In the last ten years, several different set-ups for producing images with super resolution by working in the near field have been reported. A good overwiew of the subject can be found in some recent review papers [1-3]. The techniques can be split roughly into two categories. Super-resolution may be obtained by detecting in the far field the light scattered by a small part of the sample under very localized illumination (illumination mode Scanning Near-field Optical Microscope), or, alternatively, by detecting the near field very close to the surface illuminated from the far field (detection mode SNOM). The most efficient way to, produce a localized illumination is the use of coated tapered fibers first introduced by Betzig et al. [4] (see Fig. 1a). Localized detection can be achieved by bringing the narrow tip of an optical fiber close to the surface and detecting the signal coupled into the fiber (see Fig. 1b). Alternatively, a small scatterer may be introduced in the near field so that the scattered light can be detected in the far field (see Fig. 1c). In this paper, we shall discuss the second type of experiments. We shall also restrict the discussion to elastic scattering, thus excluding fluorescence.