Lens–mirror combinations with maximal concentration

Abstract

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 Fresnel lens plus V-trough has been built, and test data are presented.