大光程差PEM-FTS的快速光谱重建

弹光调制傅里叶变换光谱仪(PEM-FTS)的调制光程差是高速、非线性变化，每秒可产生上万张干涉图。为了实现高速等时间采样干涉信号的快速光谱反演，对大光程差弹光调制干涉信号的特性、加速非均匀快速傅里叶变换算法(NUFFT)进行研究。加速非均匀快速傅里叶变换算法是基于卷积核函数插值的快速傅里叶变换算法，此算法的核函数类型、参数τ、延伸影响因子q、过采样率μ等参数的选择对算法准确度以及复杂度有影响。在分析这些参数对算法影响的基础上，在μ=2，q=10，τ=1×10-6时，将加速的NUFFT算法应用于弹光调制傅里叶变换光谱仪中，重建了632.8 nm的激光和氙灯光谱，复原的632.8 nm激光光谱的频率偏差小于0.013 52，插值时间小于0.267 s。实验表明加速的NUFFT算法有较快的运行速度和小的频率偏差，能快速准确地重建大光程差PEM-FTS的光谱。

The Technology of Fast Spectral Reconstruction in the Longer Optical Path Difference PEM-FTS

The optical path difference of the photoelastic modulator Fourier transform spectrometers(PEM-FTS) changes rapidly and nonlinearly, while the instrument preserves the speed as high as about 105 interferograms per second, so that the interferograms of PEM-FTS are sampled by equal interval. In order to fleetly and accurately reconstruct these spectrums, the principle of PEM-FTS and accelerated NUFFT algorithm were studied in the present article. The accelerating NUFFT algorithm integrates interpolation based on convolution kernel and fast Fourier transform(FFT). And the velocity and precision of the algorithm are affected by the type and parameter τ of kernel function, the single-side spreading distance q and the oversampling ratio μ, and so on. In the paper these parameters were analysed, under the condition N=1 024, q=10, μ=2 and τ＝1×10-6 in the Gaussian scaling factor, and the accelerated NUFFT algorithm was applied to the longer optical path difference PEM-FTS to rebuild the spectrums of 632.8 nm laser and Xenon lamp，The frequency error of the rebuilt spectrums of 632.8 nm laser is less than 0.013 52, the spent time of interpolation is less than 0.267 s. the velocity is fast and the error is less. The accelerated nonuniform fast Fourier transform is fit for the longer optical path difference PEM-FTS.