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Updated: Aug 11, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
Published on: December 30, 2025
Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to
Raphaël Desbiens1, Pierre Tremblay, Jérôme Genest
1Centre d'Optique, Photonique et Laser, Département de Génie Electrique et de Génie Informatique, Université Laval, Québec, Canada.
Abstract:
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 interferogram 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 log2 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.
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