The infrared search and track system (IRST) is a type of special electrical optical (EO) system that can be used in various scenarios to fulfill situation awareness, reconnaissance, and tracking of targets. We proposed a homogeneous coordinate transformation method to analyze the residual image wandering induced by the rotation of the scanning platform and the compensation fast steering mirror and help with the commonly trivial selection of the telescope magnification and the objective focal length. The analysis and simulation are carried out with specified IRST optics, which adopt a 640 x 512 array and 15 mu m pitch detector, in a focal range of 60 mm similar to 360 mm, and a scan speed of 360(circle)/s to 60(circle) /s at 50 fps, and optical specifications are determined further. The presented optical system, with only three kinds of common infrared materials, works at 3.7 mu m similar to 4.8 mu m, demonstrates good image performance and tolerance characteristics, and shows potential in manufacturing. Also, the resulting image wandering of 8 mu m, less than a 0.6-pixel size, at an integral time of 16 ms, proves the correctness of the method and makes the scheme of considerable interest for electrical optical systems.