We suggest using the theory of linear programming to design diffractive superresolution elements if the upper bound of the intensity distribution on the input plane is restricted, and using variation theory of functional or wide-sense eigenvalue theory of matrix if the upper bound of the radiation flux through the input plane is restricted. Globally optimal solutions can be obtained by each of these theories. Several rules of the structure and the superresolution performance of diffractive superresolution elements are provided, which verify the validity of these theories and set some limits of optical superresolution.
© 2002 Optical Society of America
Original Manuscript: March 23, 2002
Revised Manuscript: June 3, 2002
Manuscript Accepted: June 3, 2002
Published: November 1, 2002
Haitao Liu, Yingbai Yan, Qiaofeng Tan, and Guofan Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002)