J. Eur. Opt. Society-Rapid Publ. 21, 13( 2025) 143
of target detection can increase the accuracy of identification [ 10, 11 ]. Studies have shown that potassium salt is a basic ingredient in flame suppressant formulations [ 12 ], and during combustion, two distinctive characteristic spectral lines for potassium are observed. Therefore, developing a method for rocket target identification via spectral signal detection of potassium salt combustion instead of infrared radiation characteristic detection is feasible [ 13 – 15 ]. Spatial heterodyne spectroscopy( SHS) is a new type of ultrahighresolution remote sensing spectral detection technology. Compared with traditional Fourier transform spectrometers, SHS has greater luminous flux, resolution and a unique advantage in the fine detection of weak spectral signals [ 16 – 18 ]; its application in the detection of potassium salt combustion characteristic spectral lines has practical importance. In actual detection, the detection of potassium combustion strongly interferes with the background signal of the sky. Under long-distance conditions, the intensity difference between the two is 3 ~ 4 orders of magnitude or greater, and the potassium combustion signal is often hidden in the atmospheric background and difficult to distinguish. The extraction and identification of the weak signals of this type of aliasing spectrum is the focus of this research. In this study, the sky was used as the background, and a potassium lamp light source was used to simulate the potassium combustion signal. The extraction of the potassium characteristic signal from the strong background spectrum was experimentally investigated, and the principal component analysis( PCA) method was used on the measurement data [ 19 – 21 ]. The principal components of the mixed signals were separated by reducing the dimensionality of the spectral data and the information redundancy between the data. The potassium signal was restored and extracted via the Principal Component Regression( PCR) method. Combined with the Non-Local Means( NLM) denoising algorithm, the qualitative identification and quantitative analysis of potassium lamp signals were ultimately achieved.
2 Methods
2.1 SHS principle
The SHS uses a new type of modulated spatial interference spectrometer that has the characteristics of small volume, high throughput, and a large field of view; moreover, it has a clear advantage in the detection of the characteristic peaks of spectral lines with weak signals, and its structure is illustrated in Figure 1.
Under ideal circumstances, the interferogram collected by the SHS can be expressed by formula( 1):
IðxÞ ¼
Z 1
�1
BðrÞf1 þ cos½8pðr� r 0 Þx tan hŠgdr; ð1Þ
where x represents the position of the detector pixel, B( r) represents the spectrum of the incident light, r represents the wavenumber of the incident light, r 0 represents the Littrow wavenumber, and h represents the angle between the grating normal and the optical axis.
Fig. 1. Basic principles of SHS.
In actual detection, the expression of the original interferogram collected by the SHS is shown in formula( 2):
IðxÞ ¼ Ax ð Þþ
Z 1
�1
Bk ð ÞexpðikxÞdk; ð2Þ
where A( x) is the background noise and B( k) is the characteristic spectrum of potassium.
In this study, SHS is used to detect the weak potassium signal in the tail flame. However, formula( 2) shows that the original spectral information of the tail flame radiation is affected by the background signal, and a large amount of background noise affects the accuracy of the feature signal identification. Therefore, the potassium signal needs to be further extracted.
2.2 PCA-NLM algorithm
In applications, the measurement spectrum is usually composed of a mixture and superposition of the spectra of multiple different components. In studies, the spectra of one or a few components are often the focus, and the spectra of other components are considered interference. An important part of this research is to effectively separate the spectrum of the target component of interest from the interference. PCA is a method of dimensionality reduction and can separate complex datasets using orthogonal transformation. Its application to the analysis and processing of the spectral data can reduce the correlation among the original variables of the spectrum and decompose the information from the different components in the original spectrum into different principal components. The information contained in each principal component can also be quantitatively analysed based on the eigenvectors of each principal component.
The raw spectral data can be expressed as an n-dimensional random variable X. The dataset X is analysed via PCA. After orthogonal transformation, the