Fourier-Transform Imaging Spectroscopy (FTIS) has recently become a widely used tool for spectral imaging of biological fluorescent samples. Here we report on a novel double-pass FTIS system, that is capable of obtaining an excitation as well as an emission spectrum of the fluorescent sample with only a single sweep of the interferometer. This is achieved by modifying an existing FTIS system, placing the excitation source before the interferometer so as to spectrally modulate the excitation as well as the detection. An analysis of the acquired signal allows for the reconstruction of the excitation as well as the emission spectrum of each fluorophore assuming an independence of the two spectra for each fluorophore. Due to the patterned excitation generated by the Sagnac interferometer a substantial degree of optically sectioning is achieved at excitation wavelengths. Further analysis of the acquired data also enables the generation of optically sectioned emission images. A theoretical analysis and experimental data based on fluorescent beads are presented.