A number of cameras have been introduced that sweep the focal plane using mechanical motion. However, mechanical motion makes video capture impractical and is unsuitable for long focal length cameras. In this paper, we present a focal sweep telephoto camera that uses a variable focus lens to sweep the focal plane. Our camera requires no mechanical motion and is capable of sweeping the focal plane periodically at high speeds. We use our prototype camera to capture EDOF videos at 20fps, and demonstrate space-time refocusing for scenes with a wide depth range. In addition, we capture periodic focal stacks, and show how they can be used for several interesting applications such as video refocusing and trajectory estimation of moving objects.