Maximum White Luminous Efficacy of Radiation Versus Color Rendering Index and Color Temperature: Exact Results and a Useful Analytic Expression

We calculate numerically the spectral power distributions (SPDs) which maximize luminous efficacies of radiation (LERs) for white light of particular color rendering indices (R-a's) and color temperatures (CTs). We find that, except for the very highest color rendering indices, the spectra are spiky rather than continuous. We present a useful analytic expression for the dependences of the maximum white luminous efficacy of radiation (MWLER) on R-a and CT and discuss these dependences. We propose that, for any white light source of a given R-a and CT, its absolute spectral efficiency is simply the ratio of its LER to the MWLER at that same R-a and CT. We discuss the absolute spectral efficiency, defined in this way, of various lighting technologies: incandescent, fluorescent, high-intensity discharge, and solid-state lighting. Finally, we discuss the possibility of alternative MWLERs based on alternative indices for color rendering quality.