Desbiens Raphaël, Tremblay Pierre, Genest Jérôme, Bouchard Jean-Pierre
Centre d'Optique, Photonique et Laser, Département de Génie Electrique et de Génie Informatique, Université Laval, Québec, Canada.
Appl Opt. 2006 Jan 20;45(3):546-57. doi: 10.1364/ao.45.000546.
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.
傅里叶变换光谱仪的仪器线型（ILS）以矩阵形式表示。对于所有与波数成比例的线型效应，ILS矩阵在光谱域和干涉图域中表现为转置。ILS矩阵在干涉图域中的新表示形式对产生自变迹的潜在过程给出了深刻的物理解释。在干涉图域中工作避免了考虑有限光程差影响的问题，并允许对方程进行适当的离散化。引入了一种基于分数傅里叶变换的O(N log2 N)快速算法，该算法允许将恒定分辨能力线型应用于理论光谱或正向模型。ILS积分形式通过实验数据得到验证。
