## 3 Results  
The representation of the wavefront in terms of Zernike polynomials obtained using such a procedure was saved as a new sequence of frames. Thus, we have the sequence of wavefronts presented in terms of Zernike polynomials separated by intervals of 500 \(\upmu\)s.  
It is possible to obtain the spectrum for each Zernike polynomial by using the discrete Fourier transform [21]. Figure 2 represents the time dependence of the defocus aberration (Zernike polynomial #3). For a more detailed demonstration of the changes in magnitude, a sample fragment with a length of approximately 7 ms is shown. Figure 3 shows the defocus power spectral density. For this graph, a portion of the sample size of 4096 elements was used to increase the speed of calculations. That gave a resolution along the frequency axis of approximately 0.5 Hz. After taking the integral of the spectral power density, we obtained some analogs of energy for each aberration. The concept of the energy cannot be strictly defined in relation to the phase, however, the formulas we used to calculate this value are similar to the formulas for energy calculation. Nevertheless, since there is a direct relationship between turbulence and the distortion of the wavefront (the stronger the turbulence, the greater the distortion of the wavefront), this value, according to our opinion, can characterize the real energy of the turbulent airflow. For this reason, in the text of the article, we shall use this term in quotation marks--\"energy\". Figure 4 presents the results of integrating the power spectral density data obtained for the first eight Zernike polynomials. Figure 3: Power spectral density for Zernike coefficient #3 (defocus). Figure 2: Time sampling for Zernike coefficient #3 (defocus). The graphs in Figure 4, upon reaching some frequency, come to saturation, which indicates the absence of any significant contribution to the amplitude of the high-frequency components. The frequency at which saturation occurs can be taken as the bandwidth of different polynomials (Figure 5). Thus, one of the consequences of [PERSON]'s hypothesis [22], according to which low-order aberrations have a lower frequency compared to high-order aberrations, is confirmed. This can be explained by the fact that in our experiments, the fan heater was installed at a short distance from the laser beam. The warm air jet, among other things, was reflected from the cold optical table and from the screen that blocked the access of the airflow to other elements of the optical circuit. When mixing with the cold air of the laboratory, the heat flow formed turbulent vortices. In particular, the Fried parameter was determined, which turned out to be equal to 10 mm. Apparently, for these reasons, in our experiments, the airflow was more turbulent than laminar, and the [PERSON] hypothesis was generally followed. Figure 4: Spectral energy for first eight Zernike polynomials. Figure 5: Bandwidth of the first 24 Zernike polynomials. On the other hand, it is possible to build a graph that reflects the saturation amplitudes for each coefficient \(c_{i}\) (Figure 6). From the examination of this figure, it can be seen that defocus (Z3) and spherical aberrations (Z8, Z15, and Z24) have a smaller amplitude compared to the rest of the aberrations (coma, astigmatism). In general, from the experimental point, it is understandable as the flue of the heated air is perpendicular to the direction of the beam distribution and thus the asymmetry should be observed. This information should be useful in optimizing the spatial arrangement of the wavefront corrector control elements. If you take the integral of the values shown in Figure 6, then you can obtain a graph displaying the integral energy concentrated in the first N Zernike polynomials (Figure 7). Figure 6: Distribution of turbulence energy over Zernike polynomials. Figure 7: Normalized turbulence integral energy over first N Zernike polynomials.