针对传统长波红外成像光谱仪难以同时实现弱遥感信号下高信噪比和小型化的现状，在数值孔径NA为0.19和0.33，工作波段为8~12 μm下，设计并对比分析了两种具有同心结构的Offner凸面光栅和Dyson凹面光栅光谱仪，借助Zemax软件，获得了它们的最优解。当NA1=0.19时，两者均能理想成像，Offner结构大小为245 mm×213 mm×111 mm，调制传递函数(MTF)大于0.38，光谱分辨率为35 nm，谱线弯曲小于4.8% , 色畸变小于12.8%；Dyson结构大小为308 mm×61 mm×49 mm，MTF大于0.48，光谱分辨率为12 nm，谱线弯曲小于0.047%，色畸变小于0.138%。当NA2=0.33时，Offner结构无法理想成像，Dyson结构仍有很好的像质，大小为317 mm×88 mm×88 mm，MTF大于0.71，光谱分辨率为1 nm，谱线弯曲小于0.015% ,色畸变小于0.028%。设计结果表明，长波红外波段中，相对于Offner结构，Dyson结构具有数值孔径大、体积小、光谱分辨率和传递函数高以及谱线弯曲和色畸变小的优点。

In view of the difficulties in traditional long-wave infrared imaging spectrometer which is hard to realize a high signal-to-noise ratio and miniaturization as well under the weak remote sensing signal, two types of concentric optical systems, Offner convex grating and Dyson concave grating imaging spectrometers, are designed and analyzed under the common numerical apertures (NA) of 0.19 and 0.33 with spectral range of 8~12 μm. The optimal structures are achieved by optical design software Zemax. The two structures both have a perfect image at NA1=0.19, the size of Offner structure is 245 mm×213 mm×111 mm, value of modulation transfer function (MTF) is higher than 0.38, spectral resolution is 35 nm, smile is lower than 4.8% and keystone is lower than 12.8%. The size of Dyson structure is 308 mm×61 mm×49 mm, value of MTF is higher than 0.48, spectral resolution is 12 nm, smile is lower than 0.047% and keystone is lower than 0.138%. Dyson has an ideal image at NA2=0.33 different from Offner. The size of Dyson structure is 317 mm×88 mm×88 mm, value of MTF is higher than 0.71, spectral resolution is 1 nm, smile is lower than 0.015% and keystone is lower than 0.028%. It is obvious that Dyson structure possesses advantages of larger numerical aperture, smaller volume, higher spectral resolution, higher MTF, lower smile and lower keystone in long-wave infrared wavelengths compared with Offner structure.