One optical system comprises a first optical surface, a faceted second optical surface, and a faceted third optical surface. The optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the third optical surface. Between the second and third optical surfaces the rays making up the first and second bundles form discrete sub-bundles each passing from a facet of the second optical surface to a facet of the third optical surface. The sub-bundles do not form a continuous bundle in a phase space that has dimensions representing the position and angle at which rays cross a surface transverse to the bundle of rays.