Resolution and super-resolution in inverse diffraction

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In this tutorial paper we discuss the concept of resolution in problems of inverse diffraction. These problems have direct applications in areas such as acoustic holography and can also be considered as intermediate steps of more general problems of inverse scattering. We justify the generally accepted principle that the resolution achievable is of the order of the wavelength of the radiation used in the experiment. Moreover we indicate two cases where super-resolution, i.e. resolution beyond the limit of the wavelength, can be achieved. The first is the case of near-field data where super-resolution is possible thanks to the information conveyed by evanescent waves. The second is the case of subwavelength sources, where super-resolution is possible thanks to out-of-band extrapolation of far-field data. Simple algorithms for obtaining this result are also described.