# Advancing Sustainable Textile Metrology: Reflectivity Measurement with Controlled Light Sources
## 2 Materials and Methods
### Methods  
Fundamental to the analysis of illuminance and reflectivity of textile samples are three key laws. The Inverse Square Law provides general information on the distribution of light [33]. It describes how the intensity of light decreases as the distance from the light source increases and is formulated as follows:  
\[E=\frac{I}{d^{2}} \tag{1}\]  
where E is illuminance (lx); I is the light source intensity (cd); and d is the distance from the source (m). In this study, the distance between the light source and the samples is fixed, eliminating the need for measurement corrections. However, the law remains important for interpreting differences in illuminance across different light sources. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**Pattern**} & \multirow{2}{*}{**Simulation Technical Face**} & \multirow{2}{*}{**Simulation Technical Back**} & \multirow{2}{*}{**Knitted Samples**} & \multicolumn{2}{c}{**Density**} \\ \cline{5-6}  & & & & **Wales/** & **Courses/** \\ \hline \multirow{3}{*}{A} & \multirow{3}{*}{Single jersey} & \multirow{3}{*}{**Simulation Technical Back**} & \multirow{3}{*}{**Knitted Samples**} & \multirow{3}{*}{**10 cm**} & \multirow{3}{*}{**10 cm**} \\ \cline{5-6}  & & & & & & \\ \cline{5-6}  & & & & & & \\ \cline{5-6}  
The Reflectance Ratio directly characterizes the properties of the tested materials. It is defined as the ratio between the reflected illuminance and the incident illuminance [34], expressed as follows:  
\[R=\frac{E_{m}}{E_{0}} \tag{2}\]  
where R is the reflectance coefficient (dimensionless quantity); E\({}_{m}\) is the measured illuminance with the sample (lx); and E\({}_{0}\) is the measured illuminance without the sample (lx). In this study, the reflectance ratio is used to assess the impact of reflective threads on the reflectivity of textile samples. Higher values of R indicate increased light reflection, while lower values suggest a higher degree of light absorption by the material. [PERSON]'s Cosine Law describes the dependence of illuminance on the angle of incidence of light on a given surface [35]. It is defined as follows:  
\[E_{\theta}=\frac{E_{0}}{\cos\theta} \tag{3}\]  
where E\({}_{0}\) is the illuminance on an inclined surface (lx); E\({}_{0}\) is the illuminance under perpendicular lighting (lx); and \(\theta\) is the angle of incidence of light. Equation (3) is relevant when the measured samples are not illuminated perpendicularly. If the light sources are positioned at different angles relative to the samples, this may affect the measured illuminance. In this case, Lambert's Cosine Law provides the necessary theoretical foundation for interpreting the experimental results. The required equipment for performing the described in this study reflectivity measurements with controlled light sources includes the following:  
* Luxmeter;
* Light Booth with controlled light sources;
* Black pad background to reduce ambient reflections;
* Stand or fixed position for the luxmeter;
* Textile sample with reflective properties. For conducting the experiment, a controlled lighting environment is used, namely the Light Booth (from BYK-Gardner GmbH, Geretsried, Germany) with different controlled illuminants (Figure 1). Four of them are used in the measurements, namely: daylight D65 (Class B); Incandescent light A, Department store light CWF, and Department store light TL84. Figure 1: The used light booth with controlled lightening. The intensity of the reflected light is measured with a digital LED luxmeter P5086 (from PeakTech Pruf- und Messtechnik GmbH, Ahrensburg, Germany)--Figure 2. The distance between the light source and the sample remains constant. The distance when measuring with the luxmeter is also constant, as the device is placed on a stand. The light beams fall perpendicular to the reflective surface. The luxmeter is also positioned perpendicular to the plane of the surface being measured. Figure 3 illustrates the steps of the proposed method.