Error Analysis of Integrated Absorbance for TDLAS in a Nonuniform Flow Field
Round 1
Reviewer 1 Report
Generally the authors tackled an interesting topic with huge impact on real world applications of the very promising tool TDLAS. I am promiting TDLAS and therefore think that applications would really benefit from solving the problem the authors raised. However, the authors generated a whole bunch of simulations and theoretical concepts detailing their part of the problem. In the end I have difficulties to follow whether the authors do have the right feeling when balancing the importance of their narrow look on the problem as compared to the full variety of problems.
So, two major criticisms from my side:
a. the authors don't look to any other problem spectroscopists must tackle even before they come to the problem the authors want to tackle when applying their method to real applications , i.e. what about pressure, tempature, and line parameter uncertainties when measuring species in combustion scenarios?
b. the authors do not provide any general tool to other spectroscopists, at least I cannot find it; so, how to make use of their results?
My recommendations:
1: line overlap error should not be coupled into non-uniformity error; both are different things.
2: talking about IA error, before other errors and uncertainties such as line parameters, pressure, temperature need to be quantified when the IA error is to be evaluated;. the error due to (e.g., line parameters, pressure, temperature), should be compared to the IA error to grate the importance of IA error and to conclude on the dominating factor.
3: the authors should first point out for their TDLAS measurements (at the target conditions) what is the main/the typical measurement uncertainty and then state when the IA error becomes significant.
4: can't understand why the authors put 'isolated spectra' in Fig 8 (and 9?), in real world, they never get those.
5: less important more my personal feeling, however worth to think about - it is not easy to follow the text as the authors define too many parameters which are quite difficult to remember when reading.
Author Response
Reviewer 1
Generally the authors tackled an interesting topic with huge impact on real world applications of the very promising tool TDLAS. I am promiting TDLAS and therefore think that applications would really benefit from solving the problem the authors raised. However, the authors generated a whole bunch of simulations and theoretical concepts detailing their part of the problem. In the end I have difficulties to follow whether the authors do have the right feeling when balancing the importance of their narrow look on the problem as compared to the full variety of problems.
So, two major criticisms from my side:
Comment 1: the authors don't look to any other problem spectroscopists must tackle even before they come to the problem the authors want to tackle when applying their method to real applications, i.e. what about pressure, tempature, and line parameter uncertainties when measuring species in combustion scenarios?
Response: Thanks for the reviewer's point of view. There are many factors involved in the uncertainty analysis of any measurement system. For spectrum measurement, the uncertainty of many parameters (including pressure, temperature, line parameters, etc.) will affect the final measurement results. They have been extensively discussed by many studies.
However, as a key intermediate variable of TDLAS technology, the integral absorbance error (IA error) is also very important, and is usually ignored in previous studies. As stated in the paper, the IA error is the systematic error of the measurement system itself, and is affected by the way of measurement object coupling with the measurement system, so that its uncertainty can be considered independent of the uncertainty of other parameters. Therefore, it is necessary to analyze its error separately, which indicates the feasibility of applying TDLAS technology in the non-uniform flow field.
The relevant content has been added in the fourth paragraph of the Section 1 in the revised manuscript.
At the same time, considering the presumption of the estimation method proposed in this paper, the uncertainty of other parameters (such as pressure, temperature, line parameters) can be ignored when estimating the IA error.
The relevant content has been supplemented in section 4.2 in the revised manuscript.
When estimating the uncertainty of the measurement object (such as concentration), the combined effect of the IA error and the error of other parameters can be comprehensively considered according to the specific measurement requirements and the error transfer function.
Comment 2: b. the authors do not provide any general tool to other spectroscopists, at least I cannot find it; so, how to make use of their results?
Response: We must admit that, limited by the non-uniformity of the flow field and the complexity of the TDLAS technology, it is difficult to provide a comprehensive error estimation method. This work is a preliminary exploration to achieve this goal, and its focus is to provide an analytical method to help users of TDLAS better understand its applicability in a non-uniform flow field environment.
At the same time, based on the analysis, we also proposed a simple method for estimating the integral absorbance error in a non-uniform flow field. The method consists of four simple steps:
- Divide the quasi-uniform flow field.
