*Article* **Development of Singular Points in a Beam Passed Phase Screen Simulating Atmospheric Turbulence and Precision of Such a Screen Approximation by Zernike Polynomials**

**Feodor Kanev 1,\*, Nailya Makenova 1,2 and Igor Veretekhin <sup>1</sup>**


**Abstract:** This article addresses two issues. Firstly, it was shown that if the initial phase of a Gaussian beam is specified by the sum of Zernike polynomials or by a screen simulating atmospheric turbulence, in the process of propagation, singular points appear in the wavefront of such a beam. With the use of numerical simulation, the dependence of the vortices number on the distortion characteristics and on the distance traveled by the beam was determined. The second problem analyzed in the article is the problem of a phase screen approximation by a series formed by Zernike polynomials. The carried out numerical experiments made it possible to determine the dependence of approximation accuracy on the screen parameters and on the number of polynomials entering the basis of approximation.

**Keywords:** adaptive optics; atmospheric turbulence; optical vortices; Zernike polynomials
