共轭傅里叶变换校正成像光谱重构

李苏宁; 朱日宏; 高志山; 李建欣

doi:doi:10.3788/aos201131.0412010

光学学报, 2011, 31 (4): 0412010, 网络出版: 2011-03-30

共轭傅里叶变换校正成像光谱重构

Fourier Conjugate Correction Spectral Reconstruction for Fourier-Transform Spectrometer

论文大纲

李苏宁 ^*朱日宏高志山李建欣

作者单位

南京理工大学电子工程与光电技术学院, 江苏南京 210094

傅里叶光学成像光谱重构光谱曲线傅里叶变换共轭校正 Fourier optics imaging spectroscopy reconstruction spectrum Fourier transform conjugated correction

摘要

傅里叶变换干涉成像光谱仪的光谱重构过程主要基于光源光谱和其对应干涉图的傅里叶变换对关系。采用傅里叶变换或余弦傅里叶变换方法可完成重构，但该两种方法由于没有消除变换过程中由引入相位信息和边界条件而产生的误差，会给光谱重构精度尤其是光谱强度重构精度造成负面影响。针对该问题，提出了一种针对傅里叶变换干涉成像光谱仪的共轭校正光谱重构方法，利用傅里叶变换的共轭性质，首先对预处理后的干涉图作共轭对称，然后采用傅里叶变换求得共轭光谱项及共轭校正项，再通过这两项校正得到真实光谱。经仿真和利用氦灯进行实验，可以验证，相对传统的光谱重构方法，该方法兼顾了干涉图和光谱图的实数域问题，同时也解决了余弦傅里叶变换的边界条件问题，采用重构光谱与定标光谱差值的均方根值进行评价，相比于定标光谱，该方法的重构光谱频率一致性和强度一致性均优于0.1%，较之传统方法，其对于光谱强度的重构精度一致性可提高5%，对傅里叶变换成像光谱仪的光谱重构方法研究工作具有指导意义。

Abstract

The spectral reconstruction theory of Fourier-transform imaging spectrometer is based on the Fourier-transform relationship between the spectrum of the source and the interferogram so that the spectral reconstruction can be simply achieved by using Fourier transform or Fourier cosine transform. However, the traditional Fourier transform solution is carried out in the complex-number field and the result is also a complex-number sequence. To acquire the real-number reconstructed spectrum, people usually use the real part or the absolute magnitude of the transformation result as the reconstructed spectrum, which will introduce in an extra-phase to the spectrum and lead to inaccuracy of reconstructed spectral intensity. Although reseachers use Fourier cosine transform to avoid the extra-phase problem effectively, this solution has a boundary condition problem which cannot be avoid and may also lead to inaccuracy of reconstructed spectral intensity. To solve the problem, on the base of the analysis of traditional reconstruction solutions, an improved spectral reconstruction solution based on Fourier conjugate correction (FCC) for Fourier-transform spectrometer is developed and discussed. Firstly the conjugated symmetrical form of the interferogram sequence is created by the use of the original interferogram captured, and then the conjugated symmetrical spectrum and the correction element can be acquired by carrying out Fourier transform to the sequence. By using the conjugated symmetrical spectrum and the correction element, the real-number spectrum sequence can be calculated. By carrying out both the simulation and the experiment using helium lamp, it can be concluded that the FCC solution can avoid either the extra-phase problem caused by discrete Fourier transform (DFT) solution or the boundary condition caused by discrete Fourier cosine transform (DCT) solution effectively and improve the reconstructed spectral intensity accuracy.

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李苏宁, 朱日宏, 高志山, 李建欣. 共轭傅里叶变换校正成像光谱重构[J]. 光学学报, 2011, 31(4): 0412010. Li Suning, Zhu Rihong, Gao Zhishan, Li Jianxin. Fourier Conjugate Correction Spectral Reconstruction for Fourier-Transform Spectrometer[J]. Acta Optica Sinica, 2011, 31(4): 0412010.

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