Dear Rob,
thanks for submitting the revised version of your manuscript. I received one reviewer report and also read the manuscript again myself. I think the paper is in good shape, but I ask you to consider the comment by the reviewer on the gain (matrix), as well as my comments, which are listed below.
Best wishes,
Christian

Specific comments:
Page 2, line 10: “presented in (Kremser et al. 2016)” -> “presented in Kremser et al. (2016)”

Page 2, section 1.1, line 15: “SO measurements” may be misleading, because the SO molecule also plays an important role in stratospheric sulphur chemistry. Can you use a different abbreviation for solar occultation (throughout the manuscript)?

Page 2, line 17: “while providing 5%“.
The differences in aerosol extinction coefficients between SAGE II versions 6.2 and 7 reach 40% at certain altitudes and latitudes. I’m not sure, if the 5% accuracy can really be provided then.

Page 2, line 23: “24 occultations per day“.
Why 24? For a typical LEO the satellites complete about 14-15 orbits daily. If sunrise and sunset occultation observations are carried out, this amounts to about 30 occultations per day. If only, e.g., sunrise measurements are carried out, as for SCIAMACHY, the number of daily observations is 14-15.

Page 3, line 31: “by (Bourassa et al., 2007)” -> “by Bourassa et al. (2007)”

Page 7, line 3: “pertrurbed“

Page 7, line 10: “median radii”.
I think the correct term is “mode radii” here (see online document by R. G. Grainger entitled “Some Useful Formulae for Aerosol Size Distributions and Optical Properties”). We also use the wrong term in the past.

Page 8, line 16: “tropics at 30 km is shown in Fig. 9”.
The figure caption states that Fig. 9 shows results for 20 km altitude. Please correct. Also, the particle size (and hence also the Angstrom-exponent) changes with altitude, which will affect the correction. Is this an important effect?

Page 9, line 26: “For an optically-thin LOS, we can use the SS” .
Is this really true? Even for an optically thin LOS, there may be a significant multiple scattering component. Perhaps you can simply state that you use the single scattering approximation, if it is used?

Page 10, line 1: “whic“

Page 11, equation (4): please consider the comment by reviewer #1. Does the statement “if one assumes a diagonal averaging kernel” perhaps refer to the weighting function matrix, rather to the averaging kernel matrix?

Page 11, equation (5): please define I$_m$ and I$_c$

Page 13, line 29: “multitple“

Page 14, line 30: “The third condition occurs primariily in regions with low $beta_a$ values, typically where sinking air prevails in the UT/LS region.”
The UTLS region is usually characterized by relatively large extinction coefficients (also seen in your Fig. 20). Small extinction coefficients are typical for the mid-stratosphere, right?

Page 14, line 31: “primariily”

Figure 1: The paper already contains a very large number of Figures and I’m wondering if Fig. 1 is really necessary?

Figures 2 and 7 are partly redundant and can perhaps be combined in a single Figure?

Caption, Fig. 1: “in (Thomason and Peter, 2006)” -> “in Thomason and Peter (2006)”

Caption, Fig. 7: “of (Griffioen and Oikarinen, 2000)“ -> „of Griffioen and Oikarinen (2000)”

Caption, Fig. 15, line 3: “to product“ -> “to produce” ?

Caption, Fig. 16: I suggest mentioning the tangent height in the caption, too.

Fig. 19, abscissa label: “Coefficien” -> “Coefficient”

Fig. 20: I think the ordinate label should read “Altitude (km)”, not “Tangent height (km)”

Dear Rob,

many thanks for uploading a revised version of your manuscript. All points have been addressed well and I accept the paper for publication in AMT.

I congratulate you and your co-authors on the acceptance of your paper.

Best wishes,

Christian von Savigny