Abstract
Two-dimensional fractional Brownian motion (FBM) is a good model for stellar wave fronts distorted by Kolmogorov turbulence. However, the time series generated by the movement of such a wave front past an observation point does not explain the reported predictability of measured wave-front slopes. Rescaled-range analysis, a technique for detecting dependence among samples in a series, and a correlation-dimension algorithm that tests for the presence of deterministic chaos were applied to series of real, measured, stellar wavefront slopes. These tests suggest that the source of correlation and predictability is the low-pass spatial filtering of the FBM wave front by the lenslets of an adaptive-optics wave-front sensor and that the process is not chaotic. A simple modeling procedure is described for generating time series of measured wave-front slopes with the correct temporal characteristics.
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