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由于传统的快速傅里叶变换(FFT)只适用于均匀采样的情况,对非均匀采样的干涉数据直接进行FFT会导致反演光谱的失真。针对该问题,国外的很多学者对非均匀快速傅里叶变换(NUFFT)方法进行了研究,并形成了比较成熟的理论。将NUFFT方法应用到干涉数据的光谱反演中,对不同采样频率和不同非均匀程度下的光谱反演精度进行了分析仿真,可以看出,在部分欠采样情况下,采样频率是影响光谱反演精度的主要因素;在过采样情况下,光程差的非均匀采样程度是影响反演精度的主要因素。实际应用中,需要综合考虑数据量、采样频率和光程差的非均匀采样程度来确定最终的参数。为了保证光谱反演的精度,获取的干涉数据中不存在部分欠采样是最基本的原则。
Since conventional Fast Fourier Transforms (FFTs) are only suitable for uniform sampling, performing FFT directly on the non-uniformly sampled interference data can lead to distortion of the inverted spectrum. In response to this problem, many foreign scholars have studied the non-uniform fast Fourier transform (NUFFT) method, and formed a relatively mature theory. The NUFFT method is applied to the spectral inversion of the interference data, and the spectral inversion accuracy under different sampling frequencies and different non-uniformities is analyzed and simulated. It can be seen that in the case of partial undersampling, the sampling frequency is the influence of spectral inversion The main factor of the accuracy of the performance; In the case of oversampling, the degree of non-uniform optical path difference sampling is the main factor affecting the accuracy of the inversion. In practice, the final parameters need to be determined by considering the amount of data, the sampling frequency and the degree of non-uniform sampling of the optical path difference. In order to ensure the accuracy of spectral inversion, it is the most basic principle that there is no partial undersampling in the acquired interference data.