变间隙法布里-珀罗干涉光谱仪光谱复原方法分析

Analysis of Spectral Restoration Method for Variable Gap F-P Interference Spectrometer

变间隙法布里-珀罗(F-P)干涉成像光谱仪以体积小、高光通量、高空间分辨率和高光谱分辨率等众多优势特性,成为研究热点。由于其干涉条纹不是正弦条纹,因而无法直接用快速傅里叶变换获得精确光谱曲线。详细推导了变间隙法布里-珀罗(F-P)干涉仪多光束干涉原理和其光谱复原原理,给出干涉条纹与光谱曲线的数学关系;从理论上证明了光谱复原方法的可行性和必要条件,并给出理论误差。此外,还基于MATLAB进行了仿真和光谱成像系统实物实验,验证了理论分析的正确性。为F-P干涉成像光谱仪的工程化提供了理论依据,并对设计中的参数确定具有指导意义。

Variable gap Fabry Perot(F-P)interferometric spectrometer imaging system has become a research hotspot because of its small size,large luminous flux,high spatial resolution,high spectral resolution and many other advantages.Because the interference fringes are not sinusoidal,the exact spectral curves cannot be obtained directly by fast Fourier transform.In this paper,the multi beam interference principle and spectral recovery principle of variable gap Fabry Perot(F-P)interferometer are derived in detail,and the mathematical relationship between interference fringes and spectral curves is obtained.Then,the feasibility and necessary conditions of the spectral recovery method are proved theoretically,and the theoretical error is given.In addition,the spectral imaging system based on MATLAB is simulated,and the physical experiments are carried out to verify the correctness of the theoretical analysis.It provides theoretical basis for the engineering of Fabry Perot(F-P)interference spectrometer imaging system,and has positive guiding significance for the determination of parameters in system design.