A Mathematical Model for the Action Spectrum of Steady-State Pupil Size in Photopic Vision with Insight into Healthful Lighting

The pupillary light reflex, which has been seen as an important noninvasive and objective indicator of autonomic nervous system function, can be used for evaluating the impact of different lighting conditions in buildings on circadian behaviors, assessing ipRGC function in healthy and diseased retinas, and explaining luminance adaptation. However, the mechanism by which the intrinsic and extrinsic signals of ipRGCs regulate the steady-state pupil size under continuous lighting stimuli is still not clearly understood after decades of exploration. This paper presents a new experimental protocol with a large hemisphere LED screen as the stimulation device, allowing for a more realistic and comprehensive study in architectural spaces, which can potentially inform the design of lighting systems in buildings that promote healthy vision and comfort. Results reveal that both intrinsic and extrinsic signals participated in the process of regulating pupil size under continuous lighting conditions. Based on the findings, a new mathematical model was further proposed to calculate the contribution of these two signal sources to the changing intensity of melanopic radiance. The research outcomes also provide new insight into the mechanism of visual perception and adaptation and the nonvisual effect of eyes under different light conditions. Results suggest that the contribution of extrinsic signals may have been underestimated in previous studies since the extrinsic signal increases with reducing intensity in photopic conditions with lower melanopic radiance.