The luminous efficiency of a system consisting of a spherical, thermal radiator at the center of a selectively reflecting spherical shell is investigated from a theoretical point of view. Various spectral reflectances for the spherical shell have been assumed, and computations are made both for a blackbody and a pure tungsten radiator. The effect of variation in radiator temperature and visible bandwidth transmitted by the shell, as well as the question of stability, is considered. Expressions for the luminous efficiency are derived and used for computation of specific examples. These indicate that to obtain a high luminous efficiency for a radiator of emissivity substantially smaller than 1, a perfect, or nearly perfect reflectance of the shell in a fairly small band around the region of high-energy output from the radiator, is more important than a uniform and fairly high reflectance over a larger spectral region. It is also shown that the introduction of a transparent spherical shell of reflectance 0.1, between the radiator and the reflecting shell, leads to a relatively small decrease in efficiency.
B. HISDAL, "Luminous Efficiency of a Thermal Light Source," J. Opt. Soc. Am. 52, 395-400 (1962)