## 2 Materials and Methods
### Circadian Stimulus  
#### 2.4.1 Calculation Metrics of Illumination  
To ensure the well-being of children and proper circadian entrainment--facilitating adequate sleep and activity patterns throughout the day--the lighting metrics are based on circadian response. Consequently, the circadian stimulus (CS) is the chosen metric to evaluate the potential of daylight to support sufficient circadian entrainment during both play and sleep periods. [PERSON] et al. developed a sophisticated mathematical model of human circadian phototransduction grounded in the current understanding of retinal neuroanatomy and neurophysiology [78]. This model, which quantifies non-visual responses to light, particularly focuses on light-induced nocturnal melatonin suppression. The model incorporates several key elements:  
* Spectral sensitivity: it characterizes the spectral sensitivity of the retinal circuit, defining \"circadian light\" (CL) as a single, instantaneous photometric quantity. * Empirical data: the model utilizes published psychophysical studies of nocturnal melatonin suppression using lights of different spectral power distributions. * Neurophysiological basis: it accounts for the participation of intrinsically photosensitive retinal ganglion cells (ipRGCs), as well as rods and cones, in circadian phototransduction via neural connections in the retina. * Spectral opponency: the model includes spectral opponent mechanisms in the distal retina that provide synaptic connections to the ipRGCs. This comprehensive approach allows the model to characterize both the spectral and absolute sensitivities of the human circadian system to light, represented as circadian light (CL\({}_{\text{A}}\)). The model's ability to predict responses to complex light environments makes it a valuable tool for understanding and designing lighting in various contexts, such as architectural spaces, workplaces, and treatment of circadian rhythm disorders. Recent research has further refined our understanding of the spectral sensitivity of human circadian responses. Studies have shown that the spectral sensitivity of circadian phase resetting and melatonin suppression changes dynamically with light duration. This suggests that the relative contributions of different photoreceptors may vary over the course of light exposure, with cones potentially playing a significant role in the initial response, followed by a dominant melanopsin contribution over longer durations [79]. The mathematical development of _CS_ is expressed in Equation (2):  
\[\text{CS}=0.7\cdot\left(1-\frac{1}{1+\left(\frac{CLA}{355.7}\right)^{1.1026}}\right) \tag{2}\]  
The value ranges from 0.0, which indicates no suppression, to 0.7, representing the saturation point where further increases in light intensity or spectral quality no longer result in a significant enhancement of melatonin suppression. This prediction assumes that the typical observer is exposed to the given lighting conditions for one hour, with a standard pupil diameter of 2.3 mm. For effective circadian entrainment, a CS value of 0.4 is typically considered sufficient, as this threshold is enough to support biological alignment and maintain healthy circadian rhythms. The assessment of melatonin suppression levels (CS) is determined based on the specific illuminance (E) and the spectral composition of light reaching the occupants' eyes. Data gathered during both phases underwent systematic processing and analysis using multiple tools. Microsoft Excel (v2412) [80] was employed to structure and examine the recordedmeasurements in spreadsheet format, while the CS Calculator 2.0 software [45; 81; 82; 83; 84] was used to model the circadian stimulus (CS) under various lighting conditions. CS calculations correspond to the minimum light exposure required by the human eye to achieve adequate melatonin suppression--equating to a CS value of 0.4 during daytime activities [59] and 0.2 during the sleep period.