Seeing within the fractional Brownian motion model for the turbulent wave-front phase

We have previously modeled the turbulent wave-front phase by using a fractional Brownian motion Q. Opt. Soc. Am. A, Vol. 21, N degrees 10, pp. 1962-1969, October 2004). Non-Kolmogorov turbulence is primarily considered within this approach. Now, in this work we study the relationship between seeing, usual measure of quality associated to a ground-based telescope, and Hurst exponent, characteristic parameter of a fractional Brownian motion. The theory behind the differential image motion monitor (DIMM), a standard and widely used instrument for seeing measurements, is reviewed by us. It is shown that there is a direct connection between both parameters. Thus, it is concluded that Hurst exponent is a quantifier of the atmospheric turbulent state.