数字微镜哈达玛光谱仪谱线弯曲的分析与修正

由于数字微镜（digital micro-mirror device, DMD)哈达玛变换光谱仪其成本低，光能利用率高及无运动部件等优势，逐渐成为光谱仪领域的研究重点。研制了一款基于DMD的哈达玛变换光谱仪。为了解决光谱仪谱线弯曲造成的光谱分辨率下降的问题，对基于DMD的哈达玛变换光谱仪中的谱线弯曲所引起的谱带混叠进行了分析。首先，导出了谱带混叠与谱线弯曲的关系式。然后，提出了两个过程来解决谱带混叠，一是通过调整DMD编码条纹，使DMD所编码的谱带最大限度地与标准谱带重合; 二是通过数据处理对谱带混叠进行修正。最后，通过对谱线曲率半径为5.8×104，7.8×104和9.7×104 μm等六种情况下谱带混叠进行了分析与修正，拟合出光谱混叠和修正效果与谱线曲率半径的关系。结果表明： 对于不同程度的谱线弯曲经过这两个过程修正后，分辨率都会改善到接近光学系统的分辨率, 说明这两个过程对修正谱线弯曲具有普适性、并且方法简单、有效。

Analysis and Correction of Spectral Curvature in Hadamard Transform Spectrometer with DMD

Due to the advantages of its low cost and high utilization rate of light energy and no moving parts ,Hadamard trans-form spectrometer with DMD has become a focus in the research of spectrometer .In order to solve the reduction of spectral reso-lution caused by the spectral curvature of Hadamard transform spectrometer with DMD (Digital Micro-mirror Device) ,the spec-tral aliasing in the spectrometer was investigated .Firstly ,the mathematical relationship of spectral aliasing to radius of spectral curvature was deduced .Then ,two procedures were proposed to solve the spectral aliasing .One is making the DMD encoded spectral band accordant with the standard spectral band as far as possible by adjusting the DMD-encoded stripe ,and another is correcting remaining spectral aliasing by means of data processing .Finally ,by analyzing and correcting spectral curvature in six situations of the curvature radius of 15.8 × 104 ,7.8 × 104 ,9.7 × 104 μm and etc ,we fit out the relationship of spectral aliasing and spectrum correction effect of spectral curvature to the curvature radius .The simulation indicates that the spectral resolution increases to the resolution of optical system .It shows that the proposed methods are universal ,simple and effective in the im-provement of spectral resolution .