SUPERRESOLUTION IN CONFOCAL SCANNING MICROSCOPY .3. THE CASE OF CIRCULAR PUPILS

In two previous papers it has been shown that there resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data by a singular-system analysis. This result was proved both in the case of coherent and in the case of incoherent illumination (fluorescence microscopy) but the analysis was essentially restricted to the one-dimensional problem. As a byproduct the two-dimensional problem with square pupils was also considered. In this paper we investigate the more realistic case of circular pupils. The singular system of the relevant integral operator is computed, both for coherent and incoherent illumination, using a discretization method previously developed by two of the authors. In this way we show that the significant improvements in resolution which may be achieved in the one-dimensional problems are also obtainable in the two-dimensional case.