The Green's formulation for phase unwrapping is generalized to the case of circular phase-support regions. A phase-unwrapping method, believed to be new, is developed in which two forms of the Green's function are used, one in a closed form and the other in the form of a series of Helmholtz equation eigenfunctions to satisfy homogeneous Neumann boundary conditions in a circular domain. The contribution of the rotational part of the wrapped phase gradient that is due to phase-gradient inconsistencies (residues) is accounted for in the unwrapped phase. Computational results on the reconstruction of a simulated wave front in the presence of aberrations, and on unwrapping real synthetic aperture radar interferograms, show the usefulness and reliability of the method when applied to regions where the conventional rectangular support regions are impractical.
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