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Complex object wave recovery from single-shot interference pattern is animportant practical problem in interferometry and digital holography. The mostpopular single-shot interferogram analysis method involves Fourier filtering ofcross-term but this method suffers from poor resolution. For obtaining fullpixel resolution, it is necessary to model the object wave recovery as anoptimization problem. The optimization approach typically involves minimizing acost function consisting of a data consistency term and one or more constraintterms. Despite its potential performance advantages, this method is not usedwidely due to several tedious and difficult tasks such as empirical tuning offree parameters. We introduce a new optimization approach Mean gradient descent(MGD) for single-shot interferogram analysis that is simple to implement,robust and does not require any free parameters. The MGD iteration does not tryto achieve minimization of any cost function but instead aims to reach asolution point where the data consistency and the constraint terms balance eachother. This is achieved by iteratively progressing the solution in thedirection that bisects the descent directions associated with the error andconstraint terms. Numerical illustrations are shown for recovery of a stepphase object from its corresponding off-axis as well as on-axis interferogramssimulated with multiple noise levels. Our results show full pixel resolution asevident from the recovery of phase step and excellent rms phase accuracyrelative to the ground truth phase map. The concept of MGD as presented herecan potentially find applications to wider class of optimization problems.

Mean Gradient Descent: An optimization approach for single-shot interferogram analysis