A Novel Mid-Infrared Narrowband Filter for Solar Telescopes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a theoretical parameter study for extending ultra high-resolution guided-mode resonance filters (GMRF) to the long-wave infrared for solar telescope applications. I think the study is well-motivated,  but the results are incremental, and one-third of the paper is consumed with the restatement of decades-old derivations which add nothing original and are not properly attributed. My recommendations for revision are below.

1. In Section 1, add a brief (few sentence) overview of the process of retrieving magnetic field using the Zeeman effect in spectral lines to help motivate the need for ultra-high spectral resolution.  Also, the FWHM requirement of order 0.01 nm (Line 69) should be justified with some discussion of the line width and line shape of the longwave IR lines of interest. Line 69 references Stenflo 1985 [10] to justify the requirement, but the Stenflo paper looked at spectral lines with 10-20x shorter wavelength, so thermal broadening would be correspondingly less.
2. Section 2 does not seem to add anything new and presents some concerns about attribution to earlier papers. It consists of a grating derivation from Gaylord et al. 1985 [30] merged with a waveguide derivation from Wang & Magnusson 1995 [31]. I suggest stating only the key equations from each reference with attribution instead of showing the entire derivation. If the full derivations remain, the paper needs to be explicitly state which derivations are reproduced from which reference.
   1. Gaylord et al. 1985 [30] are referenced only once in line 50, but in fact equations 3-17 come directly from equations 2-25 in Gaylord et al. 1985. In some places, the text connecting equations in the Gaylord derivation is copied word for word.
   2. Wang & Magnusson 1995 [31] are referenced only once in line 190, but equations 22-28 come from equations 2-15 in Wang & Magnusson 1995 (not always in the same order).
   3. Figure 1 is copied from Wang & Magnusson 1993 [17].  This needs to be attributed explicitly and in the caption, e.g. “reproduced from [17] Fig. 1”.
   4. Equation 29 does not appear in Wang & Magnusson 1994 [32] as referenced, and I cannot find it in that exact form in any of the other references I searched. Please fix the reference.
3. The results in Section 3 are somewhat incremental. The theory already exists, the code presumably already exists, and the new result seems to be the particular set of parameters that enables the code to theoretically produce a very narrow bandpass in the longwave IR. However, it’s not clear whether this is achievable in practice. More detail in the following areas would help justify that the results are worthy of publication.
   1. This section uses rigorous coupled-wave analysis (RCWA) to produce the results but provides no description or citation for the particular RCWA code used. This information should be added. Adding some discussion of how the code has been validated would improve the reader’s confidence in the results presented.
   2. In the caption of Figure 5, you mention “grating thickness d” but you only show the value of m, not d. You don’t provide epsilon_1, so I could not get d from Equation 29. Give d and epsilon_1 explicitly, or restate Equation 29 to use refractive index, which is given in line 228 – 229.
   3. Compare the parameters used here directly with the ones used to design other longwave IR filters with wider FWHM (e.g. Gupta & Mirotznik 2018 [25]).  Explain what in your parameter set enables you to achieve the much narrower passband (is it just the half-wavelength grating thickness?). Explain why earlier studies have not attempted this.
   4. Related to the above, explain whether the theoretical results are achievable in practice and the major impediments to manufacture. In particular, I would like to see some discussion of the allowable tolerance on grating thickness to maintain the required FWHM (i.e. how much m can deviate from its ideal even integer value).  Is this tolerance achievable in practice?

Author Response

Dear reviewer:

We are truly grateful to your critical comments and thoughtful suggestions. Based on these comments and suggestions, we have made careful modifications on the original manuscript. All changes made to the text are highlighted in the re-submitted files. We hope the revised manuscript will meet the requirement of Universe. The followings are our point-by-point responses to all the comments.

