Super-resolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks

For pt.III see ibid., vol.7, p.655 (1991). In the previous papers the authors proposed and discussed a method, based on a singular-system analysis of the low-numerical-aperture limit for improving the resolution of a confocal scanning microscope. They show that this method can be implemented by the use of a special optical mask which can be computed by this analysis. They discuss one-dimensional and two-dimensional problems both in the coherent and in the incoherent case. Some exact results obtained for one-dimensional problems are used to understand the numerical results obtained for two-dimensional problems. For the two-dimensional incoherent problem they also extend the investigation to the case of lenses with high numerical aperture.