Tj. Flynn, 2-DIMENSIONAL PHASE UNWRAPPING WITH MINIMUM WEIGHTED DISCONTINUITY, Journal of the Optical Society of America. A, Optics, image science,and vision., 14(10), 1997, pp. 2692-2701
Given an interferometric phase image of a surface profile, the task of
two-dimensional phase unwrapping is to reconstruct the profile by add
ing multiples of 2 pi to the image. Discontinuities in the unwrapped p
hase must be restricted to areas of noise and true discontinuity in th
e profile. Such areas can often be identified by their low quality. Th
is suggests that the unwrapped phase should be chosen to minimize a we
ighted sum of discontinuity magnitudes. An algorithm is presented that
computes such an unwrapped phase from any initial guess. The elementa
ry operation of the algorithm is to partition the image into two conne
cted regions, then raise the unwrapped phase by 2 pi in one of the reg
ions, reducing the weighted sum; this is done repeatedly until no suit
able partitions exist. The operations are found by creating paths that
follow discontinuity curves and extending them to form complete parti
tions. The algorithm terminates when no path can be extended. The beha
vior of the algorithm and the benefits of weighting are illustrated wi
th an example. (C) 1997 Optical Society of America.