Please see the attached pdf

Review of "Total power calibration in FTIR emission spectroscopy for finite

interferograms" by Lukas Heizmann et al.

This paper investigates the radiometric calibration of spectra measured by an FTIR spectrometer in emission configuration. The authors refer to the method presented by Revercomb et al. (1988), state that they have to modify it to apply it to finite, asymmetric interferograms and show an example of how simulated calibrated spectra look when applying the radiometric calibration in different ways. The simulated data represent the measurement situation for the NYAEM-FTS.

I have a major problem with this paper: It does not become clear, why the calibration method described by Revercomb et al. should not work for NYAEM-FTS, since they propose a method which is also valid for one-sided interferograms (page 2315, left column, last paragraph). This is basically represented in eq. 15 of the present paper. The argumentation of the authors, why this equation should not be valid for finite interferograms, is not convincing to me. It is extremely hard to follow the argumentation, because the symmetric and asymmetric truncation functions are not given explicitly and thus, also the results shown in Fig. 2 are not traceable. I have the impression that some of the deviations between the different methods may stem from approximations (e.g., taking only the real part as stated in line 147) which are maybe not justified. 

Overall, the results are not convincing and the need for a modification of the Revercomb calibration approach is not clear (I don't see why a correct application of the Revercomb approach should not work).

One motivation of the authors for this paper is that a quantitative error analysis is needed for the NYAEM-FTS. Such an error analysis would be a valuable publication, and the aspects of phase issues induced by beamsplitter emission and water vapour lines in the calibration data could be addressed there - preferably supported with real data. 

Please find below some more detailed comments on the different sections of the paper.

In the first part, theoretical considerations are presented, which basically repeat the calculations already given by Revercomb et al. 

Section 2 repeats the calculations already given by Revercomb et al. 

Section 3 discusses the effect of spectral absorption lines in blackbody measurements and basically states that the effect cancels out in the instrument setup of NYAEM-FTS, because the radiance from the atmosphere and the radiance from the blackbodies passes the same air masses. This is important when estimating possible error sources in the calibration setup. It should be noted, however, that this is an aspect which is rather independent of the calibration method by Revercomb et al.

Section 4 deals with the the problem that in FTIR emission spectroscopy, the different phases of the instrument contributions have to be taken into account, such that simply using the magnitude of the spectra as input to the calibration formula does not work. This again is a repetion of the work presented by Revercomb et al.

At the end of the paragraph the authors state that "it is only true for infinite interferograms that the transmittance cancels in the quotient" without explaining why this shoud be the case. As long as the spectral resolution of all types of measurements (atmosphere and blackbodies) stays the same, I don't see why the transmittance should not cancel.

In Section 5, the effect of a truncation function, which describes the finite interferogram measurement, is discussed. Unfortunately, neither a symmetric, nor an asymmetric truncation function is given explicitely, such that it is difficult to follow the argumentation.

Next, I don't understand the intension of eq. 19. It tells me that the calibrated spectrum is the input radiance, convolved with the truncation function, but it does not make use of any calibration measurements anymore. 

In eq. 20, only the real part is taken, although the truncation function is asymmetric. If I understand Sakai et al. correctly, the assumption of eq. 20 is only valid if the asymmetry is small compared to the interferogram length which is not the case for NYAEM-FTS. So, again, what is the use of this equation? How valid is this approximation for NYAEM-FTS? 

For the simulated dataset, which is described in lines 160 ff, I am missing a description of how the instrument self-emission, including beamsplitter emission with a phase of 90 degrees is included. If such instrument contributions are not added, you cannot demonstrate that they are handled correctly during calibration. 

Concerning the discussion of the convolution effect, it is not clear to me, what exactly is done. The main point is that the truncation is not explained, especially the difference between the symmetric and asymmetric truncation. The stronger the asymmetry, the more the result of eq. 20 will change compared to the case of the symmetric truncation. Since it is not well explained what exactly is done for calculating the best estimate, the equal sided Revercomb and modified unequal sided Revercomb (which seem to give identical results) and unequal sided Revercomb, respectively, I also cannot follow the results shown in Fig. 2.

When it comes to the effect of water vapour lines in the blackbody spectra and the truncation of interferograms, it is not clear why these have an impact on the calibration quality (in the frame of this theoretical study). As long as the interferogram truncation is identical for the blackbody and the atmospheric interferograms, the line shapes should be affected in the same way, such that no error is introduced. In real life, I would still expect an effect if the lab conditions are not perfectly stable and humidity and/or temperature of the lab air vary over time.