FTIR (Fourier transform infrared) emission spectroscopy is an established tool in atmospheric remote sensing. It is used to validate radiative transfer calculations, to continuously measure the thermodynamic state of the atmosphere (temperature and water vapor content) and the radiative properties of clouds . It has also been used in trace gas and aerosol retrievals . Contrary to solar absorption spectroscopy no sunlight is required in emission spectroscopy. It has the advantage that diurnal cycles can be monitored better and it also works during (polar) night. One of the well-known instruments commonly deployed for ground-based FTIR emission spectroscopy is the AERI (Atmospheric Emitted Radiance Interferometer, ) which measures down-welling radiation in the mid-infrared spectral range with a resolution of 1 cm⁻¹. It records equal-sided interferograms.

The spectral resolution of the AERI is one of the limiting factors for vertical sensitivity to trace gases . In solar absorption spectroscopy it is common to use much higher spectral resolution in order to fit line shapes which contain information about the vertical trace gas distribution in the atmosphere . In order to achieve higher resolution in emission spectroscopy, we deploy a new instrument, the NYAEM-FTS (Ny-Ålesund emission Fourier transform spectrometer) in Ny-Ålesund, Svalbard, in single-sided interferogram mode. Its maximum optical path difference for the long interferogram side is 11.25 cm and about 1 cm for low-resolution double-sided phase spectra. A detailed description is given in Sect. . The instrument is used for aerosol retrievals and trace gas retrievals are currently being developed.

When measuring infrared radiation in solar absorption geometry, the transmission through the atmosphere is often of interest, i.e., which fraction of the incoming solar radiation is absorbed by the atmospheric gases of interest. To this end we do not need to know the absolute radiance of the incoming radiation. A fit to the broadband background of the solar spectrum suffices. This is different when measuring emission spectra. Most applications, e.g., trace gas retrievals, retrievals of the thermodynamic profiles or aerosols require absolute radiance calibration. This is usually achieved in a process called total power calibration using two light sources with an emissivity close to 1 (blackbodies) at different temperatures which are measured in a sequence with the actual atmospheric measurements. Since the emission of black bodies is known exactly by Planck's law, provided that the exact temperature of the blackbodies and their wavenumber dependent emissivity are known, we can use linear interpolation between the hot and cold blackbody to calibrate the atmospheric signal. This procedure assumes a wavenumber dependent linear response of the instrument to the incoming radiance S, i.e., of the measured electric output signal Sm of the detector in the required energy range. The detector response can be described by 1Smν=rνSν+Siν where ν is the wavenumber, r the responsivity of the instrument, S the incoming radiance and Si the radiation emitted from the instrument itself, which is important in the thermal infrared spectral region that we consider. The radiation emitted from the instrument itself has in general a different responsivity, since it originates mainly in the beam splitter and therefore only passes through or is reflected on the beam splitter, instead of both, as for the incoming radiation . But since we are not interested in the exact quantity of internal radiation, we absorb this prefactor into Si. Since Eq. () holds for the unknown radiance of an atmospheric scene Ss, the hot blackbody and the cold blackbody for which the radiances Sh and Sc are known theoretically by the Planck law, we have three equations that we can solve for the three unknowns Ss, r and Si: 2Sm,n(ν)=r(ν)Sn(ν)+Si(ν) for n = s, c, h. So 3Sm,sν-Sm,cνSm,hν-Sm,cν=Ss(ν)-Sc(ν)Sh(ν)-Sc(ν) and we can thus solve for Ss(ν) to get the calibrated spectrum 4Ss,calibν=Sm,sν-Sm,cνSm,hν-Sm,cνShν-Scν+Scν.

The blackbody spectra in this equation may not be ideal Planck functions in the real world, but may be modified by the emissivity of the surface of the blackbody, reflections from the surrounding lab, absorption lines and band absorption features from gases in the lab air. We treat this issue in Sect.  by using infrared radiative transfer calculations to model realistic blackbody spectra.

extended the simple linear interpolation calibration scheme in order to incorporate the internal infrared emission from the beam splitter of the instrument with its peculiar phase properties. The resulting method presented is the standard for total power calibration in FTIR emission spectroscopy. In Sect.  we review the main idea in order to incorporate phase errors in the calibration scheme. We extend the treatment by incorporating realistic blackbody spectra from Sect.  which neglect.

