Complex object wave recovery from a single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of the cross term, but this method suffers from poor resolution. To obtain full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this method is not used widely due to several tedious and difficult tasks such as empirical tuning of free parameters. We introduce a new optimization approach, mean gradient descent (MGD), for single-shot interferogram analysis that is simple to implement. MGD does not have any free parameters whose empirical tuning is critical to the object wave recovery. The MGD iteration does not try to achieve minimization of a cost function but instead aims to reach a solution point where the data consistency and the constraint terms balance each other. This is achieved by iteratively progressing the solution in the direction that bisects the descent directions associated with the error and constraint terms. Numerical illustrations are shown for recovery of a step phase object from its corresponding off-axis as well as on-axis interferograms simulated with multiple noise levels. Our results show full pixel resolution as evident from the recovery of the phase step and excellent rms phase accuracy relative to the ground truth phase map. The concept of MGD as presented here can potentially find applications to a wider class of optimization problems.

中文翻译：

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平均梯度下降：单次干涉图分析的一种优化方法。

从单发干涉图样恢复复杂的物波是干涉测量和数字全息术中的一个重要的实际问题。最受欢迎的单次干涉图分析方法涉及交叉项的傅立叶滤波，但是这种方法的分辨率较差。为了获得完整的像素分辨率，有必要将物波恢复建模为一个优化问题。优化方法通常涉及最小化由数据一致性项和一个或多个约束项组成的成本函数。尽管该方法具有潜在的性能优势，但由于一些繁琐而艰巨的任务（例如自由参数的经验调整），该方法并未得到广泛使用。我们为单次干涉图分析引入了一种易于实现的新优化方法，即平均梯度下降（MGD）。MGD没有任何自由参数，它们的经验调整对于物波恢复至关重要。MGD迭代未尝试实现成本函数的最小化，而是旨在达到数据一致性和约束条件彼此平衡的解决方案。这是通过在与误差和约束项相关联的下降方向一分为二的方向上迭代进行求解来实现的。示出了用于从其对应的离轴以及具有多个噪声水平模拟的轴上干涉图恢复阶跃相位对象的数字图示。我们的结果表明，从相位阶跃的恢复中可以明显看出全像素分辨率，并且相对于地面真相图具有出色的rms相位精度。