 

This paper presents a theoretical parameter study for extending ultra high-resolution guided-mode resonance filters (GMRF) to the long-wave infrared for solar telescope applications. I think the study is well-motivated,  but the results are incremental, and one-third of the paper is consumed with the restatement of decades-old derivations which add nothing original and are not properly attributed. My recommendations for revision are below.

1. In Section 1, add a brief (few sentence) overview of the process of retrieving magnetic field using the Zeeman effect in spectral lines to help motivate the need for ultra-high spectral resolution.  Also, the FWHM requirement of order 0.01 nm (Line 69) should be justified with some discussion of the line width and line shape of the longwave IR lines of interest. Line 69 references Stenflo 1985 [10] to justify the requirement, but the Stenflo paper looked at spectral lines with 10-20x shorter wavelength, so thermal broadening would be correspondingly less.

Reply:  we add a brief introduction to solar magnetic fields and spectral resolution for Zeeman effect, please see lines 66-88 in revised paper in detail. The measurement of solar magnetic fields can be achieved by analyzing the splitting or polarization of spectral lines produced by the Zeeman effect. However, these magnetic signals are usually weak and mixed with the thermal Doppler broadening of the lines, making their detection and interpretation challenging. Ultra-high spectral resolution is critical to distinguish the polarization information from the Doppler-broadened profiles, enabling more precise and reliable extraction of magnetic field information. In the mid-infrared band, although the Doppler broadening is greater, the spectra splitting distance is also larger due to the Zeeman effect. Therefore, a high spectral resolution is still important, please see figure 1 and its corresponding description in text.

2. Section 2 does not seem to add anything new and presents some concerns about attribution to earlier papers. It consists of a grating derivation from Gaylord et al. 1985 [30] merged with a waveguide derivation from Wang & Magnusson 1995 [31]. I suggest stating only the key equations from each reference with attribution instead of showing the entire derivation. If the full derivations remain, the paper needs to be explicitly state which derivations are reproduced from which reference.

Reply: Thanks for your good suggestion. We reorganized Section 2, listing only the key equations from each reference.

1985. Gaylord et al. 1985 [30] are referenced only once in line 50, but in fact equations 3-17 come directly from equations 2-25 in Gaylord et al. 1985. In some places, the text connecting equations in the Gaylord derivation is copied word for word.

Reply: We have deleted equations (4)-(16) and retained only equations (3) and (17), please see equations (3) and (4) in revised paper.

1. Wang & Magnusson 1995 [31] are referenced only once in line 190, but equations 22-28 come from equations 2-15 in Wang & Magnusson 1995 (not always in the same order).

Reply: We have deleted equations (23)-(27) and retained only the key results, please see equations (10) in revised paper.

1. Figure 1 is copied from Wang & Magnusson 1993 [17].  This needs to be attributed explicitly and in the caption, e.g. “reproduced from [17] Fig. 1”.

Reply: We add “reproduced from [27] Fig. 1” in caption, please see figure 2 in revised paper.

1. Equation 29 does not appear in Wang & Magnusson 1994 [32] as referenced, and I cannot find it in that exact form in any of the other references I searched. Please fix the reference.

Reply: Wang and Magnusson (1994) [32] presented the results shown in Figures 3 and 4, along with their conclusions. However, we have independently edited Equation 29. Hence, you can not find the same formula. But we are sure the formula is exactly right.

3. The results in Section 3 are somewhat incremental. The theory already exists, the code presumably already exists, and the new result seems to be the particular set of parameters that enables the code to theoretically produce a very narrow bandpass in the longwave IR. However, it’s not clear whether this is achievable in practice. More detail in the following areas would help justify that the results are worthy of publication.
   1. This section uses rigorous coupled-wave analysis (RCWA) to produce the results but provides no description or citation for the particular RCWA code used. This information should be added. Adding some discussion of how the code has been validated would improve the reader’s confidence in the results presented.

