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J. Eur. Opt. Society-Rapid Publ. 21, 13( 2025)
Fig. 7. Spectral diagram of each principal component.( a) First principal component spectrum;( b) Second principal component spectrum;( c) Third principal component spectrum;( d) Fourth principal component spectrum;( e) Fifth principal component spectrum; and( f) Sixth principal component spectrum.
the peak; thus, this characteristic peak of potassium could not be observed either. These results indicated that the potassium signals from the lamp were hidden in the atmospheric background signal. To identify the potassium target, the potassium signals need to be extracted from the atmospheric background.
In this study, the PCA was performed on six sets of interferometric data obtained under clear-sky conditions to extract the potassium lamp signal from the mixed spectra. The potassium lamp spectrum measured in the laboratory was used solely as a reference for comparison with the final results and did not directly participate in the data processing. The extraction steps of potassium signals via the PCA are as follows: the interferogram collected by the SHS was obtained by preprocessing the interferogram to obtain the average spectrum; then, the above steps were repeated for the six pieces of hybrid interferogram collected in the experiment. The average spectral data from the six groups were used and reconstructed as a new matrix T =( t 1, t 2,... t i), i = 1,2,... 6. After the reconstructed spectral data matrix was processed via the PCA algorithm, six principal components Y 1, Y 2,... Y i, the projection value of each principal component S ij, and the eigenvalue k i were obtained. The PCA decomposes the mixed spectra into principal components with varying contribution rates through a dimensionality reduction approach. Each principal component corresponds to distinct signal components, as illustrated in Figure 7. Figure 7a shows the atmospheric background signal, and Figures 7b and 7c show the potassium signal from the lamp, and the remaining three principal components were random noise. Therefore, by performing PCA on the six groups of mixed spectra
Table 3. Statistics of the contribution rates of each principal component.
The i-th principal component Contribution rate %
1 99.7668 2 0.1727 3 0.0468 4 0.0050 5 0.0047 6 0.0040
that were hidden by the strong atmospheric background, separation of the atmospheric background signal and the potassium signal were successfully achieved.
The amount of information contained in the spectrum of the different principal components can be reflected in the contribution rate. According to formulas( 3) and( 4), the contribution rate of each principal component was obtained and are listed in Table 3.
Table 3 shows that the contribution rate of the first principal component was 99.77 %, and this component was the atmospheric background signal and corresponded to the strong background characteristics of the measurement mixed signal. The contribution rates of the second and third principal components were 0.17 % and 0.047 %, respectively. They both reflected the characteristics of the potassium signals, but their contribution rates differed by an order of magnitude; these results indicated that the spectrum of the potassium signal was mainly contained in the second principal component. Additionally, the potassium