文|梁佐佐

作为一名研究生，写期刊文章时要死要活，倘若要是一审意见是大修（major revision），心中怕是惊喜中透露着一丝疲惫——此时，你真得撸起袖子加油干，对每个返修意见表示臣服且认真修改。除修改文章外，回稿信必然要向编辑施展“才华”。本文，编者仅就自己的情况陈列出编辑的返修意见和自己的回稿信，回稿信的格式可供同学们参考，但具体的回复需视自己情况而定！

返修意见包含：1）审稿人对文章具体问题的疑惑；2）英语行文不规范；3）图片质量不够高；4）创新行的质疑；5）文章逻辑混乱；6）文章缺乏与已有方法学的相互比较，等等几乎所有可能的意见==。

在当初收到这么多且致命的审稿意见时，真是快要哭了，因为没有要求补充实验，只给10天修改时间。连续三天期间睡了十来个小时的觉，绞尽脑汁做了文章修改、写了回稿信（response letter）。

返修意见（太**长了，大家可直接跳到回稿信部分）：

Manuscript ID: 348443     Type: research article Title: A Quantitative Spectral Component Analysis Method Based on Maximum Likelihood 

Author: ********; Institute of High Energy Physics 

Dear ********: 

Before making a final decision on your manuscript, I would like to give you an opportunity to address the reviewers’ concerns. The reviews are appended below. 

It is the policy of Optics Express to allow only one revision cycle; therefore it is important to respond to all of the reviewer points carefully and to make it evident that you have done so.  For this reason, please provide a response letter to note any changes that have been made to the manuscript and indicate their locations.  You will upload your response letter in the online system.  Of course, you may not agree with the reviewers on every point. In this case, your responses and reasoning should be clearly presented because your manuscript might be sent for re-review upon resubmission. 

In addition to the reviewer comments, it is important that you address the production notes included below. These contain format changes that are necessary for your paper to comply with the style guidelines of Optics Express, should your paper be accepted for publication. 

Please submit your revised manuscript within 10 days via the Optics Express online system at http://prism.osapublishing.org/Author 

Revised manuscripts that arrive after the 10-day deadline may be treated as new submissions and be given a new submission date. 

Be sure to upload the native file, such as Word with embedded figures, or zipped TeX with .eps or .pdf figures. If uploading your revision in Word format you will also be given the opportunity to upload the source files of your artwork in eps, pdf or tiff format. Please carefully proofread your paper before resubmission. Optics Express articles are not copyedited. 

Thank you for your contribution to Optics Express. If you have any questions, please contact the journal assistant at opex@osa.org. 

Sincerely, 

Rajesh Menon 

Associate Editor, Optics Express 

--------------------------- 

--------Reviewer Comments-------- 

Reviewer 1: 

Questions/comments? 

1. Is Fi, described in equation 9, a good metric for identification precision? What if the estimated value, pi, is much higher then the true value, pi', therefore giving high Fi, when precision is low? Is precision controlled at each iteration step, and Fi always less than one? 

2. Please describe how the numbers in equations 10 and 11 were derived? 

3. How do you explain the different trend for 60Co identification (blue curve on the Fig.11)? 

4. VERY IMPORTANT! Please improve the quality of the text, sentences are often poorly constructed and hard to read. 

Also correct the typos, like referring in text template generation to fig.2 not fig.3 and naming columns as rows in table captions. 

5. Consider to group some figures, like fig. 7- 11 for better presentation. 

Reviewer 2: 

The manuscript reports a quantification method based on Maximum likelihood estimation using expectation maximization (MLEM) for quantitative spectral component analysis. Efficiency of the proposed method was confirmed on experimental and simulated gamma spectroscopic data with high precision. However, the following concerns need to be addressed before it can be considered for publication. 

1. Expectation maximization algorithm for maximum likelihood estimation is not a new method for quantitative analysis of spectroscopic data.  Similar applications have been reported in the following references. 

1) A. Steinborn, S. Taut, V. Brendler, G. Geipel, and B. Flach, "TRLFS: Analysing spectra with an expectation-maximization (EM) algorithm," Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 71, pp. 1425-1432, 2008. 

2) Néstor Cornejo Díaz; Maximum Likelihood estimation using expectation maximization applied to ambient dose equivalent measurements, Radiation Protection Dosimetry, Volume 182, Issue 2, pp. 285–293, 2018. MLEM has also been successfully utilized for quantitative gamma-ray spectroscopy, as shown in the reference below: 

3) L. J. Meng and D. Ramsden, "Improved quantitative gamma-ray spectroscopy using a standard 3 inch NaI detector," in 2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149), pp. 6/277-6/281 vol.1, 2000. 

