用Burg算法提升空间调制傅里叶光谱仪分辨率与定阶方法

马铎轩; 彭月祥

光学与光电技术, 2018, 16 (2): 55, 网络出版: 2018-06-01

用Burg算法提升空间调制傅里叶光谱仪分辨率与定阶方法

Spatial-Modulated Fourier Spectrometer Resolution Improvement Based on the Burg Algorithm and Order Determination

论文大纲

马铎轩 ^*彭月祥

作者单位

北京工业大学应用数理学院, 北京 100124

摘要

对于空间调制傅里叶光谱仪来说,由于数据长度受到CCD像元数量和最大光程差的限制。而分辨率大小反比于数据的实际长度,因此通常经过傅里叶变换所得到的分辨率是受到了数据长度的限制的。除了增加CCD像元数量、更改像元尺寸、改善光路等改变硬件的方法外,还可以使用现代谱估计的方法,通过对数据建立模型进行外推,从而有效扩充数据长度,提高分辨率。利用Burg算法,计算空间调制傅里叶光谱仪所得数据的自回归(AR)模型功率谱。通过此方法获得的计算结果在适当的AR模型选阶的情况下,具有高计算分辨率的特点,并且在获得数据的空间频率较低、像元数量较少的情况下仍然拥有一定的频率分辨能力。实验计算了不同选阶之下,FFT算法和不同选阶下Burg算法测量结果与其稳定程度,说明了Burg算法的选阶对光谱分辨率有着切实的影响,而且应用补零的FFT算法虽然无法提高光谱的分辨能力,但是会通过减少栅栏效应增强光谱计算分辨率,并且稳定程度与Burg算法在适当选阶下相近。

Abstract

For the spacial modulated Fourier spectrometer, the data length is limited by the number of CCD pixels. And the frequency resolution is inversely proportional to the actual length of the data, so the resolution obtained by the usual Fourier transform is limited by the length of the data. Except for the method of changing the hardware by changing the number of CCD pixels and changing the cell size, the modern spectral estimation method cam be also used. The data model is estblished and extrapolated, so as to extend the length of data and improve the resolution. In this paper, the Burg algorithm is used to calculate the power spectrum of the auto-regressive model of the data obtained by the spacial modulated Fourier spectrometer. The results obtained by this method have the characteristics of high computational resolution in the case of the appropriate AR model selection order, and still have some frequency resolution ability when the spatial frequency of the data is limited. Experimental results show that the order of Burg algorithm effects frequency resolution and although spectral resolution can not be improved by using zero fill before FFT, it obtains a result whose stability is similar to the result using Burg algorithm.

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马铎轩, 彭月祥. 用Burg算法提升空间调制傅里叶光谱仪分辨率与定阶方法[J]. 光学与光电技术, 2018, 16(2): 55. MA Duo-xuan, PENG Yue-xiang. Spatial-Modulated Fourier Spectrometer Resolution Improvement Based on the Burg Algorithm and Order Determination[J]. OPTICS & OPTOELECTRONIC TECHNOLOGY, 2018, 16(2): 55.

用Burg算法提升空间调制傅里叶光谱仪分辨率与定阶方法

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