The phase-shifting digital holography (PSDH) is a widely used approach for recovering target signals by their interference (with reference signals) intensity measurements. Such reference signals are traditionally from multiple shots (or multiple phase-shiftings) of the reference wave. However, the imaging of dynamic target signals requires a single-shot PSDH approach, namely, such an approach depends only on the intensity measurements from the interference with the single reference signal (being from the single phase-shifting of the 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 target signal with a single reference signal. 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.