A new type of infrared spectroscopic ellipsometer has been designed and constructed. A double-Fourier-transform method, i.e. Fourier transforms carried out as both functions of the photon energy and azimuthal angle, is used. Using the configuration of synchronous rotation of the polarizer and analyzer (RAP), and according to four cosine frequencies of Fourier transform, the optical constants can be obtained with any one of two sets of ac signal calculations. After a revised model being used to correct the data error arising from the slight anisotropy of analyzer the data self-consistency is improved to be better than 1% by comparing two sets of data. The spectra of the dielectric function for a Au film sample were measured and fitted with the Drude model. The result shows a very good agreement between experiment and theory.