In a stepped-mirror-based static Fourier transform infrared spectrometer, the expansion lenses based on classical lenses has several lenses, large aperture and overall length, and its volume and mass have major proportion comparing to the whole system. That limits the development of micro- miniature and lightweight spectrometer seriously. However, compound eye is helpful to solve the problem because it has these advantages including of compact structure, smaller volume and lighter weight. In this paper, the structure parameters of compound eye consist of three microlens arrays are analyzed by the method of matrix formalism and optimized by optics design software, and the stop array for weaken the stray light is designed. Finally, the interferogram and the recovered spectrum of the spectrometer are obtained by the ray tracing software, and the result shows that the designed expansion compound eye can meet the application requirement of the spectrometer.