Atmospheric turbulence parameter analysis based on the slope dynamic and spatial behavior of the Shack–Hartmann wavefront sensor

The Shack–Hartmann Wavefront Sensor (SHWFS) remains the most prevalent and robust instrument for characterizing atmospheric turbulence in adaptive optics. Its capability to quantify key parameters—such as the Fried parameter, Greenwood frequency, and the refractive index structure constant—stems from its direct, geometric measurement of local wavefront slopes. To measure Fried coherent length​, which defines the coherence diameter of the atmosphere, one analyzes the spatial statistics of these slope measurements over time. The variance in the reconstructed wavefront phase is directly proportional to the ratio between the aperture diameter and Fried parameter. This allows one to assess whether a specific correction system will be effective under current seeing conditions. Simultaneously, by observing the temporal evolution of these shifts at high frame rates (often exceeding 1 kHz), the Greenwood frequency can be derived. In this work, we present the results of the estimation of the Fried coherence length as spatial characteristics and Greenwood frequence analysis as a dynamic parameter of atmospheric turbulence, based on the data from the Shack–Hartmann wavefront sensor obtained in moderate turbulence medium at a distance of 250 m with a 130 mm radius transmitting/receiving telescope. Turbulence parameters measured using a WFS without correcting the laser radiation wave function were examined. The data obtained from the SHWFS are the temporal displacements of the lens raster's focal points, so to find the spectrum of these oscillations, it is sufficient to take the Fourier transform of the obtained data. Since the data are presented as a discrete sample, and the number of samples is generally not a multiple of 2 to the power m, a discrete Fourier transform was used. It was shown that the spectrum of turbulence does not exceed 100 Hz and the Fried parameter is not less than 50 mm.