针对傅里叶变换光谱仪中的非线性光谱复原精度低的问题,研究了一种基于快速高斯网格(FGG)法的非线性光谱复原方法。首先研究了基于FGG法的非均匀傅里叶变换理论,利用仿真结果验证了FGG法的高复原精度及其可行性。搭建了双折射偏振干涉光谱测量实验装置,利用该方法对非等间隔采样的干涉信号进行了光谱复原处理,复原结果与光谱仪的测量结果基本一致。理论仿真和实验结果均表明,采用FGG法能够有效实现非线性光谱复原。 Aiming at the problem of low nonlinear spectral restoration accuracy in Fourier transform spectrometer, a nonlinear spectral restoration method based on fast Gaussian grid (FGG) method is studied. Firstly, the non-uniform Fourier transform theory based on FGG method is studied. The simulation results verify the high recovery accuracy and feasibility of FGG method. A birefringence polarization interference spectrometer experimental setup was set up. By using this method, the interference signals sampled at different intervals were subjected to spectral restoration. The reconstructed results were basically the same as those of the spectrometer. The theoretical simulation and experimental results show that the FGG method can effectively achieve nonlinear spectral recovery.