The Linear Measure Instrument (LMI) based on image processing techniques is the major equipment for measuring the swinging mirror fixed on space infrared camera. Traditional error analysis methods neglect the facula streaking effect, so the measure uncertainty is increased. A model of facula displacement, pixel noise and facula gray centroid algorithm is established. The model indicates that if the facula displacement in exposure time is far less than the static facula size, the dynamic measure error is closed to static measure error. However, if the ratio between facula displacement and facula static size is bigger than 6%, the variance of dynamic gray centroid algorithm error will be 20% more than static error variance. Then the exposure time shall be reduced and emergent power of light source shall be increased to reduce the dynamic measuring error of gray centroid algorithm.