There is an incompleteness in which becomes important when considering real world blackbody spectra with absorption lines: the finiteness of real-world interferograms is not considered, and the comment therein that the calibration method can equally applied to one-sided interferograms is incorrect as we elaborate in Sect.  and Appendix . The main motivation for this work is to apply total power calibration to the newly deployed NYAEM-FTS with error estimates on the radiance due to the finiteness of the interferograms. For this we present a complete theoretical treatment which is in principle relevant for all real-world measurements where Revercomb's total power calibration method is applied.

In Sect.  we first present the mathematical description of the issue. We apply equal- and unequal-sided truncation to the three interferograms involved in the calibration and investigate its effect on the calibrated spectrum. We show that the problem of unequal-sided interferogram truncation can always be reduced to the problem of equal-sided interferogram truncation by means of an additional phase correction step within the calibration routine, using a low-resolution phase spectrum obtained from the blackbody measurements. This is important because the error introduced by the application of total power calibration with unequal-sided finite interferograms can be substantially larger than the error introduced by equal-sided finite interferograms. This means that the usage of unequal-sided interferograms to obtain higher spectral resolution poses no greater fundamental limitation than that of equal-sided interferograms of the same resolution. In Sect.  we perform a case study for the NYAEM-FTS. Before we apply the calibration to real measurements of the instrument, we use radiative transfer modeled spectra to estimate the effects of finite interferograms on the measured spectra, since infinite interferograms are not available from measurements. We present quantitative differences between the best estimate on the spectrum from truncated interferograms as described by , the standard Revercomb method applied to unequal-sided interferograms and the new method including a phase correction step, which is equivalent to applying the standard method to equal-sided interferograms as we show in the mathematical treatment. Such an analysis allows us to quantitatively assess the radiance error arising from finite interferograms and the improvements by using the new method presented here. We show in the case study how this can be used to make informed decisions, for example, on retrieval window selection, and whether it is beneficial for a specific use case to apply the modified calibration method including the additional phase correction or not. We then apply the calibration to measurements by the NYAEM-FTS and check for detector linearity and phase stability of the instrument as a prerequisite for calibration.

The NYAEM-FTS is deployed at Ny-Ålesund, located 78.9° N, 11.9° E at the coast of Kongsfjorden in the north eastern part of Spitsbergen, the main island of the Svalbard archipelago in the Arctic ocean east of Greenland. Average temperatures and water vapor mixing ratios range from -12.0 °C and 1.2 g kg⁻¹ in March to 5.8 °C and 4.7 g kg⁻¹ in July .

The French–German AWIPEV research station is one of the main sites in Arctic environmental research and is manned around the year. One of its major components is the AWIPEV atmospheric observatory, where meteorological parameters, radiation, aerosols and trace gases are routinely measured. The NYAEM-FTS has been deployed there because of its high latitude, site infrastructure and support as well as many available complementing measurements being taken at this site. Of special importance are coincident and colocated measurements from radiosondes, radiation measurements from the BSRN (Baseline Surface Radiation Network), aerosol and trace gas measurements from in situ stations and solar absorption FTIR from TCCON (Total Carbon Column Observing Network) and NDACC (Network for the Detection of Atmospheric Composition Change).

Emitted atmospheric infrared radiation enters the AWIPEV observatory via a pneumatically actuated automated hatch on the roof. It automatically opens and closes depending on weather conditions. Wind speeds need to be below 15 m s⁻¹, no precipitation or snow drift are permitted to keep the instrument safe in Arctic conditions. The NYAEM-FTS is mounted as a table-top device inside the observatory about 2 m below the roof inlet. The laboratory is temperature controlled to 21 to 25 °C. The radiation coming vertically down is deflected by a motorized gold mirror to enter the emission port on the backside of the spectrometer.

At the center of the NYAEM-FTS is the commercial FTIR spectrometer Vertex 80 by Bruker. It was chosen because it has a smaller number of mirrors than the 125 HR used for solar absorption spectroscopy at the same site while still providing a relatively high resolution of 0.08 cm⁻¹ when operated in single-sided interferogram mode. The Vertex 80 is available as an open and an evacuated version, which is then called Vertex 80v. We use the open configuration which needs no entrance windows. Since the moving arm of the interferometer is operated via an air cushioned slide and the sample chamber is additionally purged with dry air, there are no issues expected due to water vapor in the instrument. The field of view of the instrument is 22.25 mrad for maximum throughput while the view into the sky is not obstructed by the hatch in the roof. A liquid nitrogen cooled MCT (mercury cadmium telluride) detector is used, sensitive to photon energies that allows for a wavenumber range of 400 to 2500 cm⁻¹. An automated LN₂ refill station is used, which needs to be refilled by a station engineer once per week. Cooling to such low temperatures is necessary to suppress noise for the detection of thermal radiation emitted at atmospheric temperatures. A HeNe laser is used in the instrument for position tracking of the movable mirror. The instrument is equipped with an auto alignment feature using a 4-quadrant diode to optimize the laser signal intensity and phase.

