Analysis of symmetry properties in focal area at presence in a focusing element with periodic angular dependence

The analysis of symmetry properties of distribution in focal area is carried out at focusing of light with periodic phase angular dependence of a kind sin (m "fi") or cos (m "fi"). On the basis of such phase dependence it is possible to describe the majority of wave aberrations. It is analytically shown that at odd values m focal distribution will be the real function that provides a simple way of generation of the set wave aberrations by means of binary diffractive optical elements. Such possibility can be useful at sharp focusing when presence of certain wave aberrations allows to reduce the sizes of a focal spot. Numerical modeling confirms analytical calculations and shows that change of radial parameters allows to change a configuration of focal distribution but symmetry in the central part basically is defined by parity m: for even m is observed symmetry of 2m order, and for odd - the symmetry is m order.