弹光调制傅里叶变换光谱仪(PEM-FTS)的调制光程差是高速、正弦变化的，每秒可产生10万张干涉图。为了实现等时间采样干涉信号的快速、低误差光谱反演，三次样条插值算法、带有相位补偿的离散傅里叶变换(NDFT)算法和加速非均匀快速傅里叶变换算法(NUFFT)分别被应用到PEM-FTS的数据处理系统中。研究发现，对等时间采样弹光调制干涉数据进行光谱反演，加速NUFFT算法数据处理速度比较快，较相位补偿的NDFT算法高一个数量级，是三次样条插值后快速傅里叶变换算法的2倍，且采样点数越多此算法优点越突出；有比较高的精度，其偏差小于0.00054。该算法可以应用于弹光调制傅里叶变换光谱仪中。

The optical difference variation of the photoelastic modulate fourier transform spectrometers (PEM-FTS) is sinusoidal and high-speed, so more than 105 interferograms per second is acquired. In order to fleetly and accurately recover the spectrums of the signals which are sampled by equal interval, the cubic spline interpolation algorithm, nonuniform discrete Fourier transform (NDFT) with phase compensation algorithm, and accelerating nonuniform fast Fourier transform (NUFFT) algorithm are applied in the data processing system of PEM-FTS. It is found that the accelerating NUFFT is fast, and its speed is an order of magnitude higher than that of NDFT with phase compensation, and two times of that of the FFT with cubic spline interpolation algorithm. The advantage of the method is obvious when the number of sampling points is increased. And the precision of the method is high with its deviation less than 0.00054. The method can be applied in PEM-FTS.