Design of three-dimensional superresolution filters and limits of axial optical superresolution

Theories to design a three-dimensional superresolution filter (TDSF) for confocal microscopy are proposed that can obtain a globally optimal solution through linear programming. The designed TDSF is proved to be a phase-only element introducing a phase delay of 0 or pi. Five design examples of the TDSF are presented to demonstrate the validity of these theories. Regardless of transverse superresolution, a curve of S-eu(G(a)(+/-)) defined as the maximum value of Strehl ratio S under the axial resolving power of G(a)(+/-) is calculated to set the fundamental limits of axial optical superresolution. Finally, what is to our knowledge a novel analytic expression of S-eu(G(a)(+/-)) is deduced. (C) 2003 Optical Society of America.