A new technique for the least-mean-squares (LMS) phase-unwrapping method is developed that incorporates the concept of branch cuts between phase singularities (residues), which are usually associated with the path-following gradient integration technique. These branch cuts are introduced by decomposition of the least-mean-squares unwrapped phase into two separate components. The first results from the transverse part of the wrapped phase gradient, which is induced by residues of the original phase, and the second component is due to a potential component, independent of the residues. This decomposition allows the reconstruction of phase patterns with a high level of accuracy and consistency with the initial (wrapped) phase, even when only partial knowledge of the placement of branch cuts between residues is available. We show how the residue-induced phase, ignored by conventional LMS phase estimators, is reconstructed for a given boundary-value problem. The method is illustrated with interferometric quality-control measurements of optical fiber-connector terminations and also with synthetic aperture radar interferometry. These experiments demonstrate the high accuracy of the method in practical situations in which only a limited number of branch cuts are available.
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