Resolution and super-resolution

Many papers have claimed the attainment of super-resolution, i.e. resolution beyond that achieved classically, by measurement of the profile of a feature in the image. We argue that measurement of the contrast of the image of a dark bar on a bright background does not give a measure of resolution, but of detection sensitivity. The width of a bar that gives an intensity at the center of the bar of 0.735 that in the bright region (the same ratio as in the Rayleigh resolution criterion) is λ/(13.9×numerical aperture) for the coherent case with central illumination. This figure, which compares with λ/(numerical aperture) for the Abbe resolution limit with central illumination, holds for the classical case, and so is no indication of super-resolution. Theoretical images for two points, two lines, arrays of lines, arrays of bars, and grating objects are compared. These results can be used a reference for experimental results, to determine if super-resolution has indeed been attained. The history of the development of the theory of microscope resolution is outlined.