Performances of Polarization-Retrieve Imaging in Stratified Dispersion Media

Round 1

Reviewer 1 Report

I would like to thank the authors for detailed answers to my comments. At the given stage, only one problem remains for discussion within the review. My comments on this problem are given in the attached file.

Comments for author File: Comments.pdf

Author Response

We have revised our manuscript according to reviewer's suggestion. Some English expressions have also been modified in the revised manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

The authors have sufficiently answered to the reviewers' comments and made an effort to improve the clarity of the article as well as the they have given necessary numbers in order to judge their results. Thus, the scientific community will be able to reproduce their findings and benefit from their research.

I recommend the article for publication.

Author Response

We have revised our manuscript according to reviewer's suggestion. Some English expressions have also been modified in the revised manuscript.

Author Response File: Author Response.docx

Reviewer 3 Report

This paper presents an interesting work about polarization retrieval imaging performance in stratified dispersion media. Due to the inhomogeneous distribution of light-scattering particles in the atmospheric environment, it is very difficult for optical remote sensing to monitor the natural phenpmena on the earth from the satellite. Authors proposed an active imaging model based on the Monte Carlo (MC) algorithm in the 10 km atmosphere from the satellite to the ground. The model is also called active remote sensing, which actively emits electromagnetic waves and receives reflected signals for imaging.

According to the local atmospheric environment, the particle parameters of clear and cloudy weather are carefully investigated, including particle number density, scattering coefficient, absorption coefficient and equivalent radius at different height. Authors combine the stratified dispersion model and polarization-retrieve (PR) theory to apply actual scenes. This manuscript introduces four different scenes in clear weather and provides calculation results about the optical thickness and transmittance of different scenes, which are very similar to the actual standard. Through simulations, authors showed that the PR imaging method can be used for object recognition in media with higher turbidity. Compared with intensity imaging, degree of polarization (DoP) and polarization differential (PD) imaging methods, PR imaging can clearly distinguish the target and its background. When the atmosphere at 0-2 km near the ground becomes more turbid, the original Muller matrix can also be used to retrieve the target to a certain extent based on the PR method. In addition, authors have considered the retrieval capabilities of three kinds of wavelengths and introduced image evaluation indicators to prove the reliability of the method. Overall, authors could improve the quality of imaging and suggest new research directions for optical remote sensing imaging.

The manuscript is well organized and clearly delivers the main claims. The PR method is important for information retrieval and optical remote sensing. Authors carefully considered many possible issues and the established transmission model in line with the actual environment. Therefore, this paper can be recommended for publication in Remote Sensing.

Author Response

We have revised our manuscript according to reviewer's suggestion. Some English expressions have also been modified in the revised manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I don't mind the publication of the manuscript

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The full referee report is attached in a single pdf-file. 

Comments for author File: Comments.pdf

Author Response

See the attached file.

Author Response File: Author Response.docx

Reviewer 2 Report

As a whole, the text of the manuscript is of significant interest to readers. However, I have the following critical comments and recommendations:

