# Regulated Power Supply with High Power Factor for Hyperspectral Imaging Applications
## 4 Experimental Results
### Evaluation of Performance for the Hyperspectral Image Application
#### 4.2.4 Light Stability Evaluation  
After analyzing the transient behavior of various power supplies by measuring their steady time, the next step was to evaluate their performance during the steady state. Our focus was on assessing the stability of the light signal, which involves measuring the variation in light intensity over time. To accurately quantify this stability, we examined the spread of light-intensity values over time, typically using the standard deviation. However, the standard deviation is affected by the mean light-intensity value, and our experimental setup did not allow for uniform electrical power output for each light source under evaluation. Therefore, we employed the coefficient of variation, which is the ratio of the standard deviation to the mean, as a more effective metric for comparing variables sources with varying mean intensities. For this purpose, we used the inverse of the coefficient of variation as our stability metric, providing a measure of light stability with high values when there are smaller variations in light intensity over time. In signal processing and image processing, the ratio between the mean and the standard deviation is known as the signal-to-noise ratio (SNR), and we used this metric for quantifying light stability. The SNR was calculated according to Equation (10), where \(\mu\) and \(\sigma\) refer to the mean and the standard deviation of the light intensity over time (\(light\)). In this case, the mean light intensity across the different wavelength was used. To ensure a reliable quantification of light stability, the SNR was determined using the data from the final 10 s of each measurement, providing a safety margin beyond the point at which steady state was achieved. \[SNR(dB)=20 log_{10}\bigg{(}\frac{\mu(light)}{\sigma(light)}\bigg{)} \tag{10}\]  
The light stability in terms of the SNR for the different power supplies and illumination modes is presented in Figure 16 (data available in Supplementary Materials Table S1). The boxplot reveals that all tested power supplies maintained a high SNR exceeding 45 dB, indicating robust light stability independently of the power supply. However, there are differences in SNR between the different power supplies. When comparing the performance of the different power supplies, CPS-2 exhibited the superior SNR, while CPS-1 showed the inferior SNR. The performance of the power supply developed in this study (PPS) falls between those of two commercial power supplies. To quantify the differences in SNR presented in Figure 16 for the different power supplies, we performed a statistical analysis on the data. Initially, we assessed the normality of the data using  
Figure 15: Steady time for the different types of power supplies (PPS, CPS-1, and CPS-2). (**a**) Reflectance mode. (**b**) Transmittance mode. the Shapiro-Wilk Test, which indicated that the data did not follow a normal distribution. Consequently, we conducted a Kruskal-Wallis test, a non-parametric alternative to ANOVA, appropriate for cases where the normality assumption is not satisfied. This test was used to evaluate whether there were significant differences in SNR across the different power supplies. The results of the Kruskal-Wallis test revealed significant effects for reflectance measurements (H-statistic = 24.58, \(p\)-value = 4.60 \(\times\) 10\({}^{-6}\)) and for transmittance measurements (H-statistic = 23.69, \(p\)-value = 7.16 \(\times\) 10\({}^{-6}\)). These findings suggest that at least one power supply exhibited a significantly different SNR compared to the others. To identify which specific power supplies showed significant differences, we applied [PERSON]'s post hoc test. For reflectance measurements, [PERSON]'s test indicated significant differences between CPS-1 and CPS-2 (\(p\) < 0.0001) as well as between PPS and CPS-1 (\(p\) = 0.02296), while no significant difference was observed between PPS and CPS-2 (\(p\) = 0.06676).