An interactive mid-air display including a display that presents a graphical user interface (GUI), optics projecting and rotating the GUI above the display such that the GUI is visible in-air in a plane rotated away from the display, a sensor including light emitters projecting beams towards the projected GUI, light detectors detecting reflections of the beams by objects interacting with the projected GUI, and a lens structure maximizing detection at each detector for light entering the lens structure at a respective location at a specific angle θ, whereby for each emitter-detector pair, maximum detection of light corresponds to the object being at a specific location in the projected GUI, in accordance with the locations of the emitter and detector and the angle θ, and a processor mapping detections of light for emitter-detector pairs to corresponding locations in the projected GUI, and translating the mapped locations to coordinates on the display.