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Deals with the reconstruction of the contrast function of a dielectric cylinder with rectangular cross section starting from the knowledge of the electric scattered far field produced under the incidence of plane waves. We analyze the set of the reconstructable Fourier harmonics of the unknown permittivity contrast function with linear and quadratic approaches. This set depends on the ranges of the wavenumbers β, of the angles of incidence θi of the impinging plane waves, and of the observation angles θo. We discuss a simple way to describe such a dependence, which allows us to find out that the set of the retrievable harmonics for the quadratic approach contains that for the linear one. Moreover, our investigation points out how increasing the amount of independent data through a multifrequency/multiview measurement scheme allows us to enlarge the set of the retrievable unknown harmonics with respect to a multifrequency/single-view one. Our analysis is confirmed by numerical results. Memory storage requirements and processing time consumption for the quadratic approach are greatly reduced thanks to the massive use of the fast Fourier transform algorithm.