Redundant spacing calibration: phase restoration methods.
Résumé
New methods for redundant spacing calibration (RSC) are proposed. These are based on recent studies concerning phase calibration and the related phase unwrapping problem. In the corresponding theoretical framework, two subspaces of the baseline phase space, the unknown-spectral-phase space K and the aberration baseline phase space L, play an important role. An interferometric device for which the intersection of K and L is reduced to {0} is said to be of full phase. For any imaging device of this type, including those for which the traditional recursive approach fails, the phase restoration problem can be solved in the least-squares sense. When the closure phases are strongly blurred, global instabilities may occur. Their analysis appeals to concepts of algebraic number theory: Z-lattice, reduced basis, and nearest lattice point. In all cases, the separation angle between K and L must be as large as possible. The imaging devices based on the RSC principle should be designed accordingly. All these problems are illustrated by considering the phase restoration problems encountered in passive remote sensing by aperture synthesis.The difficulties related to possible correlator failures are examined in this context.