The constant brightness theorem, says that the optical power flow per unit of area and solid angle cannot be increased though a passive optical system: luminance is invariant. The theorem, although fundamental, is not complete as it is traditionally stated as it is well known that higher brightness can indeed be achieved inside a high refractive index (RI) material, where the diameter of the diffraction limited spot is reduced by the square of the RI of the material. A concentrator with an area reduction ratio less than or equal to the square of the ratio of RI from input to output is therefore in principle capable of accepting all input modes. For photovoltaic (PV) systems where the solar energy enters the system in air (RI≈1) and is absorbed in a high index PV (RI≈3.5), the theoretical concentration is 3.52=12.25. To achieve this level of concentration will require development of transparent, high RI materials, but concentration factor of the order ~5 over the solar spectrum is possible with readily available materials. This allows for non-pointing, concentrated systems that not only improve efficiency and reduce the needed amount of PV material, but also efficiently capture diffuse light, whose percentage can be very significant even on clear days.
N. Vaidya, R. Dauskardt, and O. Solgaard, "AGILE: Axially Graded Index LEns as a non-tracking solar concentrator," in Renewable Energy and the Environment, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWD2.