Considering the development of the need for small volume and light weight of spectral imaging systems on airborne platform, the characters of several main imaging spectrometers was analyzed and the present paper focuses on introducing imaging spectrometers featuring a grating or a prism disperser .A compact hyperspectral imaging system based on Offner relay configuration is reported. Combining the characters of the concentric Offner relay, and knowing the system design parameters, two novel kinds of spherical spectrometer systems using dispersive elements in divergent and convergent beam were designed. Moreover, the system MTF, spot diagram and the curves of smile and keystone were analyzed. The results show that these two kinds of Offner spectrometer achieve the purpose of a compact form of remote sensing system with excellent imaging quality close to diffraction limit. At the same time, decreasing the smile and keystone to a small (0.1) fraction of a pixel assures uniformity of acquiring spectral data.