Two-dimensional phase unwrapping with minimum weighted discontinuity

Abstract

Given an interferometric phase image of a surface profile, the task of two-dimensional phase unwrapping is to reconstruct the profile by adding multiples of 2π to the image. Discontinuities in the unwrapped phase must be restricted to areas of noise and true discontinuity in the profile. Such areas can often be identified by their low quality. This suggests that the unwrapped phase should be chosen to minimize a weighted sum of discontinuity magnitudes. An algorithm is presented that computes such an unwrapped phase from any initial guess. The elementary operation of the algorithm is to partition the image into two connected regions, then raise the unwrapped phase by 2π in one of the regions, reducing the weighted sum; this is done repeatedly until no suitable partitions exist. The operations are found by creating paths that follow discontinuity curves and extending them to form complete partitions. The algorithm terminates when no path can be extended. The behavior of the algorithm and the benefits of weighting are illustrated with an example.