Reply: we employ the DiffracMod module in the Rsoft software. This module uses the RCWA to precisely calculate the transmission and reflection efficiencies. We add the description about Rsoft software in revise paper, please see the first paragraph in Section 3. We have replicated the results (the following figure) of Gupta & Mirotznik 2018 (figure 3(a) in their paper), demonstrating that the calculation method is effective. It is noted that Gupta & Mirotznik had a mistake in Table 1, the values of h_wg and h_g were written in reverse.

 

29. In the caption of Figure 5, you mention “grating thickness d” but you only show the value of m, not d. You don’t provide epsilon_1, so I could not get d from Equation 29. Give d and epsilon_1 explicitly, or restate Equation 29 to use refractive index, which is given in line 228 – 229.

Reply: In lines 234-237 in revised paper, we have added a description of the relationships among various parameters, based on this, the value of d can be calculated.

1. Compare the parameters used here directly with the ones used to design other longwave IR filters with wider FWHM (e.g. Gupta & Mirotznik 2018 [25]).  Explain what in your parameter set enables you to achieve the much narrower passband (is it just the half-wavelength grating thickness?). Explain why earlier studies have not attempted this.

Reply: We are able to replicate the results of Gupta & Mirotznik 2018 (as above). However, we regret that making a direct comparison with their work proves challenging. The two applications have distinct goals. Their research is primarily focused on notch filters, where a bandwidth typically between 10 - 20 nm is enough. In fact, such a ultra-narrow bandwidth is a unique requirement for solar magnetic field observations. So I think that the reason early scholars didn't attempt it was mainly due to the lack of application scenarios, except for in solar telescopes. However, in solar physics, we are the team that attempts the possibility of using a GMRF as an ultra-narrowband filter.

1. Related to the above, explain whether the theoretical results are achievable in practice and the major impediments to manufacture. In particular, I would like to see some discussion of the allowable tolerance on grating thickness to maintain the required FWHM (i.e. how much m can deviate from its ideal even integer value).  Is this tolerance achievable in practice?

Reply: We added the tolerance analysis on grating thickness in revised paper, please see lines 269-272 and figure 8. it is shown that FWHM varies approximately linearly with the thickness error, and an error of 0.05μm is acceptable.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This work gives the mathematical and design framework for creating a guided mode resonance filter for the mid infrared, a new type of filter that could greatly improve the study of spectra in this wavelength band, similar to a Fabry-Perot interferometer in the visible. This is a very interesting and potentially influential tool that should be published in this journal. Scientifically I am satisfied with this work, however the presentation and context is lacking and should be improved before publication. 

In general there are a few open questions that have no been addressed by this paper that may be trivial, but should still be discussed. 

1) Why is this filter aimed for solar observations? Such a filter would also be very valuable for night-time observations and labs. Perhaps the throughput is very low and only the Sun is bright enough? If this would work for other instruments, I suggest that the scope be widened from just solar telescopes to other telescopes. 

2) While this is an instrumental work, I lack context for why this wavelength band is important. It is mentioned a few times in the work that observing in this band is a critical issue, but never why. Please add this context. 

3) The work is missing citations from the Brazilian infrared group. E.g. Kaufmann, Simoes, Kudaka. I believe that reading and including their papers about their '30 THZ' observations would  not only help the manuscript, but also provide valuable context for point 2. 

4) Discussion: Could you discuss the implications and limitations of this better? What would this filter be used for? How big van the field of view be, how long would a telescope need to integrate? I'm not asking for simulations, but some kind of estimate would he helpful! 

5) Could perhaps a fiber be used to force the angle of incidence to be correct? Can the fiber or filter be tilted to scan the wavelengths like a Fabry-Perot interferometer? If wide wavelength ranges can be scanned, even a small FOV could be useful. If fibers work, then this would also be useful for stellar observations. 

I will now go into the points that are related to line numbers.

