An approach based on two-dimensional iterative nonlinear regression for retrieving phase information from single-frame interferograms was formulated and tested for fluid- and heat-flow measurements. Even though an initial crude phase assignment—i.e., fringe-order numbers at limited data points—is needed, the approach does not require complete phase unwrapping as in conventional techniques. Testing of computer-simulated and real interferometric data shows stable convergence and accurate phase extraction. The method works well under a high noise level, including broken fringes or contaminated regions, with a good noise-cleansing capacity. It provides accuracy at image- or opaque-object boundaries and directly offers spatial-gradient values. A weakness, however, can be intensive computation in the iterative estimation. The method is a good candidate for single-frame interferogram reduction.
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