The authors need to highlight the original contribution in the manuscript and the unique  advantages of the proposed method. 

2. The process of the algorithm was clearly presented, but it suffers from some errors and drawbacks as listed below: 

1) The line below Fig.2. It should be Fig.3 rather than Fig.2 that depicted the specific process of generating template library. 

2) It is suggested to change the subtitle 2.3 to be “Radionuclide Quantification Performance”, and the index “identification precision” to be “quantification precision”, because it involves not only the qualitative analysis, but also quantitative analysis. 

3) Equation 12, the normalization method for calculating the probability density spectrum should be moved to section 2.2, which would make the algorithm progress easier to undersand. 3. It’s unclear what sets of data (especially sets 2-4) were obtained experimentally or from simulations. If they were obtained experimentally, what were the experimental parameters? It would be nice to  have experimental data for the combinations of multiple radionuclides to truly test the method. 

4. Table 3, Fig. 14 

It appears that the accuracy information is only available for single radionuclides. What about the accuracy data for the combinations of multiple radionuclides? 

5. It is important to quantitatively compare the proposed method with other widely accepted algorithms for each set of data, regarding accuracy and computing time. How long does it take for the iteration process? 

6. What is the lower count limit that the proposed method can work effectively to quantify the desired components from the measured spectrum? 

--------Pre-Production Review-------- 

Please confirm that all of your funding sources have been added into your Prism submission in the Fees and Funding step. 

Capitalize only the first letter of your title, except for proper names, elements, and abbreviations. 

Citations such as "In Ref. 10" should not be used. It should be "In [10], Smith et al...."  

Capitalize only the first letter of your section headings, except for proper names, elements, and abbreviations.   

The text included in Fig. 1 is illegible. Resize the figures so that the text is able to be read. 

Format your figure or table captions to look like this: Fig. 1. Figure caption. OR Table 1. Table caption.  

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Abbreviate the single word "equation" to "Eq." and the plural word "equations" to "Eqs." throughout the text, except when either word appears at the beginning of a sentence. 

When citing multiple equations in your text, it should be formatted like this: Eqs. (1) and (2) or Eqs. (1)–(3). 

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Abbreviate the single word "figure" to "Fig." and the plural word "figures" to "Figs." throughout the text, except when either word appears at the beginning of a sentence.   

Ensure that your entire table and their entire captions fit on a single page. Move the table to the next page, if necessary.   

The Acknowledgments and Funding heading should be on a separate line, rather than in line with the acknowledgments and  funding text. 

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Capitalize only the first letter of your journal article titles, except for proper names, elements, and abbreviations. 

回稿信（我也要写的更条例、更更更长！）：

Manuscript ID: 348443     Type: research article

Title: A Quantitative Spectral Component Analysis Method Based on Maximum Likelihood

Author:*******; Institute of High Energy Physics

Dear Rajesh Menon and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “A Quantitative Spectral Component Analysis Method Based on Maximum Likelihood” (ID: 348443). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Responds to the reviewer’s comments:

Reviewer #1: 

1. Response to comment: Is Fi, described in equation 9, a good metric for identification precision? What if the estimated value, pi, is much higher than the true value, pi', therefore giving high Fi, when precision is low? Is precision controlled at each iteration step, and Fi always less than one?

Response: It is really true as Reviewer suggested that the previous metric Fi is not appropriate to describe the circumstance where pi is higher than pi’. We have re-written the Fi at Line 171 in the manuscript to evaluate the difference between the pi and pi’ and these changes will not influence the results shown in this paper but are more adaptive for potential scenarios. The precision Fi is obtained until its value tends to be stable after a large number of iterations, i.e. 100, 200 or 1000, and the selection of suitable iterations is discussed at Line 345-349 in the manuscript and it deserves to be studied in further work. Fi should really be less than one and the one means that the estimated pi is same to pi’ while smaller Fi denoting larger difference between pi and pi’.

