We thank the referee for useful comments and suggestions. We have responded
to all of them and have marked the corresponding text changes in blue fonts.

> 1.- Section 2 first paragraph. It says “S is the source-function vector,
> which, under the assumption of local thermodynamic equilibrium (LTE),
> can be approximated as S≡(Sν(T),0,0,0), where Sν(T ) is
> the source function.” I think what the authors really want to say is
> “can be approximated as S≡(Bν(T),0,0,0), where Bν(T )
> is the Planck function.”

Yes; we have now changed the text correspondingly.

> 2.- Equation 5 uses a factor epsilon that is called emissivity that is
> poorly defined. The relation between Stokes Q and U and the transverse
> components b_theta and b_phi is very complex (even in LTE) if one goes to
> the exact formulation of the radiative transfer equation. Equation 5 is an
> approximation. Understanding the assumptions behind equation 5 requires
> a better definition of the emissivity (even if later is set equal to 1).
> Note that the radiative transfer equation for polarized light uses an
> emissivity too, but it is unclear as the authors refer to it.

We have rephrased the sentence and now write "where $\epsilon$ in the present 
context is a proportionality constant that depends on the heliocentric angle".
Additionally, we have added a sentence acknowledging this point which states 
"Equation~(\ref{PfromB}) is an approximation of the otherwise complex relation
between Stokes $Q$ and $U$ to the transverse components $b_\theta, b_\phi$."
All these changes are highlighted in blue in the manuscript.

> 3.- Section 3.1 and discussion on the wavelengths of SDO. The paper says
> several times that the wavelengths closer to line center are lambda_2 and
> lambda_3. This is true when there are no Doppler shifts of the lines cause
> by solar conditions (solar rotation, Evershed flow) or by the satellite
> orbital motions. This is recognized in Sections 3.6 (when explaining the
> change in sing of E for AR 11542) and in Section 3.7 where the orbital
> velocity of SDO is explicitly mentioned. This is correct, but the SDO
> orbital velocity and the combination of Solar rotation can contribute to
> a Doppler shift of 6 km/s. This shift is as large as 120 miliangstroms,
> meaning that line center in extreme cases will be centered on lambda_1
> or lambda_4. Thus, these wavelengths are also potentially impacted by
> Faraday rotation, admittedly less than the two central ones.

We modified and added the following lines in section 3.1 to acknowledge
the concerns raised by the referee "We study these ARs on the central meridian,
so the Doppler shifts due to solar rotation and Evershed flow are minimised. 
However, there are also Doppler shifts due to the orbital velocity of {\em SDO}, 
resulting in the line core being sampled by $\lambda_2$ or $\lambda_3$. We note that
in extreme cases these shifts due to the orbital velocity could be large
enough for the line core to be sampled by $\lambda_1$ or $\lambda_4$.
For these reasons, we".

> 4. The paper ends with this statement “Stokes V carries with it
> additional information about the directionality of the line-of-sight
> magnetic field, which has not been used in the present study.” This is
> not entirely correct. The authors have used inversion codes in the paper
> (VFISV and HeLIx+) that do use Stokes V. Please rephrase admitting that
> it is only in using equation 5 that Stokes V is not used.

We have now rephrased this sentence and write "Except for the cases
where we inferred Stokes Q and U from the components of the transverse
magnetic field through Eq. (5), Stokes V has not been used ..."


Additionally, we have uploaded the analysed data set online with a DOI number and
we have added a line (with a footnote) at the end of Section 3.1 to mention this,
"The dataset containing the shell-integrated spectra defined in Eq. (3), 
along with maps of E and B for each AR can be found in an online catalog 1."

Thank you!
Regards