Total power calibration in FTIR emission spectroscopy for finite interferograms

The NYAEM-FTS (Ny-Ålesund emission Fourier transform spectrometer) measures thermally emitted atmospheric radiation at a resolution of 0.08 cm ⁻¹ at Ny-Ålesund, Svalbard, since August 2019. To achieve this resolution, the spectrometer records interferograms in single-sided mode with a maximal optical path difference of 11.25 cm. The commonly used total power calibration procedure in FTIR (Fourier transform infrared) emission spectroscopy first described by Revercomb et al. (1988) is strictly speaking only valid for double-sided, infinite interferograms. In order to correctly apply total power calibration to the NYAEM-FTS, we investigate the effect of interferogram truncation on calibrated mid-resolution emission spectra, describe the underlying theory, and quantify the errors in a case study. While application of the Revercomb formula might lead to large errors in the unequal-sided case, we show that one can obtain the same spectral estimate as from equal-sided interferograms. This is achieved by modifying Revercomb's method by incorporating a phase correction procedure using low-resolution phase spectra from the blackbody measurements. Since an error estimate requires idealized, quasi-infinite interferograms, we include a case study using simulated atmospheric and blackbody spectra with a line-by-line radiative transfer model, allowing e.g. for making informed decisions on retrieval window selection. For the mid-resolution use case with Arctic atmospheric conditions, we find that the effect of truncation on the spectral radiance measurement is generally well below 0.04 % in winter and 0.02 % in summer in spectral regions commonly used in trace gas retrievals with the AERI (Atmospheric Emitted Radiance Interferometer) and that the retrieval bands could be extended up to 1350 cm ⁻¹ . At higher wavenumbers where strong water vapor absorption lines in the blackbody spectra are present, the effect can be substantially larger. We also find that the method presented here reduces the maximal error in a band just below 1350 cm ⁻¹ from 0.39 % to 0.07 % in winter and from 3.4 % to 0.6 % in summer for unequal-sided interferograms compared to the standard method. We recommend that such a quantitative analysis always be performed when applying total power calibration, since the quantitative effects are different for each use case.