Fig 1.
Spectral irradiance measurements and calculated illuminance values at the eye level.
All displayed values are based on spectral irradiance measurements with a field-of-view restriction according to the CIE S 026 standard [32]. In our case, these measurements are 24% lower than those of the unobstructed sensor diffusor. Differences in irradiance measurements from the mean were smaller than 5%, or about 1% on the log irradiance scale. Differences in wavelength peak were between 0 to 1 nm. (A) Dots show the log of the corneal irradiance (in log W/m2) of exemplary steps at their respective peak wavelength. Each dot represents a narrowband peak, similar to the spectral example distribution with a peak at 553 nm (the peak is indicated by the gray dashed line). (B) Corneal illuminance values for the narrowband light steps at each peak wavelength. Besides the standard photopic CIE-1931 V(λ) weighing for the 2° observer (black line), illuminance values were calculated based on the weightings of V10(λ) (10° observer, photopic vision, dark grey), of V’(λ) (scotopic vision, light grey), and of Veq(λ) (mesopic vision, medium grey). To show the scotopic illuminance values along with the other curves, they are drawn at half their original value (light-gray curve). (C) Corneal alpha-opic equivalent-daylight illuminance for all receptor types according to the CIE S 026 standard [32].
Fig 2.
(A) Series of peak wavelengths for each experiment and protocol. A list for the respective order of wavelength peaks is available as part of the S3 File. (B, C, D) Schematics of the first 40 seconds of each experimental protocol. Light onset after dark adaptation occurs at zero seconds (dotted black line). Traces show the average pupil diameter, with a ribbon representing the SEM. For visual reasons, only one of the two protocols sharing the same procedure is shown. These are Up (B), Central 1a (C), and Short 1 and Long 1 (D).
Fig 3.
Concepts of additive (mixed-effect) models.
(A) Construction of a smooth through basis expansion. Every smooth is constructed from a number of basis functions, usually spread evenly across the value range of a predictor. In the shown case, five cubic regression splines were used as basis functions to demonstrate the concept. The thick black line represents the final smooth function, describing the relationship between the predictor and the outcome variable. Colored traces show the basis functions. (A1) Unscaled basis functions—their type and maximum number are part of the input for model generation. (A2) Scaled basis functions—for each basis function, a respective weight is estimated by which the function is scaled. (A3) Summation of basis functions, starting with the first and then, successively, adding the others; the generated smooth can then be used for prediction. The smooth is shown as dashed curve to show that, with the addition of the last basis function (orange line), the resulting curve is equal to the smooth function. (B) Concept of global effects with random smooths. (B1) The thick black line represents the global effect, describing the average relationship between the predictor and outcome variable. Colored traces show the individual’s effect of the same predictor, demonstrating interindividual differences. The model takes these differences into account through the so-called random smooths (i.e. “random” in that their contribution depends on the subject). (B2) Random smooths are smooths describing the deviations from the global effect. The colored traces show the deviations present in panel B1. Because the global smooth and the random smooths are estimated together, the deviations disappear on average, i.e., not all deviations will tend in the same direction, but are spread around the global effect.
Fig 4.
Experimental data and circumstances.
(A) Normalized pupillary constriction (nPC) plotted against wavelength, for each of the nine protocols. The color scale shows at which point in the series a specific wavelength was presented; light yellow represents early in the series. For all but the Short protocols, points represent the average nPC during the respective last five seconds of a light step. In the two Short protocols, points represent the average nPC during the sixth second after lights-off (or sevenths second after lights-on). Traces show the mean nPC, ribbons its standard deviation. The number in the upper right corner of each plot shows the corresponding sample size. (B) Scatterplot of when subjects of a certain chronotype started their respective protocols. The color scheme is according to (C), i.e. green, red, and blue correspond to Exp. I–III, respectively. Note the lack of Lark and Owl chronotypes in Experiment I before midday. (C) Boxplot of the time of the year when the experiments took place. Preliminary measurements and parts of Experiment I took place in 2019, the other measurements in 2020.
Fig 5.
Model predictions for normalized pupillary constriction (nPC) as depending on several main predictors, when all other predictors are held at an average, constant level. Traces show the model prediction for the mean, ribbons its 95% confidence interval. Dotted lines show a peak that is discussed in the main text. In (A3, B3, and C3), the x-axis is logarithmically scaled to reflect the logarithmic transformation of irradiance in the model. (A) and (D) show dependencies in Experiment I, discussed here, (B) and (C) dependencies in Experiment II and III, respectively, discussed later. (B) The red line at the bottom of (B1) indicates where the two curves differ significantly at the 0.05 level of significance.
