Static Fourier transform spectrometers require, especially in the infrared, a spatial calibration step. Unfortunately, the superposition of fringes on the measured images has a major impact on spatial calibration and therefore on the returned spectra. We first study how to pre-process images so that spectral errors are minimized. Then, we develop a spectrum formation model that is used to correct those spectral errors. The performance, evaluated on synthetic data, is remarkable and theoretically justifies the use of this calibration concept.