## Abstract

By geometrical optics and the Rayleigh–Sommerfeld diffraction formula, theories for the design of a hybrid refractive–diffractive superresolution lens (HRDSL) with high numerical aperture are constructed. Differences between the profile of the diffractive superresolution element (DSE) with high numerical aperture and that with low numerical aperture are indicated. Optimization theory can obtain a globally optimal solution through a linear programming much more simplified than the corresponding one in Liu *et al*. [
J. Opt. Soc. Am. A **19**,
2185 (
2002)]. The rules of the structure of the designed DSE are both theoretically proved and numerically verified. Comparison of this optimization theory with the other design theories and examples of designing the HRDSL with high numerical aperture are provided. Last, some limits of optical superresolution with high numerical aperture are set and compared with those for low numerical aperture.

© 2003 Optical Society of America

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