Fig. 1. Synchronous sampling and asynchronous sampling. (a) Spectrum without leakage; (b) spectrum with leakage; (c) interferogram imaging and spectral recovery process

Fig. 2. Comparison of the ability of three classical window functions to distinguish two adjacent spectral lines. Cosine waves with wave numbers (a1) σ₁=10.1 μm⁻¹ and (a2) σ₁=10.6 μm⁻¹, as well as (a3) the synthesized signal; waveforms of signals after (b) Hamming and (c) Hanning window apodization; spectrum restoration results after (d) rectangular, (e) Hamming, and (f) Hanning window apodization

Fig. 3. Time-domain and frequency-domain graphs of improved apodization functions. (a) Time-domain graph of the improved H-G function from Ref. [12]; (b) time-domain graph of the improved pre-and-post triangular window function from Ref. [15]; (c) frequency-domain comparison of the improved H-G function and the improved triangular window function

Fig. 4. Spectra of Chebyshev window and improved Chebyshev window. (a) Comparison of Chebyshev window and Hamming window; (b) comparison of Chebyshev window and triangular window; (c) improved Chebyshev window in Ref. [16]

Fig. 5. Restored spectra obtained by processing one simulated interferogram with three window functions. (a) Simulated interferogram; (b)-(d) restored spectra after applying H-G strong apodization function, Hamming window, and Chebyshev window, respectively

Fig. 6. Interference data obtained by Chang’e-1 interferometric imaging spectrometer and restored spectra under different apodization methods. (a) Original interference data; (b) interference data after removing DC component; (c) interference data apodized with Hamming window (using the Hamming window as an example); apodization results of (d) rectangular window, (e) Hanning window, (f) Hamming window, (g) H-G strong apodization function, (h) Chebyshev window (sidelobe height is -31.5 dB), and (i) Chebyshev window (sidelobe height is -42.5 dB) functions

Fig. 7. Comparison between the spectra after weighting with two window functions and the original spectrum. (a) Apodized with Chebyshev window of -31.5 dB sidelobe height; (b) apodized with Hanning window; (c) spectrum at a=0.8; (d) spectrum at a=0.6

Fig. 8. Fusion spectra under different window function combinations. (a) Chebyshev window+H-G strong apodization function+Hanning window; (b) rectangular window+H-G strong apodization function+Hanning window+Hamming window; (c) Chebyshev window+rectangular window+H-G strong apodization function+Hanning window+Hamming window; (d) Chebyshev window+rectangular window+H-G strong apodization function+Hanning window+Hamming window+triangular window

Fig. 9. Results of applying the weighted fusion algorithms to simulated interferograms. (a1) True spectrum and degraded spectrum after noise addition; (a2) simulated interferogram; (b) restored spectra using Hanning and Hamming windows; (c) restored spectra using rectangular window and H-G strong apodization function; (d) comparison results among fused spectrum, true spectrum, and restored spectrum using Hanning window