Unwrapping of noisy phase maps: a comparison of two methods

摘要

The unwrapping of experimental phase maps is not a straightforward process and much research has been devoted recently to the development of robust algorithms that can remove 2π phase discontinuities in the presence of noise, phase inconsistencies, missing data and holes or shadows. In this paper, the performance of two recently developed phase unwrapping methods are compared. The first uses a least squares minimization formulation whose solution is provided by a fast discrete cosine transform. Areas of bad data are removed from the differential equation by means of a weighting matrix and the unwrapped phase distribution is evaluated using an iterative approach. The second is a path-independent method based in the Thikonov regularization theory. This theory finds solutions that correspond to minimizers of positive definite quadratic cost functionals. The solution to the unwrapping problem by this method is a generalization of classical least-squares. The introduction of a regularization term permits the reduction of noise and the interpolation over regions with invalid data in a stable and controlled way. The performance of both methods are compared in their application to computer generated and experimental phase maps. Their main advantages and limitations are discussed.