2. Response to comment: Please describe how the numbers in equations 10 and 11 were derived?

Response: it is really a detail which should not be neglected as Reviewer suggested and a reference [27] "Energy and resolution calibration of NaI(Tl) and LaBr3(Ce) scintillators and validation of an EGS5 Monte Carlo user code for efficiency calculations” is added at Line 226 to support and supplement our work towards energy and energy resolution calibration of the experimental setup. The equations 10 and 11 are energy and energy resolution calibration (detector response) of the experimental setup and the numbers will guide the simulation of spectra of radionuclides absent in our laboratory. The numbers in equations 10 and 11 were derived as follows. Firstly, obtained the spectra of existing radionuclides through experiments. Secondly, searched and calculated the channels and FWHMs of the full-peaks (with constant energy) of these spectra. Thirdly, fitted the relationship between channels and full-peaks to Eq. 10 and the relationship between FWHMs and full-peaks to Eq. 11. Fourthly, the fitting results are shown as Eqs. 10 and 11.

3. Response to comment: How do you explain the different trend for 60Co identification (blue curve on the Fig.11)?

 Response: We are very sorry for our negligence of the explanation of the specific trend for 60Co identification (blue curve on the Fig.11) and corresponding discussion is added at Line 349-353 . Actually, final identification result is determined when the precision (estimated pi) is stable in the curve. In fact, the initial value of pi, etc. precision (pi/pi’) is random ranging from 0 to 1 at the begin of iterative process and the precision goes to a constant with the increasing of iterations.

4. Response to comment: VERY IMPORTANT! Please improve the quality of the text, sentences are often poorly constructed and hard to read.

Also correct the typos, like referring in text template generation to fig.2 not fig.3 and naming columns as rows in table captions.

Response: We are very grateful to Reviewer for reviewing the paper so carefully. We have tried our best to improve the manuscript and have modified some confusing sentences, making them concise and easy to read. Incorrect expressions as “ fig.2 not fig.3 ” and “ naming columns as rows ” are rectified at Line 124, 325 and 330.

4. Response to comment: Consider to group some figures, like fig. 7- 11 for better presentation.

Response: We appreciate it very much for this good and sweet suggestion, and we have done it according to your ideas.

Reviewer #2: 

1. Response to comment: Expectation maximization algorithm for maximum likelihood estimation is not a new method for quantitative analysis of spectroscopic data. Similar applications have been reported in the following references.

1)A. Steinborn, S. Taut, V. Brendler, G. Geipel, and B. Flach, "TRLFS: Analysing spectra with an expectation-maximization (EM) algorithm," Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 71, pp. 1425-1432, 2008.

2)Néstor Cornejo Díaz; Maximum Likelihood estimation using expectation maximization applied to ambient dose equivalent measurements, Radiation Protection Dosimetry, Volume 182, Issue 2, pp. 285–293, 2018.

MLEM has also been successfully utilized for quantitative gamma-ray spectroscopy, as shown in the reference below:

3)L. J. Meng and D. Ramsden, "Improved quantitative gamma-ray spectroscopy using a standard 3 inch NaI detector," in 2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149), pp. 6/277-6/281 vol.1, 2000.

The authors need to highlight the original contribution in the manuscript and the unique  advantages of the proposed method.

Response: we are very glad to highlight the original contribution in the manuscript and the unique advantages of the proposed method in our work. As Reviewer pointed that expectation maximization algorithm for maximum likelihood estimation is not a new method for quantitative analysis of spectroscopic data just as the references that Reviewer had listed. But, the previous works are far from quantitative spectral component analysis and algorithm using MLEM is not the key point of our presented paper. And we had added a representative citation [19] (“An Inter-comparison of three spectral-deconvolution algorithms for gamma-ray spectroscopy," IEEE Trans. Nucl. Sci. (2000).) at Line 56 to evaluate the MELM method. These three references that Reviewer had given really deserve to be read. However, works on analysis of spectroscopic data of these references are more about the shape fitting and deconvolution of the spectra. It is very important that there is one thing in common in these three references, and it is that all test spectra is with large counts. However, in our work, the test spectra is with low-counts. That is because of the methodology used in our work is different from ones used in these three references. In our work, the methodology based on MLEM achieves a high sensitivity of spectral component analysis of low-count scenarios.

  In order to compare our work to these three references, detailed comments on these references are described as follows:

1)A. Steinborn, S. Taut, V. Brendler, G. Geipel, and B. Flach, "TRLFS: Analysing spectra with an expectation-maximization (EM) algorithm," Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 71, pp. 1425-1432, 2008.

