Two algorithmic solutions for interpolating between array manifold grid points are presented. The algorithms are for sensor arrays in vector or in scalar wavefields. The algorithms make successful use of the condition that the reciprocal DOA (direction-of-arrival) spectrum is a multilinear function in the small, i.e. over the region of adjacent grid points. Since polarization is a linear parameter subspace, a DOA spectrum can be computed without recourse to the unknown polarizations. Then, vector interpolation is replaced by bivector interpolation to address the radio wavefield case. The approach distinguishes between sensor arrays in scalar wavefields (e.g. acoustic) and those in vector wavefields (e.g. electromagnetic). Since both storage and computational load vary with the reciprocal of the grid spacing or its square, the design relationship between desired accuracy and the required array manifold grid spacing is given.
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