- Calculate the line damping parameters, normalization coefficient, and IA.
- Use line-shape parameters to find the corresponding error in the error distribution.
- Estimate the line overlap error.
We have modified the statement for readers to clearly understand the process. The detailed steps of this method have been clarified in section 4.2 in the revised manuscript.
Comment 3: line overlap error should not be coupled into non-uniformity error; both are different things.
Response: We agree with the reviewer that line overlap error and non-uniformity error are indeed different things. However, considering the actual measurement environment, especially in a high-pressure environment, line-shape distortion is often affected by line overlap and non-uniformity at the same time. In this situation, both are coupled with each other to cause the IA error. Therefore, the coupling effects must occur.
Comment 4: talking about IA error, before other errors and uncertainties such as line parameters, pressure, temperature need to be quantified when the IA error is to be evaluated; the error due to (e.g., line parameters, pressure, temperature), should be compared to the IA error to grate the importance of IA error and to conclude on the dominating factor.
Response: As we mentioned in the response to Comment 3, when evaluating IA error, the uncertainty of other parameters is negligible. At the same time, for the final measurement target, the error of other parameters (such as line parameters, pressure, temperature) is not caused by the TDLAS technology itself, so it is not within the scope of this article.
Comment 5: the authors should first point out for their TDLAS measurements (at the target conditions) what is the main/the typical measurement uncertainty and then state when the IA error becomes significant.
Response: For the non-uniform flow field, it is known that the uncertainty of TDLAS measurement still lacks a detailed analysis. Our work is to analyze the systematic error of its key intermediate variable (IA error). As we discussed in the introduction, IA errors are very likely to cause the main uncertainty of measurement.
4: can't understand why the authors put 'isolated spectra' in Fig 8 (and 9?), in real world, they never get those.
Response: As we mentioned as above, considering the practical application of TDLAS technology, the line overlap error needs to be considered. This increases the difficulty of estimating the IA error. Therefore, we need to compare the IA error in the ‘isolated spectrum’ and the ‘blended spectrum’ to analyze the effect of line overlap. Therefore, we assumed the existence of isolated spectra to analyze the effect of line overlap.
The relevant content has been added in section 4.1 in the revised manuscript.
5: less important more my personal feeling, however worth to think about - it is not easy to follow the text as the authors define too many parameters which are quite difficult to remember when reading.
Response: Thank Reviewer’s comment. The IA error in a non-uniform flow field is affected by multiple physical quantities, which is the difficult for error analysis. One of the purposes of this work is to simplify the error analysis. For this reason, we classify all physical quantities and finally focus on three line-shape parameters. For the convenience of reading, we add the explanation of parameter reduction in the context and how to complete the error analysis based on three line-shape parameters.
The relevant content has been added in section 2.2.3 in the revised manuscript.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Review of the manuscript entitled: “Error Analysis of Integrated Absorbance for TDLAS in a Nonuniform Flow Field”.
The paper presents an analysis of integrated absorbance error under a nonuniform flow field. The manuscript is well organized and clearly written.
I do not have any suggestions.
Author Response
Reviewer 2
The paper presents an analysis of integrated absorbance error under a nonuniform flow field. The manuscript is well organized and clearly written. I do not have any suggestions.
Response: We thank the reviewer for the positive comment.
Reviewer 3 Report
This manuscript is devoted to development the method of estimating the integrated absorbance error generated by signal distortion in a nonuniform flow field. The integrated absorbance error generated by the coupling of the nonuniformity, the absorption line features, and the line-shape fitting function, which are inherent to the measurement were considered. The simulations were carried out for calculation of estimation of integrated absorbance error with using the Levenberg–Marquardt fitting algorithm at various ratios of parameters of Voight line-shape etc. This manuscript is important for scientists in spectroscopic area, especially in area of diode-laser spectroscopy.
