Apodization effects in the retrieval of volume mixing ratio profiles

Norton-Beer apodization and its Fourier transform

In Fourier transform spectroscopy, apodization is used to alter the instrument line shape, reducing the prominence of its side lobes. The Fourier transform of the apodization window is of great interest as it allows us to compute or optimize the line shape. In the last decades, many apodization windows have been proposed, from which the group of Norton-Beer apodization functions gained large popularity in Fourier transform spectroscopy. While for a small set of specific Norton-Beer apodization functions analytical solutions of the Fourier transform have been presented in the past, we present here a general method, which allows us to calculate the analytical solution of the Fourier transform for any Norton-Beer apodization function. This paper also documents the free Python library called norton_beer. It contains functions to generate apodization windows and their Fourier transform following the presented analytical solution. Furthermore, new Norton-Beer apodization functions can be generated for any desired spectral resolution.

Extension of the Norton-Beer apodizing functions in Fourier transform spectrometry

Apodization is a mathematical tool used in Fourier transform spectrometry to reduce the spurious oscillation in the output spectrum. We investigate Norton-Beer apodizing functions and take advantage of the main series to introduce a family of new functions. They weigh the interferogram to zero continuously within the same optical path difference and, accordingly, improve the convergence property of the instrumental line shape (ILS) for the apodized spectrum. In the meantime, the range of spectral smearing is well reduced. Compared with the Norton-Beer functions, the new functions are more flexible in practice and are more applicable with regard to distinguishing the spectral lines, especially the weak lines, which are not too close to the center of a strong line but are still susceptible to the ringing of ILS.

Use of apodization in quantitative spectroscopy

Apodization, which is a tool frequently used for cosmetic representation and efficient modeling of a spectrum, is now also adopted in techniques for the quantitative retrieval of parameters from observed spectra. Whether apodization can help in quantitative spectroscopy is the subject of debate in the literature. We find that, when the considered spectral range is wide enough to accurately model the instrument line shape, the same results can be obtained with and without apodization of the spectrum. However, when a truncation error is introduced by the limited extension of the modeled spectral interval, apodization can efficiently reduce this error. Therefore it is possible to save computing time by using apodization.

Retrievals for the atmospheric chemistry experiment Fourier-transform spectrometer

SCISAT-1, also known as the Atmospheric Chemistry Experiment, is a satellite mission for remote sensing of the Earth's atmosphere, launched on 12 August 2003. The primary instrument on the satellite is a 0.02 cm(-1) resolution Fourier-transform spectrometer operating in the mid-IR (750-4400 cm(-1)). We describe the approach developed for the retrieval of atmospheric temperature and pressure from the troposphere to the lower thermosphere as well as the strategy for the retrievals of volume-mixing ratio profiles of atmospheric species.

Modeling the instrument line shape of Fourier-transform spectrometers within the framework of partial coherence

The instrument line shape (ILS) of Fourier-transform spectrometers is modeled within a framework that enables us to take into account the partial coherence of optical fields. The cross spectral density and the angular coherence functions are used to develop a global ILS model including all possible geometric defects that can be introduced by a realistic two-beam interferometer. Tilt and shear no longer only reduce the modulation efficiency but are presented as contributors to the ILS. The case of an incoherent secondary planar source is covered and agrees with previously known results. However, it shows a coupling among tilt, shear, and optical path difference (OPD). A quasi-coherent source is also studied. Differences between the incoherent and the quasi-coherent cases are highlighted. The relative localization of the reference laser beam in the interferometer is shown to be of significance to provide a sampling scale that minimizes the OPD, or phase, induced by angular misalignment.