconstruct most of the index properties. 15 This work reports on the basic characteristics of the centroid position of a laser spot after the light has traveled through turbulent media. It is analyzed as a …