The optical properties of the Fourier transform spectrometer such as the size of source, the ununiformity of the intensity and the aberration of the optical system are analysed. It is shown that the large size of source caused the double peaks and lower spectral resolution, the ununiformity and the aberration cause the noises on the base line. The numerical results show that the noises can be ignored as the size of source at the stop is smaller than 2.5 mm, the standard deviation of intensity is smaller than 0.5, the root-mean square (RMS) of wavefront aberration for the collimating lens is smaller than 0.05 waves, and the RMS of spot diameter for constricted lens is smaller than 30 μm. The design of optical systems is proposed.