由于中阶梯光栅光谱仪采用交叉色散的结构，在像面上呈现二维重叠光谱，光谱信息难以直接获取，所以使得光学系统设计与光谱信息处理较为繁琐。建立了一种基于边界限制的中阶梯光栅光谱仪快速设计与二维谱图的分析算法。讨论了中阶梯光栅光谱仪各性能参数的相互制约关系，建立了系统指标、结构参数与二维谱图的计算模型。该算法能够根据给定的系统指标快速计算出系统参数，根据系统参数构建二维谱图模型，并根据谱图模型评估结果对参数进行修正，提供中阶梯光栅光谱仪的快速设计与谱图分析方法。利用该数学模型设计了一台波段范围为200~900 nm，在200 nm处的分辨率为25000的中阶梯光栅光谱仪，经初步测试，仪器满足系统指标要求。

Echelle spectrograph has two-dimension spectra on the image plane for its cross-dispersion structure, which makes it hard to design and analysis. In order to overcome these difficulties, an efficient algorithm based on the limits of boundary is described. The mathematic model is developed between the system requirements, structure parameters and two-dimension echelle spectra. This algorithm can obtain the echelle spectrograph parameters quickly according to the system requirements, and establish the echelle spectra using these parameters, and then the parameters are modified according the results of echelle spectra, which provide a valuable method for designing echelle spectrograph and analysing spectra. Utilizing this model an echelle spectrograph is designed with the wavelength range of 200~900 nm and the spectral resolution of 25000 at 200 nm. After the measurement, this configuration can meet the needs of system.