The article “Implementation and application of an improved phase spectrum determination scheme for Fourier Transform Spectrometry” by Hase et. al. describes a more robust method for determining the phase spectrum of a Fourier transform spectrometer and applies the described method to a selection of instruments used for ground-based measurements of atmospheric trace gases.

This work has been carried out in the context of the European Space Agency’s Fiducial Reference Measurements for Greenhouse Gases (FRM4GHG) programme and so there is an expected focus on retrieval of greenhouse gases from absorption spectra. The presented results show that the changes in retrieved CO₂ column using the new and traditional phase determination are very modest. However, the new and more rigorous method presented can provide insight into the instrumental features of the various spectrometers presented.

The manuscript is generally well written, especially the introduction section, and the content will form a beneficial addition to the field. I would recommend that it is published subject to the changes and clarifications outlined below.

Specific comments:

Given that this work was carried out as part of FRM4GHG, the discussion of the impact of the phase determination on retrieved gas column is very limited, with quantified results only presented for one instrument and one species. It would be good to include these results for all of the instruments investigated and multiple species or spectral windows. Even if all the differences are at or below the magnitude reported for the IRcube CO₂ window, this is still a useful finding which should be noted.

In section 2 the instruments should be introduced in a more consistent way. For example, there is very little discussion of the location of any of the instruments until the Izaña IFS125HR is introduced, and a paragraph is used to describe the observatory before a second, shorter paragraph describes the instrument.

Furthermore, when describing the IRcube, it is noted that single or double-sided interferograms can be measured, but it is never made explicit which are used in this study.

A table in this section that summarises the important instrument characteristics would be very helpful to the reader.

When describing the algorithm for the new phase determination a discussion on the choice of the threshold value T would be useful. What constitutes significantly above the noise and artefact level, and what are the implications of setting this value too low?

Technical corrections:

L75. ILS should be more fully introduced

L176. The reference IFS125HR has not bee discussed prior to here. Is this the Izaña instrument?

L328. Include units after 2 ∙ 10⁻⁵

Figure5. It isn’t clear that there are two spectra plotted. Consider including a legend. The curve labelled residual isn’t really a residual in the normal sense but a difference, consider relabelling. Include a description of the curve colours in the caption.