Fig 6.
Interaction of wavelength, chronotype, and time of day.
(A1) False-color graph of model predictions for the nPC’s dependence on wavelength (x-axis) and chronotype (y-axis) for three times of day, when all other predictors (basic model) are held constant at their average. Horizontal lines show where the respective three traces shown in figure part (A2) are taken from. (A2) Model predictions for the nPC vs. wavelength for three chronotypes (trace color), and three times of day. Green traces show Larks (CT score = 70), red traces Owls (CT score = 30), and blue traces Neutral types (CT score = 50). Ribbons show the 95% confidence interval for the predicted means. (B1/B2) Like (A), but for pooled data across all experiments. See the main text for further details.
Fig 7.
Linear mixed-effect model results for nPC’s dependency on illuminance.
Model predictions for nPC vs. various measures of illuminance. Points show individual data. Thick regression lines show the fixed-effect relationship and thin regression lines random effect variation in slope and intercept by participant. The insets show R2full for the full model (fixed and random effects), and, more importantly, a partial R2illu, i.e. the proportion of variance explained through nPC’s relationship with the fixed effect of illuminance. Part (A) shows results for Experiment I, (B) for protocols with darkness between light steps in Experiment II, and (C) for protocols with thirty seconds of light, followed by nine seconds of darkness in Experiment III.
Fig 8.
Interaction of wavelength with time in Experiment II and III.
Time denotes the time (in seconds) since light onset, or light change to the respective wavelength. (A1) and (A2) show results from Experiment II, (B1), (B2), and (B3) those from Experiment III for the protocols Long 1 and Long 2. (A1) False-color graph of model predictions for the nPC’s dependence on wavelength (x-axis) and time (y-axis) for settings with (right panel), or without (left panel), periods of darkness between changes of wavelength. All other predictors are held constant at their average value. Horizontal lines indicate where the respective traces shown in figure part (A2) are taken from; continuous curves refer to the absence of dark periods, dashed curves to their presence; filled circles and triangles mark the wavelength of the respective maximum nPC value of these traces. In the right panel of A1, nPC values after the 15th second (i.e., in the Dark period) show a time-by-wavelength rendition of the post-illumination pupil reflex (PIPR). (A2) Model predictions for nPC vs. wavelength at three points in time. The right panel shows the wavelength dependency of the 6-second PIPR. Ribbons show the 95% confidence interval for the predicted means. Dotted lines with a triangle symbol represent the discontinuous setting with periods of darkness present between light steps; full lines with a filled circle show the continuous setting. The red horizontal line above the x-axis in the two left panels shows where the difference between the two settings is significant at the 0.05 level. (B1) Like (A1 right panel), but for Experiment III. Horizontal lines show where the respective traces shown in figure part (B3) are taken from, and points mark the wavelengths of the respective maximum nPC value of these traces. (B2) Like (B1), but with the nPC baseline taken from the last second of the respective previous light step. (B3) Like (A2), but dotted lines and triangles represent the scaling according to (B2), full lines and points according to (B1). The right panel shows the wavelength dependency of the 6-second PIPR.
Fig 9.
Interaction of wavelength with time in Experiment III, for protocols Short 1 and Short 2.
Time is the time (in seconds) since light onset or light change to the respective wavelength. (A) False-color graph of model predictions for the nPC’s dependence on wavelength (x-axis) and time (y-axis). All other predictors (basic model) are held constant at their average. Horizontal lines show where the respective traces shown in part (C) are taken from, and points mark the wavelengths of the respective maximum nPC value of these traces. (B) Like (A), but with a different measure of nPC where the nPC baseline is taken as the mean pupil diameter across the last second of the respective previous light step. Model diagnostics are superior to those for the Model in part (A). (C) Model predictions for the nPC vs. wavelength at three points in time after light-step onset: in the 2nd second (red traces), the 7th second (green traces), and the 15th second (blue traces); the latter two cases are also the 6-second PIPR and 14-second PIPR, respectively. Ribbons show the 95% confidence interval for the predicted means. Dotted lines with a triangle represent the scaling according to (B), full lines with a filled circle according to (A).
Table 1.
Model estimates for irradiance across all experiments.
Fig 10.
Select changes of nPC across the day in Experiment I.
Model predictions for the nPC vs. time of day for three chronotypes (left to right), and two wavelengths (blue trace 490 nm and red trace 610 nm), that were chosen for comparison with the studies by Zele et al. [27] and Munch et al. [26]. Ribbons show the 95% confidence interval for the predicted means.