1. An interactive display comprising: one or more display layers; a first illuminator positioned at a first location behind the one or more display layers; a second illuminator positioned at a second location behind the one or more display layers; a camera positioned behind the one or more display layers; a phase management mechanism configured to: control alternation of phases of the interactive display, the interactive display having a plurality of phases including at least a first phase and a second phase; when in the first phase, controlling the first illuminator to dominate over the second illuminator, and in that state causing the camera to take a first image; and when in the second phase, controlling the second illuminator to dominate over the first illuminator, and in that state causing the camera to take a second image; and an image construction mechanism configured to construct an input image using at least at least a portion of the first image and at least a portion of the second image.