# A Portable Optical Sensor for Microplastic Detection: Development and Calibration
## 3 Results and Discussion
### Functional Variance Analysis of Reflectance Measurements with Different Laser Configurations  
A Functional analysis of variance (FANOVA) was performed using a linear mixed model to investigate the influence of laser configurations on the reflectance measurements. The dataset consisted of the average reflectance values obtained at regular time intervals for blue and green lasers, both with and without optics. Grouping measurements by time intervals facilitated a direct comparison between the configurations and accounted for the inherent temporal dependence of the functional data. The linear mixed model was fitted with reflectance as the dependent variable and laser configuration as the independent variable. Fixed terms were included for each configuration, while a random term captured intra-group variations associated with repeated measurements. This approach effectively addressed the correlation within time groups. Statistical analysis revealed significant differences in reflectance measurements across configurations. For instance, the green laser without optics exhibited a substantial increase in reflectance (+0.028 units, z = 102.427, \(p<0.001\)) compared to the reference configuration, the green laser with optics. Similarly, the blue laser with optics showed a more significant increase (+0.047 units, \(z=171.488\), \(p<0.001\)), while the blue laser without optics presented a reduction in reflectance (\(-0.010\) units, \(z=-36.813\), \(p<0.001\)). These results underscore the impact of both laser color and the presence of optics on reducing variability and enhancing measurement precision. A summary of the estimated coefficients, confidence intervals, and \(p\)-values is provided in Table 2.  
Our analysis estimated the group variance to be 0.001, indicating that the measurements remain significantly homogeneous over time within each configuration. However, the model's convergence limitations suggest caution when interpreting this parameter. These coefficients confirm that subtle adjustments in laser configuration systematically influence reflectance, a finding that is particularly notable for practical applications in both controlled and experimental environments. Statistical results reinforce the prototype's robustness in detecting microplastics under various experimental configurations. The integration of FANOVA and control charts enables the identification of optimal setups, such as lasers equipped with optics, which demonstrate reduced variability and improved precision. These findings also emphasize the relevance of carefully selecting optical components based on the specific requirements of the experiment or application. This methodology highlights the importance of accounting for temporal structure and intra-group correlation when analyzing functional data. Linear mixed models offer a flexible and robust framework for assessing the impact of categorical variables on func \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **Estimated** & **Confidence** & **\(p\)-Value** \\  & **Coefficient** & **Interval (95\%)** & \(p\)**-Value** \\ \hline
**Green laser without optics** & +0.028 & [0.026, 0.030] & \textless{}0.001 \\ \hline
**Blue laser with optics** & +0.047 & [0.045, 0.049] & \textless{}0.001 \\ \hline
**Blue laser without optics** & \(-0.010\) & [\(-0.012\), \(-0.008\)] & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated coefficients, 95% confidence intervals, and \(p\)-values from the functional analysis of variance (FANOVA) for different laser configurations. The table highlights the impact of laser type and the inclusion of optics on reflectance measurements. tional measurements, allowing for precise adjustments for dependencies and variability within groups. The experimental functionality of the microscope is currently operational, allowing for image acquisition of microplastics and other materials. Although this feature is still in the beta phase, it enables initial image processing for material detection.