The Gaussian optical parameters and the most important aberration coefficients-spherical aberration coefficient and chromatic aberration coefficient are calculated.

Based on Gauss optics, the theory of afocal zoom expander is analyzed, a afocal zoom expander is designed and successfully applied.

In the paper, it is attempted to choose suitable slices of phase for beam shaping by use of binary optics, for example, the uniformization of Gaussian beam is calculated numerically.