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 variational spectral phase space K and the aberration baseline phase space L, play an important role. An interferometric device for which K ⋂ 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 elementary concepts of algebraic number theory: _Z lattice, reduced basis, and closest node. 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 points 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.

© 1999 Optical Society of America

[Optical Society of America ]

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