• In the Introduction, the accent is made only on the works of Asian authors. However, there are a number of works of experts from the European countries (including Russia) and the USA. Thus, I consider that the Introduction should be improved.
• Lines 128–129: Why were the source and receiver apertures chosen equal to 1 ×1 m²?
• Real laser sources have divergence angles, and real receivers have field-of-view angles. I did not find mention of these angles nor their values in the text.
• In lines 134–135, it was mentioned that 10⁸ photon trajectories were simulated. However, I did not find estimates of statistical computational errors in the text. I consider that values of the statistical errors of all results presented in the text must be added.
• In the manuscript, 3 wavelengths were considered: 1536, 633, and 4000 nm. Why were exactly these wavelengths chosen?
• In Table 2, the optical parameters of the atmosphere are given for λ =1536 nm. However, no data are presented for wavelengths of 633 and 4000 nm.
• I have not found in the text explicit correspondence between the characteristics of the considered and real satellite devices. In my opinion, calculations should be focused on the situations observed for real satellites.
• Lines 144–145. In Table 1 the Mueller matrices for steel, marble, and wood borrowed from [34] are presented. In [34], these matrices were measured at a wavelength of 806 nm. However, different wavelengths are considered in the text. How can you justify the applicability of these data?
• Have I understood it correctly that molecular scattering was not taken into account in the manuscript?
• The term “cloudy atmosphere” is used in the text. I think that it is better to use the term “turbid atmosphere”. As far as I know, there are more than 20 cloud types. From Table 2 it follows that the maximum value of the extinction coefficient was used for the lower layer (0–1 km). Meanwhile, a clear-air layer of the atmosphere is normally located between a cloud and the Earth surface. The atmospheric model described in the text can be that of a fog rather than of a cloud.
• Lines 161–162: “So a modified MC program is developed to apply in stratified dispersion media.” As far as I know, analogous algorithms were suggested in the 1970s (for example, see [Marchuk, G. I., Mikhailov, G. A., Nazaraliev, M. A., Darbinjan, R. A., Kargin, B. A. and Elepov, B. S., “The Monte Carlo methods in atmospheric optics,” Springer. Verlag, (1980)]). The article [P.W. Zhai, G.W. Kattawar, P. Yang Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method // Applied Optics. vol. 47, No. 8. 2008. P. 1037-1047.] was published in 2008, and the stratified model of the medium was also used in this article. Our laboratory and our colleagues from Novosibirsk (Russia) use the Monte Carlo method in the stratified dispersion media for many years. Therefore, I consider that lines from 167 to 206 must be deleted from the text.
• As I have understood, the single scattering matrix used for calculations can be found in [38]. If I am not mistaken, results presented in [38] were obtained for λ = 8 nm (Fig. 4 of [38]). Do you use these values only for λ = 632.8 nm or for two other wavelengths as well? If you use others single scattering matriсes for λ =1536 nm and 4000 nm, where is it possible to find them? If the same, how do you justify the possibility of their application?
• Line 164: a misprint: “u_e” must be replaced by “µ_e”.
• Lines 165–166: “where is a pseudo-random number between 0 and 1, and is the extinction coefficient of the medium equalling to the sum of scattering coefficient and absorption coefficient.” A misprint. Please decipher quantities entering into Eq. (6).
• Lines 244–245: ”Therefore, the DoP and PD images of the acquired irradiance are calculated by: …”. The formula for Dop is not given. A misprint.
• Line 372. I have not found the quantity C3 in formula (19). A misprint.
• In the text, the optical parameters of the atmosphere for λ =1536 nm are given. However, there are no optical parameters for the employed wavelength of 633 and 4000 nm.
• In the text I have not found an explicit description what quantity in Figs. 5d and 7 is denoted by PR. In Fig. 6, “DoP (PR)” is shown. Therefore, it is possible to assume that in Figs. 5d and 7, the degree of polarization is shown derived after using Eq. (5). This quantity must be defined in an explicit form and the definition must be added to the text.

Author Response

See the attached file.

Author Response File: Author Response.docx

Reviewer 3 Report

The authors demonstrate imaging of a target through a model atmosphere via an effective Mueller Matrix inversion. The simulations ground on the Monte Carlo algorithm under the assumption of randomly distributed particles using Mie scattering theory. The reconstruction of the target relies on the characterization of the atmospheric model by the effective Mueller Matrix which was made possible by placing a laser source close to the target. The authors show successful reconstructions of the target under varying parameters like laser wavelength, particle size and weather conditions and compare it to other polarization filtering techniques namely the degree of polarization and the polarization difference.

The idea of using the effective Mueller Matrix as a tool for image reconstruction through a model atmosphere is novel to the best of my knowledge. The manuscript is clearly written and well structured. To fully appreciate and comprehend the results that were presented, a few more details and explanations are necessary:

 

You mentioned in the text that the MM would describe the optical properties completely. From reference 31 we can obtain that it is sufficient to measure with 4 polarization states that describe the scattering system completely (unpolarized, 90° linear, 45° linear, and right circular) through the radiative transport equation. However in your approach you launch 4 linear polarizations and 2 circular polarizations to describe an “effective” Mueller Matrix? Is this choice justified by the scattering properties? Does it vary with the particle size of the scatterers?

 

The fact that you need to characterize the model atmosphere in both directions requires placing a laser near the target to measure the upward direction eMM. Perhaps you could stress more the importance of this key element, since the technique is not comparable to a blind object detection. Following from that, could you give some perspective to work around this or if not possible, some applications in which such a situation occurs where you can place a laser near the target of interest?

