We describe a constrained optimization approach for demodulation of single-shot interferograms corresponding to step phase objects. The demodulation problem is formulated as a minimization problem for a cost function consisting of a L2-norm squared error term and a gradient-based penalty (total variation) suitable for step objects. The optimization approach is tested with two methods that use complex (or Wirtinger) derivatives for the iterative solution update. The first simplistic method has a free parameter and thus provides a family of solutions. The second method is practically more valuable in that it is adaptive in nature and automatically leads to an appropriate solution. Both the off-axis case with straight line fringes and the on-axis case with closed fringes are treated in a unified manner. Excellent recovery of the phase of the step object suggests that the optimization approach as presented here is capable of providing full detector resolution, which is usually difficult to achieve in single-shot interferogram analysis.
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