A 120 nm-180 nm far ultraviolet(FUV)imaging spectrograph with two detectors was developed.A method for establishing an analysis model of its sensitivity and signal-noise-ratio(SNR) was proposed based on the signal statistical detection theory and the threshold detection theory.First,the distribution of photoelectric current of accepted signals and the probability of the system noises were studied.Then the mathematical models of sensitivity and SNR of the instrument were deduced by introducing detection prob...