Use of a 4-aperture DIMM instrument for atmospheric coherence time estimation: an analytical development

We report on an analytic method to estimate the Fried parameter r₀, average wind speed v¯, and subsequently the atmospheric coherence time τ₀ via a 4-aperture differential image motion monitor (DIMM) instrument. The theory developed here shows that the velocity of defocus aberration is statistically related to atmospheric turbulence parameters which are measured by means of angle of arrival (AA) fluctuations. Then, using the variance of the defocus velocity of four spots and the derived analytic relation, the atmospheric coherence time can be estimated. In parallel to the analytic work, some sequences of a star image with 700 Hz acquisition frequency are considered to simulate the atmospheric defocus and its variations by the 4-aperture DIMM instrument for the first 10 km near the ground in both one- and three-layer atmospheric models. The estimations from the analytic method are found to be in good agreement with the simulation data obtained for starlight propagating through different atmospheric conditions.