Sensing in non-line-of-sight (NLOS) is a well-known issue that limits the effective range of radar-like sensors. Existing approaches for NLOS sensing consider the usage of either metallic mirrors, that only work under specular reflection, or dynamically-reconfigurable metasurfaces that steer the signal to cover a desired area in NLOS, with the drawback of cost and control signaling. This paper proposes a novel sensing system, that allows a source to image a desired region of interest (ROI) in NLOS, using the combination of a proper beam sweeping (by the source) as well as a passive reflection plane configured as a periodic angular deflecting function (that allows illuminating the ROI). \textit{Stroboscopic sensing} is obtained by sweeping over a sufficiently large portion of the reflection plane, the source covers the ROI \textit{and} enhance the spatial resolution of the image, thanks to multiple diverse observation angles of ROI. Remarkably, the proposed system achieves a near-field imaging with a sequence of far-field acquisitions, thus limiting the implementation complexity. We detail the system design criteria and trade-offs, demonstrating the remarkable benefits of such a stroboscopic sensing system, where a possibly moving source can observe a ROI through multiple points of view as if it were static.