Atmospheric sounding requires high-resolution spectrometers, such as Fourier transform interferometers. Classical ones need moving mirrors to scan the spectrum, but static interferometers with stepped mirrors can achieve high resolution in within a narrow spectral band. CNES is developing such an instrument for CO2 flow monitoring. The breadboard includes two stepped mirrors, a separating plate, a double imaging system and a detector array. To simulate the actual instrument response, we developed a physically realistic model of the full optical system with ASAP, a software well suited for broad sources, partial coherence and non-sequential propagation. After checking the theoretical interferogram and the resulting instrument spectral response for a point source, we simulated the effects of field, coherence length and chromatism. Then we studied the complex ghost reflections between the mirrors, the separating plate, the optics and the detector, taking coherence into account. Resulting interferograms and spectra were compared to the nominal ones. It appears that the most critical ghosts are not the most intense but the best focused, especially when interfering with the nominal waves. Scatter is tolerable, as it is incoherent and relatively uniform. These results led to design improvements and alignment requirements on the breadboard. This study illustrates how physical modeling can contribute to the early design of complex, non-imaging systems.