 

Some greek letters are not defined in the right order or not defined at all (some if it could be due to format issues):

• In equation 6 “u_e” is meant to be the extinction coefficient µ_e ?
• Right below equation 6 the greek symbols are missing in the explanatory sentence

 

To avoid confusion: I assume what you call the mean free path (mfp) is the scattering mean free path and is abbreviated by the greek letter “τ”? This letter is not depicted in line 163.

 

Then in line 170 you conclude that “τ” is equal to “ξ”, should it not be “t” that is equal to “ξ”? And the letter “τ” then represents the scattering mean free path which is proportional to 1/µ_e?

 

Following this assumption, each of the ten atmospheric layers has its own scattering mean free path – when you depict in Fig. 5 the reconstruction results as a function of “τ”, this would be the average mfp over all 10 layers?

 

Accordingly, Table 2 depicts the properties of the model atmosphere in very detail which is much appreciated. However, there are two scenarios depicted which is a clear atmosphere and a cloudy one. I would naturally also expect that in the polarization retrieved images, you would have two different scattering properties of the atmosphere but in fact you have chosen 4 different scenarios. Could you relate the clear / cloudy atmospheric conditions to the scattering mean free paths of Figure 5? It is not obvious how you chose the scattering to obtain those 4 scenarios.

 

Furthermore once the previous point is clarified could you comment more precisely where the limits of the polarization retrieval methods are relating to the Table 2 weather conditions. An image retrieval through thick clouds is at least very challenging if not impossible at this point. To underline the ability of this technique, it would be very convincing if you added the PSF after the light propagated through the atmosphere for the four mean free paths of Fig. 5 for instance.

 

A follow up to the previous remark – since the quality of reconstructions seem to be of very high accuracy, I wonder if you had used any regularization during the polarization retrieval? Additionally, has there been any spatial filtering or image processing applied on the polarization retrieved images?

 

Could you perhaps make the figure and especially the images in Fig. 3 larger? Perhaps it helps to reduce the white space between image and colorbar and matrix label and image? The reader could appreciate the symmetries observed better.

 

In Fig. 4., a suggestion would be to replace “our imaging” by a name related to the imaging concept (e.g. polarization retrieval)?

 

The results depicted in Fig. 7 and Fig. 8 which show the contrast of the retrieved images as a function of the particle size is dropping sharply at an “increasing size factor” of 0.3. Do you have an explanation for this? Could you add a small discussion in the text here?

 

For Table 3, perhaps a depiction as a graph would help to visualize and make the reader comprehend the differences better.

 

A general remark – it would be nice if you enlarged the figures, especially figures 5, 7 and 9 that contain the reconstructed targets since those are the key results of the paper and they deserve more space in the article.

 

A minor typo: The power of some of the scattering and absorption coefficients in Table 2 is comprised with 2 minus signs.

 

Author Response

See the attached file.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Dear authors,

The referee report is given in the attached pdf file.

With kind regards,

Anonymous referee

Comments for author File: Comments.pdf

Reviewer 2 Report

Most of my recommendations and comments have been considered in the revised text of the manuscript that has been improved considerably. Nevertheless, I have two comments left, one of which, unfortunately, requires recalculation of some results.

1. My initial comment was: Lines 144–145. In Table 1 the Mueller matrices for steel, marble, and wood borrowed from [34] are presented. In [34], these matrices were measured at a wavelength of 806 nm. However, different wavelengths are considered in the text. How can you justify the applicability of these data?

The authors replied: Great Thanks for your comments.

I agree with your thought that the polarization property will be related to the targets’ materials, surface structures and incident wavelengths. Reference [42] (Original [34]) detected the polarization properties of different targets in the incident 804nm light, and it can be still used in other incident wavelengths, such as the reported works [S1], [S2] & [S3]. Because the core factor on the polarization property, lies in the diagonal line of the Muller Matrix, and the effect on the incident wavelengths lies in the non-diagonal line of the Muller Matrix…

My comment to author’s reply: Thanks for the explanation. In connection with it, I consider it necessary to indicate in the text of the manuscript that in calculations it was suggested that the Muller matrices for steel, marble and wood and single scattering matrices were independent of the wavelength.

