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 (SILs) 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 for any chief-ray specification. Using this treatment, a tolerance analysis is given with emphasis on thickness tolerance and limitations on field of view. Major findings include tight thickness tolerance for high-index hyperhemispheres and a tolerance window for hemispheres centered about a thickness less than the radius of curvature of the lens.