Lens–mirror combinations with maximal concentration

By the addition of suitable reflectors the concentration of a lens can be increased to the thermodynamic limit, which is equivalent to an f-number of one half. Such lens-mirror combinations are useful whenever concentration rather than image formation is important, for example, in radiation detectors and solar energy collectors. The design of lens-mirror combinations with maximal concentration is described. To the approximation that the lens has sharp focal points at off-axis incidence, the solution for the reflector is readily found to be compound hyperbolic. With proper choice of the f-number of the lens the hyperbolic reflector reduces to a V-trough or cone, an arrangement which offers considerable advantages for fabrication. The 2-D case (line focus lens) suffers from aberrations due to focal length variation with nonplanar incidence. The optical performance of 2-D lens-mirror combinations at nonplanar incidence is analyzed and evaluated for its suitability in solar energy applications. A prototype Fresn l lens plus V-trough has been built, and test data are presented.