Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferograrn domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log(2).N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data. (c) 2006 Optical Society of America.