Radiometry in line-shape modeling of Fourier-transform spectrometers

A radiometric model of the instrument line shape (ILS) of Fourier-transform spectrometers is presented. We show first that common line-shape models are based on distribution of the radiant intensity in the interferometer. The complete steps between the source and the ILS are exposed as the core of the model. Relationships between the ILS, the spectrum as measured by the instrument, and the spectrum as emitted by the scene are demonstrated from the ILS model. Then the formal radiometric modeling of the ILS is derived, including the contribution of the aperture of the optical system. The particular case of a centered circular aperture with a uniform Lambertian radiance in the field of view is discussed. Conditions are deduced to ensure that the only spectral variation of the ILS is a scaling with wave number, as is usually assumed in current line-shape models. The ILS dependence on the scene is also discussed, and the effect of taking into account the radiometry on the ILS is estimated for the case of an ideal thin lens used as a collimator.