中文摘要：

干涉光谱成像仪获取的干涉数据是一种中间数据,需要进行光谱反演才能够得到目标光谱数据,傅里叶变换方法是常规的光谱反演方法。由于干涉数据中存在非均匀采样问题,若忽略光谱混叠,直接采用快速傅里叶变换会导致反演光谱的失真,难以满足实时处理需求。针对非均匀采样干涉数据的光谱反演需求,将插值及非均匀快速傅里叶变换（NUFFT）方法应用到光谱反演处理中,对过采样及部分欠采样情况下的非均匀采样干涉数据,提出了相应的光谱反演方法,并分析了方法的适用性。最后对过采样及部分欠采样情况下的光谱反演方法进行计算机仿真,过采样情况下采用NUFFT方法反演光谱的精度要明显高于插值方法,而部分欠采样情况下插值方法反演光谱的精度要明显高于NUFFT方法,并对欠采样造成的光谱混叠有一定的修正,验证了方法的有效性。

英文摘要：

The interferogram acquired by imaging Fourier transform spectrometer （IFTS） can’t be used directly and must be recovered. The spectrum recovery processes based on fast Fourier transform （FFT） is the traditional method which is used widely. For some IFTS, the nonuniform sampling of the interferogram is often occurrs. When the aliasing is neglected, the spectrum recovered by traditional method is often distorted. When the spectrum recovery processes based on Fourier transform are used, the precision of the recovered spectrum can be ensured, but the real-time processing requirement can’t be satisfied. In order to acquire the precise recovered spectrum of the nonuniform sampled interferogram, the interpolation method and nonuniform fast Fourier transform （NUFFT） method were adopted. For the oversampled interferogram and partial undersampled interferogram, the spectrum recovery methods based on interpolation and NUFFT were presented respectively, and the applicability of these two methods is given. Finally, the computer simulation was performed, and the results indicate that NUFFT method is preferable to interpolation method not for undersampled interferogram but for oversampled interferogram.