We report a simple and stable phase detection method for holographic data storage systems. Our method needs only one image acquisition, and no additional light waves or interferometric measurements are required. The phase information is retrieved from intensities at pixel boundaries where inter-pixel crosstalk occurs owing to the spatial filtering in the Fourier plane of the input image. We numerically and experimentally demonstrate that our method can retrieve the phase signal with a sufficiently low error rate for holographic storage. We also compare the storage density of the proposed method to the conventional phase detection method.