In this paper, we consider a new class of methods for phase unwrapping of 2D images based on digital wavefront sensors. Mathematically, many wavefront sensors produce the same measurements of incoming wavefronts regardless of whether they are wrapped or not. Since typical reconstructors for these sensors are optimized to compute smooth wavefronts, it is possible to digitally ``propagate'' a wrapped phase through such a sensor, resulting in a smooth unwrapped phase. First, we show how this principle can be applied for phase unwrapping using digital Shack-Hartmann and Fourier-type wavefront sensors. Then, we apply our methods to an unwrapping problem appearing in a real-world adaptive optics project currently under development, and compare the results to those obtained with other state-of-the-art algorithms.

翻译：本文研究了一类基于数字波前传感器的二维图像相位解包裹新方法。从数学角度而言，许多波前传感器对输入波前的测量结果不因相位是否包裹而改变。由于这类传感器的典型重构器被优化用于计算平滑波前，因此可将包裹相位通过此类传感器进行数字"传播"，从而获得平滑的解包裹相位。首先，我们阐述了如何利用数字夏克-哈特曼传感器和傅里叶型波前传感器实现该相位解包裹原理。随后，我们将所提方法应用于当前正在开发的实际自适应光学项目中的相位解包裹问题，并将结果与其他先进算法的解包裹效果进行了对比分析。