Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Round 1

Reviewer 1 Report

In this review, the authors give a theoretical summary of the characterizations of the Mueller matrix. It doesn’t seem very easy to read, at least for me, a researcher in polarimetric imaging; but this work is significant for readers in the fields of polarimetry and polarimetric imaging. So, maybe the authors should take some effects to improve the review’s readability and explain how and why this characterization affects or be used in microscopy imaging. Of course, I recommend its publication. Some remarks need to be considered.

 

1. Of crucial consideration for the authors: The title is about the Mueller matrix in microscopy imaging, but there is little explanation or discussion about how these results or Mueller characterization affect microscopy imaging.
2. Each section is lengthy. Although I know this review is a theoretical one, the authors should try their best to make the reader, especially readers in the field of microscopy imaging, easy to know your contributions. So, maybe you should add some guides at the beginning or end of each section.
3. Some examples of microscopy imaging should be presented since you mention them in your title.
4. Page 16, line 540: The citations are invalid.
5. There are so many vectors and matrices. It will be very convenient for readers to list them (a table) in the front/end of the main text.
6. As a review paper, the current Conclusion seems not deep. At least it's missing some discussion about, for example, how these characterizations of the Mueller matrix affect the practical microscopy imaging, are there some questions/problems that need to be further studied…

Author Response

So, maybe the authors should take some effects to improve the review’s readability and explain how and why this characterization affects or be used in microscopy imaging.

We have been through the paper and tried to improve the readability. 

1. Of crucial consideration for the authors: The title is about the Mueller matrix in microscopy imaging, but there is little explanation or discussion about how these results or Mueller characterization affect microscopy imaging.

We agree with this comment. But the paper is already quite long. We discuss two different areas where we think the paper is applicable to imaging. So we have decided to change the title to ‘Characterization of the Mueller matrix: Purity space and reflectance imaging’ to specifically address these two areas.

1. Each section is lengthy. Although I know this review is a theoretical one, the authors should try their best to make the reader, especially readers in the field of microscopy imaging, easy to know your contributions. So, maybe you should add some guides at the beginning or end of each section.

We have separated each section into subsections to make it easier to follow the paper. We have also added introductory material at the beginning of some of these subsections.

1. Some examples of microscopy imaging should be presented since you mention them in your title.

We cite several examples from imaging. ‘Often these systems have a reflectance geometry, and include methods such as reflectometry \cite{ref-Clivas92}, reflectance microscopy \cite{ref-LeGratiet15,ref-LeGratiet19,ref-LeGratiet21}, confocal microscopy \cite{ref-Bueno02,ref-Lara06}, low-coherence interferometry \cite{ref-Davidson87} and optical coherence tomography \cite{ref-Hee92,ref-deBoer97,ref-Jiao02}. Depolarization has been found to be a useful contrast mechanism in biological and medical imaging \cite{ref-Bueno02,ref-Goetzinger08,ref-Ortega16,ref-VanEeckout17}.’

1. Page 16, line 540: The citations are invalid.

We have corrected this.

1. There are so many vectors and matrices. It will be very convenient for readers to list them (a table) in the front/end of the main text.

We have added a list of symbols at the end of the manuscript.

1. As a review paper, the current Conclusion seems not deep. At least it's missing some discussion about, for example, how these characterizations of the Mueller matrix affect the practical microscopy imaging, are there some questions/problems that need to be further studied…

Our argument is that measures of depolarization need to be chosen to provide good contrast to distinguish between different structures. We have added some discussion about this. And the second area we discuss is about reflectance imaging. We think that the points made here are original and important in calibrating imaging systems with a reflectance geometry.

 

 

Reviewer 2 Report

This is an excellent paper. I recommend it is accepted for publication.

Author Response

Thank you for your appreciation.

Reviewer 3 Report

See attached

Comments for author File: Comments.docx

Author Response

Reply to reviewer 3

 

• The historical revision given is maybe missing some relatively old but relevant papers by H-G Kuball and co-authors discussing the symmetry properties of the Mueller matrix in backscattering configuration. I refer to the papers doi: 10.1016/0301-0104(83)85227-6 and doi: 10.1016/0301-0104(87)80030-7. The more recent paper with doi: 10.1364/OL.39.006050 is also highly relevant for section 4.

We already knew about these papers, but of course we had to make a selection from the large number of relevant papers. We have added the papers by Kuball’s group, which we agree are relevant. Our main reason for not including them before was that, essentially, the main points were made earlier by Sekera and by van de Hulst. The more recent paper, by Arteaga, we agree is also very relevant to our later discussion, and so we have included that citation. We have also added a reference to a paper, by Silverman, cited by Arteaga.

 

• This discussion that the authors make about the trace condition in section 2 and later also in section 4 (m00 − m11 + m22 − m33 = 0 or its equivalent in Sinclair/Kennaugh notations) can be slightly confusing for experimentalist… Most generally, the trace condition will be satisfied for single scattering (also for ensembles of multiple scatterers), but not if there is multiple scattering. So, in many backscattering experiments (especially those of the biomedical field with a large amount of multiple scattering) the trace condition will be by far not satisfied.

This is a very good point, which we should have made, but have now included in both Section 2 and Section 4.

 

In Line 540 several references appear as [ ? ? ?]

 

These have been corrected.