Slepian transverse vector spherical harmonics and their application to near-field scanning

We introduce the Slepian transverse vector spherical harmonics (TVSH). Unlike the classical TVSH, they are orthogonal over a given truncated spherical surface and the orthogonality constants can be computed. We apply the Slepian TVSH to the problem of reconstructing the far field from spatially truncated near-field samples and show that the far field can be reconstructed accurately over the entire angular sector where the near-field samples are available.