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 π. Five design examples of the TDSF are presented to demonstrate the validity of these theories. Regardless of transverse superresolution, a curve of <i>S</i><sup><i>eu</i></sup>(<i>G</i><sub><i>a</i></sub><sup>±</sup>) defined as the maximum value of Strehl ratio <i>S</i> under the axial resolving power of <i>G</i><sub><i>a</i></sub><sup>±</sup> is calculated to set the fundamental limits of axial optical superresolution. Finally, what is to our knowledge a novel analytic expression of <i>S</i><sup><i>eu</i></sup>(<i>G</i><sub><i>a</i></sub><sup>±</sup>) is deduced.
© 2003 Optical Society of America
Haitao Liu, Yingbai Yan, Deer Yi, and Guofan Jin, "Design of Three-Dimensional Superresolution Filters and Limits of Axial Optical Superresolution," Appl. Opt. 42, 1463-1476 (2003)