A scanning illuminating device includes an emission center from which radiation is emitted in an illuminating sector. A cylindrical ring is centered on the source and is rotatably movable about a first axis. The ring includes a plurality of slits regularly distributed about its axis of rotation and having the same angular amplitude α. A cylinder portion is centered on the source and is rotatably movable about a second axis crossing the first axis at the center and forming a nonzero angle therewith. The cylinder portion includes a slit having an angular amplitude β. A first device control of the rotation of the ring, defining an elementary angular step as such that an integer N1 other than 1 meets the condition α=N1·αα. A second device controls the rotation of the ring portion defining an angular step ββ such that an integer N2 other than 1 meets the condition β=N2·ββ.