From the output atlas theoretical model of the image replicating imaging system, to improve the existing 16-band system and focused on the design of large relative-aperture and compact system, the design and optimization of 16-band spectral imaging system were performed with Zemax-EE software. This work focused on the analysis of the problem of the image aliasing resulted from the birefringence of the prisms. By matching the spectral imaging system and using the Zemax muti-configuration, the imaging quality of the system was simulated. The viewing field angle is ±1.25°, the relative-aperture is 1∶3 and the size of the system is about 220 mm (z). The modulation transfer function of every viewing field of every wavelength is more than 0.75 under the Complementary Metal Oxide Semiconductors (CMOS) Nyquist frequency situation. Compared with the existing equivalent spatial resolution of 16-band image replicating imaging spectrometer, this design is more compact which meets the requirement of miniaturization. The diffraction limit and light quantity are improved, so the imaging quality is significantly improved. The research provides a new design basis for the theoretical study of new type of snapshot imaging technology and for the design of the image replicating imaging spectrometer.