• Line 13: See point 2
• Introduction. The first paragraph contains 3-4 good opening lines, but it reads very repetitive to have them all. The author should pick 1 or consolidate the information in this paragraph. 
• Line 40: The far infrared, microwaves, and radio are not mentioned. It would also be good if one or two (review) papers could be cited for each band. 
• Line 40: Please use 'μm' and not 'um' throughout the manuscript. 
• Line 43: This is not true, the Brazilian group has and is operating small mid-IR imagers. There is also the Mexican telescope: https://scispace.com/pdf/a-solar-mid-infrared-telescope-4zp1pm8z5b.pdf
• Line 47: Please substantiate this line with a citation. 
• Line 50: Please give examples. 
• Line 66: I believe that there is a translation problem in this paragraph. 'Filtering' applies to narrowband imaging filters, and should not be used as a catch-all term. An FTS spectrum does not 'filter' the light between each measured point. I would suggest using the term narrowband observations or high-resolution spectra. Please address this in this paragraph and throughout the manuscript.
• Line 69: Please explain why this 0.01nm number is important. Many instruments work at lower resolutions, so I wonder why this is so universal. 
• Line 80: please give the required acquisition time and explain what it is needed for. 
• Line 92: two dots.
• Line 120: Please explain why untra-narrowband filtering is needed. 
• Fig1: Please give a full description of the figure in the caption, also the top layer should be colored. 
• Line 157: Please cite or explain. 
• Line 212: Could an indication of the cost be given, or how hard this is to make? How large can the gratings be?
• Fig2&3&4: Please explain these figures in the caption. Especially figure 4 is not clear to me.
• Line 248: Please give the units of the parameters in the equations mentioned. 
• Line 273: Should be Discussion and conclusion? Conclusion section is missing, but this seems to be both. 
• Line 297: you are missing some words. "In the next (project, step?) it is necessary..."

I hope that all my questions and comments are clear and help improve the manuscript.

Kind regards

The referee. 

Comments on the Quality of English Language

I believe that the work would profit from being read by a native speaker, perhaps this can be done. Otherwise I can make a more thorough read in the next round, please let me know if that is needed. 

Author Response

Dear reviewer:

We are truly grateful to your critical comments and thoughtful suggestions. Based on these comments and suggestions, we have made careful modifications on the original manuscript. All changes made to the text are highlighted in the re-submitted files. We hope the revised manuscript will meet the requirement of Universe. The followings are our point-by-point responses to all the comments.

 

 

This work gives the mathematical and design framework for creating a guided mode resonance filter for the mid infrared, a new type of filter that could greatly improve the study of spectra in this wavelength band, similar to a Fabry-Perot interferometer in the visible. This is a very interesting and potentially influential tool that should be published in this journal. Scientifically I am satisfied with this work, however the presentation and context is lacking and should be improved before publication. 

In general there are a few open questions that have no been addressed by this paper that may be trivial, but should still be discussed. 

• Why is this filter aimed for solar observations? Such a filter would also be very valuable for night-time observations and labs. Perhaps the throughput is very low and only the Sun is bright enough? If this would work for other instruments, I suggest that the scope be widened from just solar telescopes to other telescopes.

Reply: This filter features a high transmittance and holds significant value for both nighttime observations and laboratory research. At present, though, solar observations have a particular need for such ultra - narrowband filtering. In contrast, the bandwidth requirements for nighttime observations and laboratory work typically fall within the nanometer range. As a result, this paper focuses primarily on the design tailored to solar observations. Once the ultra - narrowband performance is realized, it will be much easier to meet the demands of nighttime observations and laboratory applications. Hence, in discussion section, we said “In the future, it will greatly enhance the flexibility of terminal devices and be widely applied in fields such as astronomy, military, remote sensing, and biology, showing very broad application prospects.”.

• While this is an instrumental work, I lack context for why this wavelength band is important. It is mentioned a few times in the work that observing in this band is a critical issue, but never why. Please add this context. 

Reply: We add the description in introduction, please see lines 66-88 and figure 1 in revised paper.