Radiometric calibration is done via total power calibration with two blackbodies at different temperatures. The entrance mirror is rotating such that it allows for selecting either sky view or one of the two black bodies mounted on the instrument table. We use the commercial blackbody SR800 which is temperature controlled at 110 °C. It has a square surface of 10 cm × 10 cm, a specified temperature uniformity of ±0.01 °C and an absolute temperature accuracy of 0.015 °C and an emissivity of 0.98 ± 0.02 claimed by the manufacturer. In the first version of the setup the predecessor SR80 was used as the only blackbody and the temperature alternated between 20 and 110 °C for every calibration measurement, i.e. several times per hour. This damaged the Peltier elements after several months of deployment. We thus use the SR800 now at constant high temperature and home-made black bodies at room temperature are used for the low temperature calibration point. We use high emissivity coating foil (Acktar Metal Velvet) glued to an aluminium plate with DS18B20 sensors fixed to the back side of the plate to measure its temperature continuously.

The instrument was first installed in August 2019. Due to hardware problems with the Vertex80, the NYAEM-FTS recorded increasingly often faulty interferograms which was temporarily reduced by lowering the resolution to 0.3 cm⁻¹ in August 2020. Since the instrument could not be repaired on-site, it had to be shipped to the manufacturer to replace the drive coil, leading to a longer downtime and subsequent testing in Bremen from September 2022 until August 2024.

So far we have assumed infinite intrinsically asymmetric interferograms from which we get the complex spectrum by the Fourier transform. In the real world, all interferograms are finite, which can be described by a multiplication of the infinite (potentially asymmetric) interferogram I(x) with a truncation function A(x) . Comparing to Eq. , the actual measured spectrum is then given by 16Sm(ν)=∫-∞∞I(x)A(x)e-i2πνxdν=Ĩ(ν)∗Ã(ν)=rνSν+Siνeiϕiνeiϕsν∗Ã(ν) where the tilde over the truncation function and the interferogram denote the Fourier transform. We also call à the scanning function. We can decompose the scanning function into a real and imaginary part, Ãc and Ãs, which are the cosine and sine transforms of the truncation function and arise from the symmetric and antisymmetric parts of the truncation function, respectively: 17Ã=Ãc+iÃs We insert this into the quotient of the calibration equation (Eq. ) to obtain

18Sa,calib=rSa-LcT0eiϕs∗ÃrLh-LcT0eiϕs∗ÃLh-Lc+Lc. If there were no spectral lines from the air between the blackbodies and the spectrometer, i.e., T0 = 1, only Sa would be affected by the convolution, since r, Lbb and ϕs are functions that vary slowly with ν and we can thus pull them out of the convolution with the spectrally narrow function à . In the spectral domain this can be understood as the convolution corresponds to a smoothing. With a spectrally narrow smoothing function, high-frequency components will be smoothed, whereas low-frequency components are left unchanged. In the interferogram domain this can be best understood as the interferogram of a spectrum without high-frequency components being concentrated around the ZPD. Truncation (even asymmetric as long as it contains a short section on both sides of the ZPD) does not affect the interferogram. The rest of the terms then cancel and we are left with 19Sa,calib=rSa-Lceiϕs∗ÃrLh-Lceiϕs∗ÃLh-Lc+Lc=rSa∗Ã-LceiϕsrLh-LceiϕsLh-Lc+Lc=Sa∗Ã. If the truncation is symmetric, this expression is already real, and the imaginary part only contains measurement noise. In the asymmetric case we can take the real part and we are left with 20Sa,calib=ReSa∗Ã=Sa∗Ãc which is usually what we expect as the best estimate of the spectrum in FTIR spectroscopy . Note that in the asymmetric case, we cannot use the imaginary part anymore for quality control and to estimate the noise level of the data since it does not contain only noise. At the positions of spectral lines, where there are fast intensity variations, the imaginary part shows features similar to those of anomalous dispersion .

Now, in case that any spectral lines are present in the spectra used for calibration (T0 ≠ 1), we cannot obtain this estimate, since both the numerator and the denominator contain high frequency modes and are thus affected by the convolution. Equation  then results in 21Sa,calib=Sa-LcT0∗Ãc+iÃsT0∗Ãc+iÃs+Lc where for equal-sided truncation Ãs = 0 and we get 22Sa,calib=Sa-LcT0∗ÃcT0∗Ãc+Lc.

