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The near-field-far-field (NF-FF) transformation with spherical scanning is attractive, since it allows the reconstruction of the full radiation pattern of the antenna under test from a single set of NF measurements. A truncation error affects the near-field reconstruction in the zone close to the boundary of the measurement region. It is clear that, to obtain an accurate field reconstruction in the whole measurement region and to improve the accuracy in the blind zone, it is very important to estimate a proper number of samples falling in it. The goal of this work is the extrapolation of these samples. The estimation of such data (otherwise equal to zero in the application of the OSI algorithm) gives rise to a remarkable reduction of the truncation error in the periphery of the scanning region. As a consequence, an acceptable reconstruction is attained in the whole blind zone or in a large part of it. The method is based on the sampling representation and OSI expansion, and makes use of the singular value decomposition (SVD) algorithm for determining the NF samples falling in the blind zone.