C. A. Sciammarella
Departimento de Ingegneria Meccanica e Gestionale, Politecnico di Bari, Viale Japigia 182, 70126, Bari, Italy
This article describes research carried out in the ﬁeld of optical super-resolution. The main goal of this study was to go beyond the Rayleigh limit in conventional optics and observe phenomena at the nano-range,because in certain circumstances methods such as X-ray and electron microscopy cannot be applied because of their inﬂuence on the observed specimens. In summary, the presence of a small polystyrene sphere on the optical ﬁeld of a conventional optical microscope seems to have converted the microscope into a device capable of functioning beyond the classical limit of resolution. This means that thenear-ﬁeld generated by evanescent illumination can be sensed by a microscope. Detection of particles in the range of a few tens of nanometres was achieved.
nano-crystal observation, nano-holograms, nano-optics, nanometric measurements, super-resolution
Observing optical images at the sub-micron range is at the cutting edge of current technology. This task,although very challenging, is essential to facilitate continued growth in many ﬁelds of nano-technology. The reason is that electron microscopy or X-rays that could provide the necessary short wavelengths to gather information at the nanometre and subnanometre range, in their current form, are not well suited to perform observations in many problems of scientiﬁc and technical interest. Furthermore, theenvironment required for the observation via X-rays or electron microscopy is not suitable for some types of specimens that it is necessary to study. Another concern is about the changes that may be induced in the specimen’s structure by the utilised radiation. These issues have led to the return to optics and to the analysis of the optical problem of super-resolution. The term ‘super-resolution’is used here to mean producing images beyond the limits imposed by optical instruments such as microscopes by light diffraction. It is a well-known phenomenon that optical image formation depends on the response of the system to a unit pulse, the point-spread function. This function is the origin of the concept of resolution that goes ´ back to Abbe  and Rayleigh . Rayleigh introduced theresolution limit that carries his name and is used as a standard deﬁnition in most of the literature associated with optical instruments. The idea
that it is possible to go beyond the Rayleigh limit and suggestions on how this can be done can be traced to Toraldo di Francia in 1952 . Independently of purely optical methods to go beyond the classical resolution limit, a vast effort has beenmade in developing super-resolution numerical methods. A comprehensive review of numerical methods of super-resolution from the point of view of practical applications can be found in Ref. . Two main avenues of work have been followed in this discipline of optics: (i) spatial domain methods and (ii) frequency space methods [5, 6]. Although space and frequency approaches to super-resolution can beconsidered equivalent through the Fourier transform (FT), practical applications have led to procedures and algorithms that do not easily convert from one ﬁeld to the other. If one looks at Ref. , in 1998 numerical methods were by far the ones that accumulated the largest majority of contributions. Up to that point people working in this ﬁeld approached the problem of super-resolution usingclassical optics, which is of course the source of the problem as pointed out by Toraldo di Francia . Fortunately, there are ways to gather information using light as a tool other than the classical approach to diffraction. One of the approaches goes back again to Toraldo di Francia [7–9]. One of the main methods has been the use of optical near-ﬁelds, the so-called evanescent waves . The...