A deviation from the best estimate for asymmetric interferograms compared to symmetric interferograms can be expected due to the additional term Ãs in Eq. () compared to Eq. (). Note that we cannot simply mitigate this deviation and obtain the estimate of Eq. () from unequal-sided interferograms by taking the real part of the numerator and denominator in the Revercomb formula separately, hoping that this makes the contributions of the sine transforms vanish. The phase exponents exp⁡iϕs would not cancel as they do in Eq. (). Instead, we can determine the phase ϕs from a small symmetric part around the ZPD of the difference of the interferograms from the hot and cold blackbody Ih-Ic as is commonly done in phase correction schemes like Mertz's phase correction . A low-resolution phase spectrum is sufficient, since the blackbody spectra have strong signal to noise everywhere, unlike gas emission spectra, which contain only separate narrow lines. We multiply the inverse of this phase to the numerator and denominator to make them real except for the imaginary part of Ã. Now we can indeed take the real parts of the numerator and denominator separately: 23Sa,calib=RerSa-LcT0eiϕs∗Ãc+iÃse-iϕsRerLh-LcT0eiϕs∗Ãc+iÃse-iϕs×Lh-Lc+Lc=ReSa-LcT0∗Ãc+iÃsReLh-LcT0∗Ãc+iÃs×Lh-Lc+Lc which is exactly Eq. (). Expressed in terms of the measurements we have 24Sa,calibν=ReSm,sν-Sm,cνe-iϕhcReSm,hν-Sm,cνe-iϕhc×Lhν-Lcν+Lcν=ReFIs-Ice-iϕhcReFIh-Ice-iϕhcLhν-Lcν+Lc(ν). with ϕhc being the phase of the difference interferogram Ih-Ic. With this modified version of Revercomb's calibration method, one can now obtain the same spectral estimate from unequal-sided interferograms as from equal-sided interferograms.

We measure thermally emitted atmospheric infrared radiation in Ny-Ålesund, Svalbard, with a newly installed FTIR spectrometer, the NYAEM-FTS. In order to achieve the highest possible spectral resolution, the interferometer is operated in single-sided interferogram mode. For radiometric calibration, two blackbody sources at different temperatures are used. In order to correctly apply the calibration scheme to the NYAEM-FTS measurements, detector linearity and phase stability of the instrument were tested, and we have investigated total power calibration taking into account interferogram truncation and absorption lines in the blackbody spectra. We have found that the commonly used method described by is strictly speaking only valid for double-sided infinite interferograms. Because of the convolution with the scanning function, we cannot obtain the same spectral estimate of the atmospheric spectrum after calibration, which is commonly referred to as the best estimate in FTIR spectroscopy following . We have described the underlying theory and have shown that one can always obtain the same estimate as for equal-sided interferograms from unequal-sided interferograms by modifying the calibration method incorporating an additional phase correction step. This, in general, leads to much smaller errors. We have quantified the deviations from the best estimate in a case study with simulations of realistic spectra from a line-by-line radiative transfer model. We have used representative states of the Arctic atmosphere in Ny-Ålesund where our instrument is operated. Since the Arctic atmosphere with its low water vapor content allows for using spectral regions close to strong water vapor lines in retrievals, a quantitative error analysis is important for the NYAEM-FTS. In our example, the errors in calibrated radiances are minor in common spectral bands with weak water vapor lines used for trace gas retrievals with the AERI and lie well below 0.04 % and 0.02 % for winter and summer, respectively. Above 1400 cm⁻¹ errors are very large but in those regions absorption lines are so strong that saturation effects limit the usability of the spectra. A quantitative analysis of the spectral region in between has shown that in this setup one could extend the spectral range for retrievals up to 1350 cm⁻¹ when using our modification of Revercomb's total power calibration method but beyond, errors substantially increase, especially during summer with higher humidity. We have also shown that in the case of unequal-sided interferograms the deviation from the best estimate can be reduced using the method presented here compared to the original method (in the spectral band from 1300 to 1350 cm⁻¹: the rms error from 0.04 % to 0.01 % and from 0.27 % to 0.04 % in winter and summer, respectively, the maximum deviation from 0.39 % to 0.07 % and from 3.42 % to 0.63 % in winter and summer, respectively). Since the quantitative relevance of the effects depends on the instrument, the measurement site and the intended use of the spectra, we recommend that such an analysis, which allows for estimating the radiance error arising from finite interferograms, for deciding on the necessity of applying the additional phase correction step for unequal-sided interferograms, and, for example, for making informed decisions on retrieval window selection, be performed for each individual use case.