 

2. My initial comment: Have I understood it correctly that molecular scattering was not taken into account in the manuscript?

The authors replied: Great Thanks for your comments.

Molecular scattering is an extremely microscopic thing. The scattering properties of the molecules are not considered in this work. The particle collision here only considers the Mie scattering model. The radius of the particles is on the order of microns.

My response to authors’ reply: Using the results of work [Bucholtz A. Rayleigh-scattering calculations for the terrestrial atmosphere. Applied Optics. (1995). Vol. 34. Issue 15. P. 2765-2773. Table 2] and the vertical profiles of the temperature and pressure for the summer mid-latitude model of the atmosphere (MODTRAN), I have calculated the molecular scattering coefficients at wavelengths considered in the text for the 0–10 km layer of the atmosphere. The calculated values are presented in the table below. In the table, I have also included the aerosol scattering coefficients for the clear atmosphere at λ = 1.536 mm borrowed from Table 2 of the manuscript.

Table.

z , km	P , mbar	T , K	μs,m(0.63)	μs,m(1.5)	μs,m(4)	μs
0-1	1013	294,2	6,47E-03	1,96E-04	3,87E-06	3,32E-02
1-2	902	289,7	5,85E-03	1,78E-04	3,50E-06	1,45E-02
2-3	802	285,2	5,28E-03	1,60E-04	3,16E-06	6,18E-03
3-4	710	279,2	4,78E-03	1,45E-04	2,86E-06	2,87E-03
4-5	628	273,2	4,32E-03	1,31E-04	2,58E-06	1,79E-03
5-6	554	267,2	3,90E-03	1,18E-04	2,33E-06	1,31E-03
6-7	487	261,2	3,50E-03	1,06E-04	2,09E-06	1,05E-03
7-8	426	254,7	3,14E-03	9,54E-05	1,88E-06	1,03E-03
8-9	372	248,2	2,82E-03	8,55E-05	1,68E-06	1,02E-03
9-10	324	241,7	2,52E-03	7,65E-05	1,51E-06	9,89E-04

Here z is the distance from the Earth’s surface, in km; P is  the atmospheric pressure, in mbar; T is the air temperature, in K; μ_s,m (0.63) is the molecular scattering coefficient at a wavelength of 0.63 mm, in km^–1; μ_s,m (1.5) is the molecular scattering coefficient at a wavelength of 1.5 mm, in km^–1; μ_s,m (4) is the molecular scattering coefficient at a wavelength of 4 mm, in km^–1; and μ_s is the aerosol scattering coefficient for the clear-air atmosphere at a wavelength of 1.536 mm, in km^–1.

It can be seen that at the wavelengths λ = 1.536 and 4 mm, molecular scattering is low and can be neglected, but at the wavelength λ = 0.633 mm, it is much higher. The values of the aerosol scattering coefficients at the wavelength λ = 0.655 mm are not presented in the text, but they are greater than at a wavelength of 1.536 mm. Therefore, analyzing the data presented in the table, I can conclude that molecular scattering at the wavelength λ = 0.655 mm for the clear-air atmosphere considered in the text is of the same order of magnitude and even greater than aerosol scattering. Thus, my estimates at the wavelength λ = 0.633 mm contradict to authors’ statement that “Molecular scattering is an extremely microscopic thing.” Proceeding from the results of their calculations, I consider that the results obtained for the wavelength λ = 0.655 mm are incorrect and must be recalculated taking into account the influence of molecular scattering. Only after careful consideration of this comment, the manuscript can be published.

Reviewer 3 Report

The manuscript has been improved and some major flaws have been removed.

However I would like the authors to clarify some content that is important to judge the significance of their research:

Since the definition of the optical thickness has been clarified, could you please give the value of the optical thickness that you used for the simulations of figure 5. The length is 10 km, but which extinction coefficient did you use? Was it an average from the values of Table 2?

This is a very important information since the community needs to be able to judge under which conditions the PR imaging works and what the limits are.

 

Also it is still not clear to me, in which way you used Table 2 to perform the simulations. You have defined two weather conditions and you present four different scenarios in figure 5. From your answer letter we can conclude that you changed the number density and radius of particles but this does not appear in the manuscript. Could you please add this to the text since the reader does not know how you came up with the optical thickness parameter.