Comparison of focusing properties of Gaussian beams passing through two kinds of spherically aberrated lenses

The focusing properties of Gaussian beams passing through two types of spherically aberrated lenses are studied and compared.It is show that the focusing properties depend on the type of the spherically aberrated lenses,the spherical aberration coefficient and Fresnel number.There are different conditions for different spherically aberrated lenses to achieve the focus without focal shift or beyond the geometrical focal point of the lens.