This paper describes a novel approach to partially reconstruct high-resolution 4D light fields from a stack of differently focused photographs taken with a fixed camera. First, a focus map is calculated from this stack using a simple approach combining gradient detection and region expansion with graph cut. Then, this focus map is converted into a depth map thanks to the calibration of the camera. We proceed after this with the tomographic reconstruction of the epipolar images by backprojecting the focused regions of the scene only. We call it masked back-projection. The angles of back-projection are calculated from the depth map. Thanks to the high angular resolution we achieve by suitably exploiting the image content captured over a large interval of focus distances, we are able to render puzzling perspective shifts although the original photographs were taken from a single fixed camera at a fixed position.