A novel phase unwrapping algorithm and its application to phase stepped interferometry

Abstract

Phase unwrapping is critical in the analysis of phase maps from a variety of interferometric systems. For some methods, an unwrapping error, due to noise, at some point can corrupt all subsequent phase demodulations from the corrupted point on. In images, this tends to lead to erroneous stripes in the phase demodulated data. We propose a novel phase unwrapping approach that uses a spatial binary tree image decomposition to allow maximum parallelism in implementation. At each node in the tree structure, a single unwrapping decision is made between two image blocks. The unwrapping rule used here is derived from a statistical estimate framework. Specifically, a maximum likelihood estimate of the demodulation term is used. This term can be viewed as that which minimizes a discontinuity penalizing cost function. We show that the algorithm exhibits robustness in presence of noise. The algorithm is demonstrated in a phase stepped interferometric system application.