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We discuss the error that results when the far field is reconstructed from spatially truncated near-field samples and present an effective mitigation technique based on the Slepian sequence for acoustic spherical near-field scanning. We show that the truncation error is inevitable whenever the far field is reconstructed using the classical near-field-to-far-field transformation. After discussing the Slepian sequence for a truncated spherical surface and its analytic and numerical properties, we apply it to expand truncated NF samples and derive the near-field-to-far-field transformation of the resulting expansion coefficients, from which the far field can be computed. We demonstrate the efficacy of this transformation by applying it to near-field scanning for bistatic scattering from a sphere and radiation from a current distribution.