• The work is missing citations from the Brazilian infrared group. E.g. Kaufmann, Simoes, Kudaka. I believe that reading and including their papers about their '30 THZ' observations would  not only help the manuscript, but also provide valuable context for point 2. 

Reply: Thanks for good suggestion. We add their work as referees, please see citations [11-14] in revise paper.

• Discussion: Could you discuss the implications and limitations of this better? What would this filter be used for? How big van the field of view be, how long would a telescope need to integrate? I'm not asking for simulations, but some kind of estimate would be helpful!

Reply: I'm extremely sorry, but this question is rather difficult to answer. This type of filter represents an emerging technology. Just like the Fabry - Perot (FP) cavity, it theoretically exhibits a high transmittance. Currently, the most pressing issue is its sensitivity to the angle of incidence. This is exactly the problem we will tackle first in our subsequent work. Only after resolving this problem will we be in a position to estimate parameters such as exposure time and field of view. At present, it remains a preliminary feasibility design.

• Could perhaps a fiber be used to force the angle of incidence to be correct? Can the fiber or filter be tilted to scan the wavelengths like a Fabry-Perot interferometer? If wide wavelength ranges can be scanned, even a small FOV could be useful. If fibers work, then this would also be useful for stellar observations. 

Reply: We are sure that using optical fibers is feasible, and the wavelengths can be scanned by tilting. I think this kind of filter is easier to apply in nighttime observations. Obviously, solar imaging observations are more challenging, and that's precisely the reason why we are working in this area.

I will now go into the points that are related to line numbers.

• Line 13: See point 2

Reply: We add the description in introduction, please see lines 66-88 and figure 1 in revised paper.

• Introduction. The first paragraph contains 3-4 good opening lines, but it reads very repetitive to have them all. The author should pick 1 or consolidate the information in this paragraph.

Reply: Thanks. We have revised the last few sentences of the first paragraph. Please see lines 31-36 in revised paper.

• Line 40: The far infrared, microwaves, and radio are not mentioned. It would also be good if one or two (review) papers could be cited for each band.

Reply: We add the radio and other citations in revised paper, please see lines 37-39 and referees [1-5].

• Line 40: Please use 'μm' and not 'um' throughout the manuscript.

Reply: We revise all the 'μm' throughout the manuscript.

• Line 43: This is not true, the Brazilian group has and is operating small mid-IR imagers. There is also the Mexican telescope: https://scispace.com/pdf/a-solar-mid-infrared-telescope-4zp1pm8z5b.pdf

Reply: Thanks. We add the important paper in revised text, please line 42 and referee [16].

• Line 47: Please substantiate this line with a citation.

Reply: Please see referee [16] in line 47.

• Line 50: Please give examples.

Reply: Lines 50-64 are examples for solar telescopes.

• Line 66: I believe that there is a translation problem in this paragraph. 'Filtering' applies to narrowband imaging filters, and should not be used as a catch-all term. An FTS spectrum does not 'filter' the light between each measured point. I would suggest using the term narrowband observations or high-resolution spectra. Please address this in this paragraph and throughout the manuscript.

Reply: Thanks for good suggestion. We use narrowband observations instead of filtering in some important places. Such as line 65.

• Line 69: Please explain why this 0.01nm number is important. Many instruments work at lower resolutions, so I wonder why this is so universal. 

Reply: We add the text in lines 66-88 and figure1 in revised paper.

• Line 80: please give the required acquisition time and explain what it is needed for. 

Reply: We add the context in lines 66-88 and figure1 in revised paper.

• Line 92: two dots.

Reply: We modify it.

• Line 120: Please explain why untra-narrowband filtering is needed. 

Reply: We add the text in lines 66-88 and figure1 in revised paper.

• Fig1: Please give a full description of the figure in the caption, also the top layer should be colored. 

Reply: We add it, please see figure 2 in revised paper.

• Line 157: Please cite or explain.

