We find a simple analytic expression for the inverse of an operator related to the problem of data reduction in confocal scanning microscopy. Potential applications of this result to the practical scanning-microscope problem are outlined.In two recent papers', 2 we proposed a method for enhancing resolution in confocal scanning microscopy. 3 First we summarize the main points of the procedure in the case of a onedimensional optical system with ideal lenses. Letf(y) be the complex effective transparency (or reflectivity for a reflection microscope) in the object plane; by this we mean that, for a given scanning position, the image g(x) formed by an ideal microscope with a uniformly filled illumination lens is g(x) = J sinc(x -y)sinc(y)f(y)dy,

The Large Binocular Telescope (LBT), which is currently under construction on the top of Mount Graham in Arizona, will be a Fizeau interferometer with a maximum baseline of ¡ £ ¢¤ ¡ ¥ . From the point of view of image reconstruction, the interesting feature of this instrument is that it will require routinely the use of multiple-images deconvolution methods if the aim is to produce a unique image with the resolution of a ¦ § ¢¤ ¥ telescope. Our group is working on this problem since a few years and has already produced methods and software for the data reduction problem. In this paper we provide a survey of our ongoing work.