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 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.
© 2003 Optical Society of America
Original Manuscript: July 17, 2002
Revised Manuscript: November 13, 2002
Published: March 10, 2003
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)