Geometrical analysis of third-order aberrations for a solid immersion lens

This paper gives a treatment for finding 3rd order aberrations in solid-immersion lenses (SIL) using spherical-aberration as the basis for a polynomial power expansion of the wavefront. Unlike previous work, the treatment is general for any incident and lens media, for any lens thickness, and any chief-ray specification. Using this treatment, a tolerance analysis is given with particular discussion on thickness tolerance and limitations on field of view. Major findings include very tight thickness tolerance for high-index hyperhemisphere SILs and a thickness tolerance window for hemispheres skewed to values less than the radius of curvature of the lens.