A Simplified Computational Model for Circadian Stimulus Based on Illuminance, Correlated Color Temperature, and Color Rendering Index

Circadian stimulus (<italic>CS</italic>) is a popular metric for evaluating circadian effects of light. However, the determination of its value is complicated. In this work, the possibility of developing a simplified model to accurately estimate <italic>CS</italic> values has been investigated. It is found that: i) the <italic>CS</italic><sub>2018</sub> model itself has an important limitation: a very small perturbation in spectrum could result in a significant change in <italic>CS</italic> value, which fundamentally limits the development of a simplified model based on photometric or colorimetric inputs. ii) such a limitation is effectively reduced by the latest <italic>CS</italic><sub>2021</sub> model, and therefore a simplified model can be developed to estimate the value of <italic>CS</italic><sub>2021</sub> based on illuminance, correlated color temperature, a constraint of color rending index, and the factors of the continuous light exposure duration <italic>t</italic> and the spatial distribution of circadian light exposure <italic>f</italic>. The simplified model is developed and validated by using a comprehensive data set containing 395923 lighting spectra. The small deviations in <italic>CS</italic> value, which is less than 0.087 and 0.052 for warm and cool white light sources, respectively, show that the proposed simplified model could serve as an accurate and convenient tool for practical circadian lighting design.