Comparison of Typical Window Function Characteristics in Interferometric Imaging Spectroscopy Restoration
Objective Interference imaging spectroscopy is a cutting-edge technology of visible and infrared remote sensing,which can obtain both spatial and spectral information of the earth element.The interferometric imaging spectrometer directly acquires the interferogram,which can be transformed to spectra by Fourier transform.However,the interferometer detector can only acquire a limited length interferogram,and the truncation of the real interferogram will cause sidelobe to appear in the restored spectrum,which results in false spectral information.In practical applications,apodization is employed to reduce sidelobe interference.As an important step of interference spectral restoration,apodization exerts a significant influence on the accuracy of the restored spectra.Meanwhile,there are few quantitative analyses on the performance of different types of window functions in the existing literature.Thus,we provide a detailed analysis of six typical window functions and propose a weighted fusion method for the joint restoration of multi-window functions based on their characteristics,providing references and guiding significance for the application of window functions.Methods Firstly,based on the basic digital signal processing principle,we emphasize the guiding significance of synchronous sampling in spectral calibration,the establishment of sampling rules for the detection of specific substances,and the necessity of apodization in cases of asynchronous sampling.By utilizing spectral analysis theory,the main lobe width and the height of the first sidelobe in the frequency domain of the window function are employed as metrics to assess the window function performance.Furthermore,an exploration is conducted to understand their specific influence on the restored spectrum.Subsequently,a quantitative comparison of the performance metrics for six typical window functions is carried out.Further validation is carried out using simulated interference data and CE-1 IIM data to demonstrate that H-G strong apodization and Chebyshev apodization not only effectively suppress interference from adjacent spectral lines,but also exhibit enhanced resolution,thereby improving the accuracy of the restored spectrum.Finally,based on a comprehensive understanding of the performance of different window functions,a localized weighted fusion method for joint restoration of multiple window functions is proposed to leverage the advantages of various window functions to enhance spectral representation.Finally,the effectiveness of this method is demonstrated using simulated spectra.Results and Discussions Firstly,a quantitative analysis of six typical window functions is conducted to yield the comparative results of main lobe width and the height of the first sidelobe presented in Table 3,which provides references for the application of window functions in different scenarios.The comparison indicates that the H-G strong apodization and Chebyshev window function can realize a good compromise between the main lobe width and sidelobe height.The spectral restoration results of the simulated interference data and CE-1 IIM data after apodization using different window functions(Figs.5 and 6)indicate that the H-G strong apodization function and Chebyshev apodization function can not only effectively suppress the interference of adjacent spectral lines,but also improve the resolution of the restored spectrum.In Fig.6,window functions with narrower main lobe widths exhibit strong resolution capabilities but are sensitive to noise,whereas window functions with wider main lobe widths demonstrate stronger noise resistance.On this basis,the local weighted fusion method for joint restoration of multiple window functions is proposed to integrate the characteristics of window function and thus improve the spectrum expression.Figs.7 and 8 illustrate the fusion results under different combinations of window functions.Finally,the effectiveness of locally weighted fusion is verified by simulated spectra(Fig.9).Conclusions Based on the digital signal processing theory,the Fourier transform of rectangular windows is taken as an example to point out that synchronous sampling has a guiding significance for spectrum calibration and the setting of sampling rules when detecting specific substances.Meanwhile,we also elaborate on the necessity of apodization in the restoration of interferometric spectra.To investigate the effect of different apodization methods on the restored spectrum,a quantitative comparison of the performance of six typical window functions is conducted to provide references for the application of window functions in different scenarios.Further validation by simulated interference data and CE-1 IIM data confirms that H-G strong apodization and Chebyshev window function not only reduce interference from adjacent spectral lines but also enhance the resolution of the restored spectrum.The experimental results also indicate that window functions with narrower main lobe widths exhibit strong resolution capabilities but are sensitive to noise,while those with wider main lobe widths demonstrate stronger noise resistance.Based on this,we propose a localized weighted fusion method for joint restoration of multiple window functions to enhance the spectral restoration performance of a single window function.This method leverages the advantages of different window functions,with the spectral representation dominated by a window function with strong resolution in high signal-to-noise ratio bands and a window function with strong noise resistance in low signal-to-noise ratio bands.Finally,the effectiveness of this method is validated by simulated spectral data.
spectroscopyinterferometric imaging spectrometerapodizationwindow functionspectrum restorationmultiple window function fusion
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