A collimator taking the form of a prolate spheroid (40) comprising radiation attenuating material and featuring a twisted slit comprising radiation transmissive material. The twisted slit featuring first (43) and second (44) apertures arranged such that for each entrance point in one of the apertures there is a direct pathway through the major axis ‘B’ of the prolate spheroid (40), at a pre-determined angle, to a point in the other aperture, such that a compound aperture is formed. For each compound aperture the length of the direct pathway through the prolate spheroid (40) is constant. Rotation of the collimator about the major axis ‘B’, relative to a stationary point at the first aperture (43), steers in angle the compound aperture through the collimator from said stationary point. Such an arrangement allows radiation from a source positioned at said point to be collimated into a beam, the resultant beam being scanned in angle, and the resultant collimation effect being constant across the angular range of the scan.