III Super-Resolution by Data Inversion

Publisher Summary This chapter explains super-resolution using case examples, and discusses the classical Rayleigh resolution limit and defines it in terms of the overlap between the images of two-point sources. It is shown that, in the framework of modern Fourier optics, the resolving power is characterized instead by specifying the spatial-frequency band associated with the instrument. Some important features of inversion methods are discussed to the extent that they relate to the assessment of resolution limits. The main difficulty encountered in solving inverse problems is their sensitivity to noise in the data, which can be the source of major instabilities in the solutions. The role of regularization is to prevent such instabilities from occurring. The chapter explains the problem of extrapolating the object spectrum outside the band or the effective band under the assumption that the object vanishes outside some finite known domain. The case of scanning microscopy is considered. The chapter also focuses on confocal microscopy and shows how the use of data inversion techniques allows enhancing the resolving power of such microscopes. The problem of inverse diffraction from plane to plane, which consists of back-propagating toward the source plane a field propagating in free space, is considered.