Sparse-aperture optical imaging system has affixed filling factor and certain transfer function characteristics. In order to improve the imaging performance of the system, and enhance its Intermediate Frequency (IF) information. the influence of the zoom structure on the imaging of the discrete sparse aperture system is analyzed, and the relationship between the focal length, filling factor and Modulation Transfer Function (MTF) is derived. A sparse-aperture telephoto imaging system with adjustable focal length in the range of 2857~4000mm is designed. The analysis of imaging characteristics shows that when the focal length of the system decreases, the filling factor increases, and the cut-off frequency of the MTF decreases, but the IF response of the MTF increases. Through image fusion, the clear IF fringe information of large filling factor is used to compensate the missing IF fringe information of small filling factor. The simulation imaging results show that the images obtained based on different filling factors can effectively improve the image quality of each frequency band of the whole image after fusion.