On-axis light distribution in converging spherical fields: general case

A general expression for the problem of on-axis light distribution in converging spherical waves, diffracted at a circular aperture, is obtained. The solution is valid for small as well as for high Fresnel numbers (N) and also includes a tilt in the aperture. The influence of the tilt on the focal shift related to small values of N, and the symmetry of the field with respect to the geometrical focal plane, are analyzed.