Key information in this reference: One critical result is shown in Fig.4, the first and second component of a TRLFS spectrum are fitted into several peaks using EM algorithm. In the last paragraph of Section 6, it is described as “Because the derived EM algorithm converges only locally, the fitting results depend on the start parameters. The number of components is most often a priori unknown, so the user has to start with the lowest reasonable guess (often being one) and subsequently increase this number as long as a sensible output is generated. The number of peaks per component – being six in the case of uranium(VI) – as well as the distances between the peak maxima are generally well-defined by physical constraints. Starting parameters for the positions of the peak maxima can be obtained easily by looking at the spectra’s shape, and even decent estimates for the fluorescence lifetimes are accessible, e.g. from a rough analysis of the spectrum integrated over the full wavelength range.” .

Conclusion 1: The number of components is not automatically obtained through the EM process and the final number depends on a sensible output determined by the user. But in our work, the component analysis result is automatically obtained.

Conclusion 2: The information of peaks such as the positions of the peak maxima and the number of peaks, is also obtained by the user and then the spectrum is fitted into these peaks by the derived EM algorithm. But in our work, the potential components existing in the test spectrum is invariable and the vital purpose of our work is to estimate the contribution of each component (i.e., quantitative spectral component analysis).

2)Néstor Cornejo Díaz; Maximum Likelihood estimation using expectation maximization applied to ambient dose equivalent measurements, Radiation Protection Dosimetry, Volume 182, Issue 2, pp. 285–293, 2018.

Key information in this reference: In Figs. 5 to 7, H*(10) rate spectrum is calculated by unfolding the test spectrum into the 10 peaks. In the third paragraph of Section RESULTS AND DISCUSSION, it is described as “The incident ambient dose equivalent rate spectrum was calculated by unfolding the test spectrum (Figure 5) with the ML-EM algorithm. As expected, the resolution of the calculated incident spectrum using the ideal detector response matrix, i.e. without including the detector energy resolution, was similar to the resolution of the pulse-height spectrum, as can be seen in Figure 6. In this case, the peaks related to the 609 and 662keV gamma-energy lines are not well resolved and consequently the ambient dose equivalent rate corresponding to each of these energies cannot be determined accurately.”.

Conclusion 1: The major work in this reference is to unfold the test spectrum into the spectrum of characteristic peaks (ambient dose equivalent rate spectrum). And the estimation of ambient dose equivalent rate is depending on the characteristic peaks of the special radionuclide. However, in our work, the quantitative spectral component analysis is done by using the full information of the spectrum of each radionuclide.

Conclusion 2: the analysis result of the ambient dose equivalent rate spectrum relies on the detector response (detector energy resolution), and the adjacent peaks would make the estimation accurately so that the method in this reference would be impracticable when the tested radionuclides have similar peaks. The MLEM algorithm is used to extract the characteristic peaks of tested spectrum and the components should be known in advance. But in our work, the detector response (detector energy resolution) is not under consideration since that the quantitative spectral component analysis doesn’t rely on the extraction of characteristic peaks.

3)L. J. Meng and D. Ramsden, "Improved quantitative gamma-ray spectroscopy using a standard 3 inch NaI detector," in 2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149), pp. 6/277-6/281 vol.1, 2000.

Key information in this reference: The major work in this reference is that extract the peak areas after de-convolving the test spectrum by MLEM and then estimate the cement ratio by the counts of peak areas. This work is more similar to the citation ( L. J. Meng and D. Ramsden, “An inter-comparison of three spectral-deconvolution algorithms for gamma-ray spectroscopy”, Accepted for publication in IEEE NSS.) which is cited in our work. In the first paragraph of Section RESULT, it is described as “In order to work out the peak areas, the measured energy-loss spectra were first de-convolved to take account of the effect of the response of the 3” NaI detector. This process can significantly improve the energy-resolution and the effective detection sensitivity of the detector. A comparison of the spectra before and after the de-convolution is shown in Figure 3. Clearly, most of the relatively intensive gamma ray lines can be easily resolved in the de-convolved spectra. Based on these spectra, the areas of the selected peaks can be derived easily.”. In the third paragraph of Section RESULT, it is described as “After this calibration, several test samples were prepared manually by mixing the sand and cement in different ratios. The spectra measured (1 hour) using these samples were de-convolved. The peaks-areas were extracted and used in the calculation of the cement ratio with Pakou method (Figure 6).”.

