  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.
