An illumination system for a lithographic apparatus comprises a radiation intensity filter for controlling the intensity distribution of a beam of radiation travelling along an optical axis (Z), the radiation intensity filter comprising a first member and a second member. Each of the first and second members comprise a plurality of opaque regions which are substantially opaque to the radiation beam. The first member and second member are moveable relative to one another between a first relative position and a second relative position. In the first relative position at least a portion of one of the opaque regions of the first member overlaps in the direction of the optical axis with a portion of one of the opaque regions of the second member. In the second relative position the total area of overlap in the direction of the optical axis of the opaque regions of the first member with the opaque regions of the second member is less than that in the first relative position.