The image of a single small hole in an opaque screen in a microscope of large numerical aperture is calculated. Both conventional microscopes and scanning optical microscopes are considered, the general trend being that the central peak is broadened, the outer rings strengthened and the minima made shallower as the numerical aperture is increased. In the conventional microscope the image is no longer independent of the illumination, as it is for paraxial theory.
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Sheppard et al. (1982) studied this question.
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