[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 10(5) 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 tau of kernel function, the single-side spreading distance q and the oversampling ratio micro, and so on. In the paper these parameters were analysed, under the condition N = 1 024, q = 10, micro = 2 and tau = 1 x 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.