We explore the possibility of designing correlation functions of a particle's scattering potential for producing desired scattered intensity distributions, within the validity of the first Born and far-field approximations. It is shown that for scatterers with the same average distributions of the scattering potential (refractive index) but different degrees of potential's correlation, the scattered fields with prescribed average intensity distributions can be produced. Two examples of such potentials are included: those for flat circular and ring-like scattered intensities, if considered to be a function of the scattering (azimuthal) angle. In both cases the height, width and edge sharpness can be adjusted at will. Production of the novel media is envisioned via the 3D printing or sequences of liquid crystal light modulators. (C) 2015 Optical Society of America
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