The relative contributions of exterior light sources to human circadian stimulus can be informative, considering the number of options and the significance of the issue. The intent here is to provide a first estimate of the relative contribution from sources at low levels of illumination. These results do not in any way establish any threshold or level of significance for the absolute quantity of circadian stimulus, which is known to depend on multiple interacting factors: quantity of optical radiation, duration, spectrum, direction, timing and circadian adaptation. The relative nature of this discussion is demonstrated by the way all values are scaled or presented as ratios, so the results include no absolute quantity units.
The calculations shown here combine the spectral power distributions (SPDs) of a source with an action spectrum for circadian stimulus. The SPDs mostly come from the NGDC spectrum webpage, along with CIE Illuminant A ("incandescent" on the chart) and CIE Daylight D65 ("daylight") and an unpublished SPDs for "blue sky" ("skylight") and direct sunlight ("sunlight"), and altogether include 40 polychromatic sources. All the sources were scaled to have the same quantity of photopic flux, so comparisons should be made on that basis. The action spectrum used here is developed from J. Hollan's 2004 publication, and is consistent with the ones discussed in the IES publications "Light and Health" (TM-18-08) and "Light and Health Seminar" (SEM-7-11) and the DOE publication "Light at Night" (see figures 6 & 7).
The S/P ratio is calculated using an SPD combined with the CIE scotopic and photopic sensitivity functions, to get the numerator and denominator values respectively. These visual sensitivity functions are well-publicized and discussed further here and here.
The results are scaled to make the result for "daylight" (D65) equal to 100%. The results for all 40 electric and daylight sources are shown in the figure below. The value for D65 is shown in red, and the value for Illuminant A in orange, along with labels for some other source types. A line indicating the "best linear fit through (0,0)" is also shown.
The line has a slope of 0.359 and the corresponding r-squared value is 0.96. Clearly the relationship between circadian stimulus and S/P ratio can be reasonably modelled as linear.
In fact, the linear model seems to be less accurate than a quadratic that would also pass through the origin and follow the slight "upward" curvature that the line reveals.
The linear relationship demonstrated here means that a change in light source from one S/P ratio to another can be estimated to produce a corresponding, directly proportional change in circadian stimulus. For example, if a source with S/P of 2.5 (e.g. daylight) were used to replace a source with S/P around 0.6 (e.g. HPS), then the corresponding change in circadian stimulus would be 2.5 / 0.6 or ~400%. This relative change applies to equal quantities of photopic flux, so if the change described were to result in a decrease of illumination provide by the "high S/P" source to 1/2 the quantity provided by the "low S/P" source, then the overall relative change in circadian stimulus would be (2.5 / 0.6) * 1/2 ~ 2, or to roughly 200%.
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