## 4 Evaluating the Indoor Luminous Environment and Visual Comfort Perception
### Visual Comfort Evaluation Metrics
#### 4.1.1 Quantity and Uniformity of Light  
Considering mainly the luminance (\(L\)) of the light sources and the ambient distribution that condition the actual quantity and uniformity of light falling on a surface, the following metrics have been widely used to express the lighting quality of an indoor space:  
* **Daylight Factor (_DF_):** compares the amount of light inside with the exterior during an overcast sky condition [55], the average \(DF\) across the analyzed surfaces of the building is typically requested to be greater or equal to 2% [56]. Alternatively, the appropriate \(DF\) value can be defined concerning the specified target illuminance and geographic location, following the method proposed in EN 17037 [57].
* **Daylight Autonomy (_DA_):** represents the percentage of occupied time in which a point within the analysis grid is over a defined minimum illuminance (discrete values only, e.g., complies or not). Additionally, the percentage can also include partial values when the conditions are below the established minimum threshold (ratio between obtained and minimum threshold), and are expressed as **continuous \(DA\)**(_cDA_) [58].  
* **Spatial _DA (sDA)_:** gives a notion on how much area is over the minimum illuminance for more than a certain portion of the occupied time, typically 300 lux is used for basic reading and writing activities, and these values shall be met for at least 50% of the analysis grid area [59].
* **Useful Daylight Illuminance (UID)**: calculates the percentage of the analysed time in which the illuminance in a point falls in a certain established range (normally between 300 and 3000 lux) [60]. Subcategories are also used to communicate the time in which the illuminance values falls below (underlit) or above the suggested ranges (over lit). Specifying the over lit areas can also suggest direct light discomfort risk.
* **Frequency of Visual Comfort (FVC)**: percentage of time within the analysis period during which appropriate values of average illuminance are accomplished [61]. Similar to UDI, proposes 3 ranges: Comfort, Under and Over. \[FVC=\frac{\sum_{i}wf_{it}}{\sum_{i}t_{i}}\] (1) \[wf_{i}=\begin{cases}1&E_{Under}\leq E_{Daylight}\leq E_{Over}\\ 0&E_{Daylight}<E_{Under}\sigma E_{Daylight}>E_{Over},\end{cases}\] where: \(E_{Under/Over}\): minimum/maximum illuminance threshold \(E_{Daylight}\): computed/measured illuminance value \(t\): analysis period
* **Intensity of Visual Discomfort (IVD):** time integral of the difference between the spatial average of the current daylight illuminance and the upper limit of visual comfort or the lower limit of visual comfort [61]. \[IVD=\int_{p}\Delta E(t)dt\] (2) \[IVD_{Over}\] \[\Delta E(t)=\begin{cases}E(t)-E_{Over}&E(t)\geq E_{Over}\\ 0&E(t)<E_{Over}\end{cases}\] \[IVD_{Under}\] \[\Delta E(t)=\begin{cases}0&E(t)>E_{Under}\\ E_{Under}-E(t)&E(t)\leq E_{Under},\end{cases}\] where: \(E_{Under/Over}\): minimum/maximum illuminance threshold \(E_{Daylight}\): obtained illuminance value \(t\): analysis period
* **Daylight Uniformity (\(U_{o}\)):** ratio in a given moment, or time frame, between the minimum value of illuminance on the analysis area (\(E_{min}\)) and a reference value (e.g., maximum or average) [62].