Daylight-Referenced Efficiency (DRE): A Radiometric Measure of Electric Light Source Efficiency
Photopic luminous efficacy (lm/W) weights optical power strictly against human eye sensitivity V (lambda), creating a systemic metrological penalty for electric light sources engineered with broad spectral output in the ultraviolet (280-380 nm) or infrared (780-4000 nm) bands. Similarly, metrics evaluating chromaticity, color quality, or melanopic pathways assess photoreceptor responses strictly within the visual band, offering no measure of broad-spectrum physical radiant power conversion. To resolve this limitation, we introduce Daylight-Referenced Efficiency (eta_DRE), a radiometric framework that evaluates how efficiently an electric light source converts electrical power into an optical spectrum matching natural terrestrial daylight across domain Omega = [280 nm, 4000 nm]. The framework factorizes performance into primary physical quantities: domain-restricted Wall-Plug Efficiency (eta_wall [W_optical/W_elec]), measuring unweighted electrical-to-optical conversion, and Daylight Spectral Fidelity (eta_spec [unitless, 0-1]), quantifying geometric shape match to the ASTM G173 AM1.5G solar reference via total variation distance (1 - TVD). Multiplying total optical power by spectral fidelity yields the absolute Daylight-Referenced Output Power (P_dr [W]), establishing a direct physical flux quantity for lighting specification. Dividing by electrical drive power gives the summary metric Daylight-Referenced Efficiency (eta_DRE = eta_wall * eta_spec [W/W_elec]), measuring net reference-conforming radiant output per electrical Watt consumed. The mathematical architecture is reference-agnostic, domain-extensible, and maintains provable lower-bound monotonicity for eta_wall and eta_DRE under spectral truncation. Open-source reference software is provided to facilitate deployment and standardized rating of broad-spectrum light sources.