# A Portable Optical Sensor for Microplastic Detection: Development and Calibration
## 3 Results and Discussion
### Reproducibility and Statistical Analysis  
The curve analysis is critical to understanding a dataset's behavior, especially when the relationship involves continuous variables. Repeatability in curve analysis is essential for reliable, reproducible results. Distance from the sample and operator skill level can affect reproducibility, leading to inconsistent results. We rely on standard procedures and training to mitigate these issues. Optics introduce variability due to differences in light paths and focal lengths. We account for these differences in the analysis. The average and standard deviation provide insights into the central tendency and dispersion of the data. [PERSON]'s theorem estimates the minimum proportion of observations within a certain number of standard deviations from the mean, providing a bound on the data's variability. Figure 16 shows control charts based on [PERSON]'s theorem, which identifies variability in the reflectance measurements. Using the data, we calculated the upper (red) and lower (green) control limits as three standard deviations above and below the mean (blue line). The points within these limits demonstrate controlled variability in the measurements, indicating stability during testing. Figure 17 presents the quadratic error analysis for green and blue lasers, with and without optics. The error peaks indicate moments of greater variability, potentially linked to external interferences or optical system adjustments. These findings emphasize the importance of calibrating sensors optimally, particularly in setups without optics. Functional data analysis (FDA) is another statistical approach that considers data in curves, surfaces, or other continuous variations. FDA is beneficial when the data points are highly correlated, allowing for the analysis of data that vary over a continuum, such as time or wavelength. In the context of the FDA, error handling and variance estimation play crucial roles in interpreting functional data. The reflectance curves analyzed in this study are typical examples of functional data, where each curve represents a continuous function over time. These curves vary not only in their point values but also in their global  
Figure 16: The figure compares reflectance over time for green (**a**) without optics and (**b**) with optics and blue (**c**) without optics and (**d**) with optics. Charts display mean reflectance and their upper and lower control limits at \(\pm 3\) standard deviations. Grey points within these limits illustrate controlled variability, emphasizing improved measurement stability. structures, requiring a statistical approach that can capture these complexities. The variance in FDA describes how the functions (reflectance curves, in this case) are dispersed around the functional mean. In practical terms, variance quantifies the variability of the curves between different measurements or experimental conditions. In studying the reflectance curves of different laser configurations, functional variance helps us understand how much the curves change in response to changes in laser configuration or the introduction of optical components. Standard methods to analyze this variance include mean function plots and confidence bands that represent functional confidence intervals (Figure 18). These methods visualize  
Figure 17: The figure shows the quadratic error comparison over time for reflectance measurements using (**a**) a green laser without optics, (**b**) a green laser with optics, (**c**) a blue laser without optics, and (**d**) a blue laser with optics. Plots illustrate fluctuations in measurement precision, where peaks indicate increased variability. The progressive error reduction demonstrates the system’s capacity to stabilize, highlighting the beneficial effect of optical components on measurement consistency. where and how the curves deviate significantly from the mean, offering insights into the stability and consistency of the studied laser configurations.