A scanned imaging system includes a lens system for directing radiation from a scene to be scanned onto external reflecting surfaces of a rotating polygon and onto a detector, the external reflecting surfaces including primary and secondary flat facets which rotate together on a common axis, the lens system including an image space lens system for focusing an image of the scene to be scanned in the vicinity of a primary facet, and further including an optical system for directing radiation from a primary facet to a focus at a point on or adjacent an associated secondary facet and to reflect the radiation from the secondary facet to the detector, the arrangement being such that a beam of radiation is incident on substantially the whole width of a primary facet and sweeps round with that facet as the polygon rotates.