窄带傅里叶变换光谱仪中平稳高斯噪声的理论分析

在本文所研究的空间调制型傅里叶变换光谱仪中, 在窄的光谱带宽内进行探测可以有效提高光谱的分辨率. 为了研究光源辐射噪声对系统的影响, 本文将辐射噪声归纳为一种高斯窄带的平稳随机过程, 利用线性系统分析方法, 根据统计学原理推导了辐射噪声作为随机变量通过干涉系统前后的输入信噪比与输出信噪比. 然后, 对于一个具有窄带矩形光谱的系统进行了计算仿真, 得出了信噪比增益随着光程差在不同自相关度和互相关度取值时的变化情况. 仿真结果表明, 不同光程差下的信噪比增益在相关度空间是一单调的平滑曲面, 增益极值始终沿着相关度圆的半径和周线移动, 并且经过一个光程差又回到初始的位置. 根据对信噪比增益的分析, 可以将噪声的相关度取值控制在某一范围之内, 并作为系统光源设计与测试的依据.

Theoretical analysis on stationary Gaussian random noise in narrowband Fourier transform spectrometer

The spectral resolution can be increased by detecting the optical signal in a narrowband spectrum for the Fourier transform spectrometer based on spatial modulated in our study. In this paper, to study the effect of the radiant source on the interference system, we regard the radiant noise as a narrowband stationary Gaussian random process. Using the linear system analysis method and the statistical theory, we deduce the input signal-to-noise ratio (SNR) and the output SNR after the optical signal and the radiant noise have passed through the interference system. Then we simulate the system and compare the obained result with a narrowband rectangle spectrum, and obtain the SNR gains along the optical path difference (OPD) in different autocorrelation degree and cross-correlation degree values. The simulation result indicates that the SNR gains at different OPDs in the correlation degree space each are a monotonic smooth surface. The SNR gain maximum moves along the radius and the contour of the correlation degree circle, and it returns to the initial position. after an OPD According to the analysis of the SNR gain, the autocorrelation degree and cross-correlation degree values can be controlled in a certain area, which can serve as a criterion for the design and the test of the radiant source.