Conclusion 1: the MLEM algorithm is used to de-convolve the test spectrum and estimation of the cement ratio is done relying on the peak-areas. However, in our work, the MLEM algorithm is used to do the quantitative spectral component analysis directly. In fact, the de-convolution process is very different the spectral component analysis process proposed in our work, and the MLEM itself is not the focus but the methodology is.

Conclusion 2: The estimation of cement ratio is based on the peaks-areas extracted from the de-convolved spectrum and the quantitative information is derived from the counts of peak-areas. However, in our work, the quantitative spectral component analysis is done by using the full information of the spectrum of each radionuclide.

 In our work, a robust approach is developed for spectral analysis based on MLEM, and it is verified for quantitative spectral component analysis and reaches high precision in inferring the constituents of the test spectrum. In the study set forth, exact radionuclides are detected correctly with the corresponding proportion inferred with high precision in a test spectrum. The analysis procedure is concise and efficient due to the fact that the test spectrum is forwarded to the iteration process directly after normalization. And there is no background subtraction or feature (characteristic peaks) extraction process. It is incredible that there are no extra parameters or indirect judgment process while achieving a high sensitivity of spectral component analysis of low-count scenarios.

2. Response to comment: The process of the algorithm was clearly presented, but it suffers from some errors and drawbacks as listed below:

1)The line below Fig.2. It should be Fig.3 rather than Fig.2 that depicted the specific process of generating template library.

2)It is suggested to change the subtitle 2.3 to be “Radionuclide Quantification Performance”, and the index “identification precision” to be “quantification precision”, because it involves not only the qualitative analysis, but also quantitative analysis.

3)Equation 12, the normalization method for calculating the probability density spectrum should be moved to section 2.2, which would make the algorithm progress easier to undersand.

Response:

1) We are very sorry for our incorrect writing and it is rectified at Line 124.

2) It is really a good idea as Reviewer suggested, and we have changed them all to meet Reviewer’s thoughts.

3) We have carefully considered the suggestion of Reviewer and make some changes. Given that putting Equation 12 in front is easy to cause confusion between variables, we have cited Equation 12 at Line 135 as a special note.

3. Response to comment:It’s unclear what sets of data (especially sets 2-4) were obtained experimentally or from simulations. If they were obtained experimentally, what were the experimental parameters? It would be nice to have experimental data for the combinations of multiple radionuclides to truly test the method.

Response: Considering the Reviewer’s suggestion, we have added a special note at Line 259 and sets of data (1-4) are all obtained experimentally with experimental parameters shown in Table 2. And combinations of multiple radionuclides are sets of data (2-4) discussed in this paper.

4. Response to comment:Table 3, Fig. 14

It appears that the accuracy information is only available for single radionuclides. What about the accuracy data for the combinations of multiple radionuclides?

Response: We are very sorry for our negligence of the accuracy data for the combinations of multiple radionuclides. As Reviewer suggested, we have added the accuracy data in the corresponding Figs. 7, 8 9 and 10. And sets of data (2, 3 and 4) is for the combinations of multiple radionuclides.  

5. Response to comment:It is important to quantitatively compare the proposed method with other widely accepted algorithms for each set of data, regarding accuracy and computing time. How long does it take for the iteration process?

Response: As Reviewer suggested that It is important to make a quantitative comparison between the proposed method with others. However, the previous work did not focus on the quantitative spectral component analysis and relevant spectral algorithms are not suitable to the low-count spectra tested in our paper. The corresponding time for the iteration process could be neglected under 1000 iterations and 1000 times is enough for a stable quantitative result as we have shown in the paper. And we have added a corresponding discussion towards computing time at Line 351-353.

6. Response to comment: What is the lower count limit that the proposed method can work effectively to quantify the desired components from the measured spectrum?

Response: It is really a great suggestion as Reviewer pointed out that what is the lower count limit for the effective work of the proposed method. In fact, it is a very complicated problem to search for the lower count limit since that each radionuclide is different and lower count limit may be different for each radionuclide. The Fig.11 in the paper has shown the different trend of each radionuclide at low-count. The problem of the lower count limit may be more complicated when it comes to combinations of multiple radionuclides. In addition, the 100-count scenarios shown in the paper are sufficient to demonstrate the high-sensitivity of quantifying the desired components from the measured spectrum. But, it really deserves an in-depth research in our future work to follow this great suggestion.

--------------------------

We have tried our best to improve the manuscript and made some changes in the manuscript.  These changes will not influence the content and framework of the paper.

We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.

Sincerely,

********

今天的分享就到这，下期再会==