The spectral noises or spectral resolution is the main criterion for spectrometer, but it is not suitable for tolerance analysis and optical optimization. Therefore, the system is divided into three sub-systems: the front optical system, the interferometer and the post optical system, and three different criterions are taken separately. Wavefront errors is taken as criterion by the front optical system, and then the relationship between wavefront errors and spectral noises is analysed. If the changes in wavefront errors by the manufacturing and alignment errors are calculated, the influence on system performance could also be evaluated. Spectral noises can be taken as criterion by the interferometer, and the changes in system performance is evaluated directly. The spot diameter is taken as the criterion by the post optical system. Through this way, the sensitivity for three sub-systems and the tolerance tables on the front and post optical systems are listed.