Matching the cold shield with the exit pupil of the fringe-imaging system of long-wave infrared (LWIR) spatial heterodyne spectroscopy (SHS) damages illumination uniformity of the interferogram and affects the fringe contrast, which is a significant parameter for LWIR SHS. The optical models of the fringe-imaging system considering and not considering the pupil matching of the cold shield are built to illustrate the effect on the fringe contrast. Simulations based on the optical design software ASAP are conducted to verify the fringe contrast loss for field-widened LWIR SHS. The result shows that the pupil matching of the cold shield decreases the fringe contrast of LWIR SHS and field-widened LWIR SHS by 0.049% and 0.053%, respectively, and the fringe contrast loss increases with the degree of deviation from the telecentric condition of the fringe-imaging system. © 2021 Optical Society of America.