The Richards-Wolf approach to analyze tight focusing by high-numerical-aperture aplanatic optical systems was designed to treat incident waves having a planar (or negligibly curved) wavefront at the entrance pupil. In this paper we extend the approach to incorporate also wavefronts with piecewise quasi-constant phase. The evaluation of the field distribution in the vicinity of the geometrical focus is accomplished by linear superposition of the contributions from all the segments with quasi-constant phase. As an application example, a tightly focused optical field is evaluated for a π-phase-step-modulated incident wavefront.