Research note: Calculating spectral irradiance indoors

Abstract

The spectral composition of the light that reaches any indoor work plane depends on the characteristics of the light sources and the spectral reflectances of the surrounding surfaces due to the multiple reflections experienced by the light rays along their paths from the source to the observation point. We show that in indoor spaces, the source and surface radiances must obey a definite self-consistent relationship derived from the fact that each illuminated surface point acts as a secondary source of light. It is then established that the spectral irradiance on any plane is linearly dependent on the spectral radiance of the light source. The explicit integral form of this relationship provides a theoretical framework for a quantitative description of the surface effects. Additionally, under very general assumptions, we show that the spectral irradiance can be computed from the spectral flux of the source through a simple multiplication by a wavelength-dependent function. This function, with units of inverse surface (1/m²), provides a convenient way for evaluating the effects that arbitrary changes in the source spectrum will produce on the spectral irradiance at the indoor point under study.