# Measurement of Circadian Effectiveness in Lighting for Office Applications
### Measurement Analysis
The model predictions can thus be compared to the approximation results by calculating the corresponding error estimate \(\Delta\text{CS}\) defined by  
\[\Delta\text{CS}=\left|\text{CS}_{\text{CSS}}-\text{CS}_{\text{LMK}}^{\circ} \right|, \tag{11}\]  
where the superscript circle next to \(\text{CS}_{\text{LMK}}\) symbolizes that the respective pixel summations of Equations (7) and (8), like the CSS-45 measurements, should cover the complete half space. Similarly, the relative deviation \(\Delta E_{\text{rel}}\) between the measured illuminances can be calculated using  
\[\Delta E_{\text{rel}}=\frac{\left|E_{\text{CSS}}-E_{\text{LMK}}^{\circ} \right|}{E_{\text{CSS}}}, \tag{12}\]  
where  
\[E_{\text{CSS}}=683\frac{\text{Im}}{\text{W}}\cdot\int E_{\lambda}V_{\lambda} \,\text{d}\lambda \tag{13}\]  
gives the illuminance as derived from the CSS-45 measurements. The goal is to show that both ways of measuring and estimating CS essentially yield the same result. An advantage of working with the spatially resolved luminance data rather than using integrative measures of fixed half-space geometry is that the former, in contrast to the latter, basically allows for selecting relevant light directions and weighting them accordingly to account for the nonuniform distribution of the different types of retinal receptors contributing to NIF effects. As discussed in the Introduction of this paper, evidence from literature on light-induced melatonin suppression and circadian phase shifting suggests that the circadian effectiveness of a light stimulus depends on its spatial distribution. However, studies that systematically investigated such NIF effects as a function of the direction of light exposure are still sparse and even show some inconsistencies between their reportedconclusions. This largely explains the fact that, up to the present day, there are no standardized guidelines or recommendations on how to properly weight lighting contributions from different directions of the half-space with regard to their relevance for stimulating the circadian system, in particular since the relevance of specific retinal regions and their respective sensitivity weighting have not been fully elucidated yet. In the present work, we therefore limit our considerations to three exemplary viewing angle/field of view (FOV) definitions obtained by geometrically masking the data output of the luminance imaging photometer using an ellipse equation of the form  
\[\frac{\left(x_{ij}-m_{x}\right)^{2}}{r_{x}^{2}}+\frac{\left(y_{ij}-m_{y} \right)^{2}}{r_{y}^{2}}=1, \tag{14}\]  
where \(x_{ij}\) and \(y_{ij}\) denote the pixel positions and \(r_{x}^{2}\) and \(r_{y}^{2}\) the extents of the ellipse in \(x\)- and \(y\)-directions, while \(m_{x}\) and \(m_{y}\) are the respective coordinates of the central focus point and ellipse center. The three different pixel maskings considered in this work are shown in Figure 5 and represent (a) a half-space geometry, (b) the FOV definition of CIE S 026:2018 [15], and (c) the FOV of an assumed 120\({}^{\circ}\) observer. Again, it should be emphasized that there are no official recommendations or standards yet that could guide through the process of adequately weighting light contributions originating from different directions of the half space for a proper modeling of the overall circadian effectiveness of the illumination and/or the lit environment. Nevertheless, the general methodology of the spatially resolved approximation strategy discussed in this should also be noted, and the preceding sections can easily be adapted to any suitable masking or light-direction weighting scheme once it has been established based on scientific evidence.