## 3 Hybrid Model Verification: Experimental Results and Discussion  
In order to verify the developed hybrid model of the estimation of distortions of a laser beam that passed through a scattering layer, we assembled the experimental setup. The photo of the laboratory setup is presented in Figure 7.  
Laser radiation comes from the fiber-coupled diode laser and propagates through the collimator. The collimated laser beam of 4 mm in diameter then passes through the transparent glass cuvette with the thickness of 5 mm and dimensions of 18 \(\times\) 18 mm, filled with the scattering suspension of 1 \(\upmu\)m-diameter polystyrene microbeads produced by Magsphere, Inc. (Pasadena, CA, USA) [76] with the refractive index equaled to 1.582 [52] diluted in distilled water (refractive index is 1.33). The beam resulting from the cuvette  
Figure 6: Symmetrical Zernike coefficient dependence on the concentration value of scattering medium. Figure 7: Photo of the experimental setup with a diode laser and a Shack–Hartmann sensor. is registered on the Shack-Hartmann sensor [77]. According to the specification sheet on the polystyrene microbeads, the diameter variation was within 10%. The microbeads have a smooth surface [78] so that no complicated shape-scattering diagram from a single microbead is produced. Shack-Hartmann sensor consisted of a digital CCD camera Basler A302 fs (1/2-inch sensor with the size of the receiving area equaled to 6.4 \(\times\) 4.8 mm, camera frame rate is 30 Hz) and a lenslet array (focal length--6 mm, diameter of a lenslet--150 \(\upmu\)m, total number of lenslets--greater than 1300). The distance between the Shack-Hartmann sensor and the cuvette was set to 450 mm in order to decrease the impact of the totally diffused photons on the quality of the measurements. Since we made the experiments in a very short period after the preparation of the suspension of scattering particles, the concentration during the experimental measurements was not varied; or, at least, its variation has no impact on the measurements. Moreover, for all of our measurements, we averaged hartmannograms in order to increase the accuracy. For each experiment, we prepared the new suspension. If the cuvette with the initial high-concentration solution was not used for a long period of time, we used the ultrasonic bath to split the coagulated microbeads. We analyze the average wavefront of scattered light in the circular aperture of 4.8 mm. The aperture's center and the cameras' center coincide. The initial laser beam diameter was 4 mm, whereas the aperture diameter was 4.8 mm. It was necessary to analyze how the non-ballistic photons impact on the distortions of scattered light. The average wavefront measured by the Shack-Hartmann sensor was approximated by Zernike polynomials, as it was done in the simulation. Figure 8 shows the comparison of the dependence of distortion amplitude (amplitude of distortions of the averaged wavefront) on the concentration values of scatterers. Both the model and experimental curves demonstrated similar trends of increasing the amplitude of distortions while increasing the concentration values of the scatterers. Figure 8 shows a similar trend of increasing distortions of the average wavefront of the scattered laser beam with increasing concentrations of scatterers in the medium in the range from \(10^{5}\) to \(10^{6}\) mm\({}^{-3}\), both for the model and laboratory experiment. There are a few reasons why the model curve differs from the experimental one. The explanation is schematically represented on Figure 9.  
Figure 8: Trend lines of the dependence of the amplitude of distortions on the concentration values for the simulation (red curve) and for the experiment (purple curve). Image adapted from [37]. First, in the model (Figure 9a), we did not reproduce the initial distribution of the intensity of the real laser source used in the experiment (Figure 9b). In fact, a generator of uniformly distributed random numbers is used to generate the initial distribution of photons in the model.