Aspheric coefficients of deformation for a Cartesian oval surface

In this paper we propose a mathematical model as a theoretical and practical contribution to the theory of aspheric surfaces, that allows the geometrical calculation of an aspherical refractive surface in cylindrical coordinates (r, z), that correspond to a non-degenerated Cartesian oval of revolution, according to standard formulae [ISO-10110-12 (2007)], including: vertex curvature C, conical constant K and aspheric deformation coefficients A(4), A(6), A(8), A(10) and A(14). The results are shown for an object and its respective image located at finite distances from the vertex (origin of coordinates) on the optical axis.