We describe new solutions permitting us to overcome the well-known problems encountered when employing the two main classical methods for numerical modeling of atmospherically perturbed phase screens. The first method, the fast-Fourier-transform-based numerical method, suffers from a lack of low frequencies. Subharmonics adding is an already-known solution to this problem, but no criterion has been defined up to now in order to precisely determine how many subharmonics are necessary for each given case of physical and numerical characteristics. We define two criteria and show their practical efficiency. The second, Zernike-based, method suffers, a contrario, from bad behavior of the phase screens at high spatial frequencies. To overcome this problem, due to numerical instability, we developed an algorithm based on an alternative definition of the Zernike polynomials, involving the recurrence definition of the Jacobi polynomials, as well as the relationship between the Zernike and the Jacobi polynomials. The methods described and used in this paper have been implemented within the freely distributed software package CAOS.
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