Reply: It has been deleted in revised paper.

• Line 212: Could an indication of the cost be given, or how hard this is to make? How large can the gratings be?

Reply: Currently, the grating can be made to be about 2 centimeters in size. Lithography technology is required, and the manufacturing difficulty is still relatively high at present.

• Fig2&3&4: Please explain these figures in the caption. Especially figure 4 is not clear to me.

Reply: We add the description for all the figures, especially figure 4. Please see Lines 203-214, Lines 235-239, Lines 270-273 in revised paper.

• Line 248: Please give the units of the parameters in the equations mentioned.

Reply: f and m are dimensionless.

• Line 273: Should be Discussion and conclusion? Conclusion section is missing, but this seems to be both. 

Reply: Yes, it includes discussion and conclusion. So we revise the discussion as “discussion and conclusion” as shown in line 285 in revised paper.

• Line 297: you are missing some words. "In the next (project, step?) it is necessary..."

Reply: We add “step” in line 309 in revised paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This article introduces a novel ultra-narrow band filter for solar telescopes - the guided-mode resonance grating. It derives the principles and calculation processes, and presents an initial design scheme; it analyzes the impact of parameters such as grating period, thickness, fill factor, and incident angle on the performance of the grating, providing guidance for the design and manufacture of guided-mode resonance gratings for solar telescope. The article is well written and substantiated with theory and methods. It is recommended to be accepted after answer and supplement the following questions.

• What are the different modes 𝑣 in equation (4)? (Frequencies?)
• What is the physical meaning of the ℎ component in ？ What is the range of values for ℎ？
• What is the physical meaning of the ？Describe it in detail.
• How is Figure 4 calculated, complement the calculation process.

Author Response

Dear reviewer:

We are truly grateful to your critical comments and thoughtful suggestions. Based on these comments and suggestions, we have made careful modifications on the original manuscript. All changes made to the text are highlighted in the re-submitted files. We hope the revised manuscript will meet the requirement of Universe. The followings are our point-by-point responses to all the comments.

 

This article introduces a novel ultra-narrow band filter for solar telescopes - the guided-mode resonance grating. It derives the principles and calculation processes, and presents an initial design scheme; it analyzes the impact of parameters such as grating period, thickness, fill factor, and incident angle on the performance of the grating, providing guidance for the design and manufacture of guided-mode resonance gratings for solar telescope. The article is well written and substantiated with theory and methods. It is recommended to be accepted after answer and supplement the following questions.

• What are the different modes ? in equation (4)? (Frequencies?)

Reply: ? presents different mode but not frequency. But the equation (4) has been deleted in revise paper.

• What is the physical meaning of the ℎ component in ？ What is the range of values for ℎ？

Reply: h represents a certain order in the series expansion of the grating's dielectric constant, and its range is from negative infinity to positive infinity.

• What is the physical meaning of the ？Describe it in detail.

Reply: The parameter has been deleted in revised paper.

• How is Figure 4 calculated, complement the calculation process.

Reply: We add the calculation process, please the lines 234-238 in revised paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

Thank you for the fast response to my report. I believe that the paper can be published now. My only comment now is that Fig.1 needs a better description or titles. As now it is not clear that these are Fe and Mg lines. This should be easy to fix!

I don't need to see it again, so the editor can accept it once this is done. 

Kind regards and good luck with this interesting technology. 

Author Response

Comment1：fig1 needs a better description or titles. As now it is not clear that these are Fe and Mg lines.

Reply1: we revised the fig1’s title as “Profile simulation of Stokes parameters with different observation spectral lines (Fe I at 617.3 nm and Mg I 12.32 μm) under the same solar magnetic field. Column 1: Fe I 617.3 nm with spectral resolution of 0.01nm. Columns 2-5: Mg I 12.32 μm with spectral resolution of 0.02 nm, 0.1 nm, 0.2 nm & 0.3 nm respectively”.