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The optical behaviour of the human eye is often characterized with the Zernike coeficients. Great number of measurements and statistical data are available for individuals and for various groups of people concerning the Zernike coeficients of their eyes. Although, these coeficients were obtained from measurements at discrete points and via computations using some discretization of the continuous Zernike functions, the developers of these algorithms could not rely on the discrete orthogonality Zernike functions, simply because no mesh of points ensuring discrete orthogonality was known. Only recently was such a mesh of points found and reported. In the present paper, this mesh is used to calculate Zernike coeficients for some artificial cornea-like surfaces. Tests were carried out and are reported herein on the precision of the discrete orthogonality obtained via the mentioned discretization and on the precision of the surface reconstruction. [ABSTRACT FROM AUTHOR]