The phase-shifting digital holography (PSDH) is a widely used approach for recovering signals by their interference (with reference waves) intensity measurements. Such measurements are traditionally from multiple shots (corresponding to multiple reference waves). However, the imaging of dynamic signals requires a single-shot PSDH approach, namely, such an approach depends only on the intensity measurements from the interference with a single reference wave. In this paper, based on the uniform admissibility of plane (or spherical) reference wave and the interference intensity-based approximation to quasi-interference intensity, the nonnegative refinable function is applied to establish the single-shot PSDH in Sobolev space. Our approach is conducted by the intensity measurements from the interference of the signal with a single reference wave. The main results imply that the approximation version from such a single-shot approach converges exponentially to the signal as the level increases. Moreover, like the transport of intensity equation (TIE), our results can be interpreted from the perspective of intensity difference.

翻译：相移数字全息术（PSDH）是一种通过信号与参考波干涉的强度测量来恢复信号的常用方法。传统上，此类测量需要多次曝光（对应多个参考波）。然而，动态信号的成像要求采用单次曝光PSDH方法，即该方法仅依赖于单个参考波干涉的强度测量。本文基于平面（或球面）参考波的均匀可容许性以及干涉强度对拟干涉强度的逼近，在索伯列夫空间中利用非负可细化函数建立了单次曝光PSDH。我们的方法通过信号与单个参考波干涉的强度测量来实现。主要结果表明，随着尺度增加，这种单次曝光方法的逼近版本以指数速度收敛于信号。此外，与强度传输方程（TIE）类似，我们的结果可从强度差分的角度进行解释。