Differential image motion at non-Kolmogorov distortions of the turbulent wave-front

A description of image motion characteristics is given for a general case of atmospheric turbulence. For this purpose the parameter p used in the expression F(q) similar to q(-3-p) for a 2-D power spectrum of a phase is considered as a variable term with a typical 1/3-2/3 range of fluctuations. Dependence on p of the variance Delta(2) of differential image motion was studied for stellar configurations with one, two, and a set of reference stars located in a circular area, for a circular entrance pupil and interferometers. It was shown that for non-Kolmogorov turbulence, Delta(2) is subject to significant variations even when Fried's parameter r(o) and mean square absolute image motion are fixed. The method allowing us to reduce atmospheric errors by transition to 1-D measurements of differential coordinates is considered. Orientation of coordinate axes in this case depends on the direction of wind and intensity of turbulence in atmospheric layers. Atmospheric limitations of large ground-based telescopes are discussed.