There are some points to correct or to make the information more clear:
- It is not convenient for reading that the letter “f” has some various meanings (e.g. in 121st line it is the subscript or index of species, then in 160th line it is the regression function, which is a single Voigt line-shape function, but there are regression function and indexes of f which was the one of the n quasi-uniform flow field absorption signals earlier, or it is the subscript from “fitting” here, in formula 15). It is necessary to mark all different values and subscripts by different letters. Besides it is not clear, that the letter of “β“ marks the SET of four fitting parameters (166th line), because further there is the letter of “β“ in the left part of equation, but there are all four parameters without any common symbol “β“ in the right part (formulas (15), (17)).
- Figure 2. It is necessary to clarify the numbers marked the boundaries of the colored areas in these Figures (a and b). Are they same numbers which are presented at the right scales for u and y? In this case it is not clear the position of “25” in the center of red area in the Figure 2(b).
- It is not clear where is the Data File 1 (233rd line), and it is possible to writhe here, that it is in Supplementary Materials , because this explanation is in the text of manuscript, but after text. Besides, all files in this ) archive has the name in format of “A_number-u_number.csv”. What does it mean “the Data File 1” in this case?
- It is necessary to explain the letters in Figure caption in the Figure 7. Because some letters were used earlier for other values (L, c), some captions are presented at first time (Ma (Is it Mach number?), X). Then the δ in Fig 7a is the dimension marked in figure, but in 7b it is the difference of two dimensions, etc.
- The blue line in the top parts of Figure 8 (the left top, especially) is almost invisible. And it is not clear that the black solid lines (Voight fit 1) are coincided with other lines (red lines, possibly) in the bottom part of Figure 8, isn’t it?
- There are small captions in all legends in the Figure 9, and the caption of X-axis in these figures (“δ/L) are
- There are some typos in the manuscript, e.g., “Guass” instead of “Gauss” (Figure 6 left top part); there is writing the “FADF“, though in all previous cases the Fadf fitting was written without Caps Lock.
- Authors presented results of their simulations but there are not in the text or in conclusion any comparison with results of applications of other algorithm of fitting carried out by other scientific groups.
Comments for author File: Comments.docx
Author Response
Reviewer 3
This manuscript is devoted to development the method of estimating the integrated absorbance error generated by signal distortion in a nonuniform flow field. The integrated absorbance error generated by the coupling of the nonuniformity, the absorption line features, and the line-shape fitting function, which are inherent to the measurement were considered. The simulations were carried out for calculation of estimation of integrated absorbance error with using the Levenberg–Marquardt fitting algorithm at various ratios of parameters of Voight line-shape etc. This manuscript is important for scientists in spectroscopic area, especially in area of diode-laser spectroscopy.
This manuscript describes with details the results of numerical simulation of estimation of integrated absorbance error with using the Levenberg–Marquardt fitting algorithm for Voight line-shape. In general the text is sufficiently clearly written. The manuscript can be published after minor revisions.
Response: We thank the reviewer for the positive comment.
Comment 1: It is not convenient for reading that the letter “f” has some various meanings (e.g. in 121st line it is the subscript or index of species, then in 160th line it is the regression function, which is a single Voigt line-shape function, but there are regression function and indexes of f which was the one of the n quasi-uniform flow field absorption signals earlier, or it is the subscript from “fitting” here, in formula 15). It is necessary to mark all different values and subscripts by different letters. Besides it is not clear, that the letter of “β“ marks the SET of four fitting parameters (166th line), because further there is the letter of “β“ in the left part of equation, but there are all four parameters without any common symbol “β“ in the right part (formulas (15), (17)).
Response: We thank the reviewer for the suggestion. We have thoroughly checked and revised the formulas in the text to ensure that there are no duplicate letters.
Comment 2: Figure 2. It is necessary to clarify the numbers marked the boundaries of the colored areas in these Figures (a and b). Are they same numbers which are presented at the right scales for u and y? In this case it is not clear the position of “25” in the center of red area in the Figure 2(b).
Response: We thank the reviewer and figure 2 has been modified to show the value distribution through gradient colors.
Comment 3: It is not clear where is the Data File 1 (233rd line), and it is possible to writhe here, that it is in Supplementary Materials , because this explanation is in the text of manuscript, but after text. Besides, all files in this ) archive has the name in format of “A_number-u_number.csv”. What does it mean “the Data File 1” in this case?
Response: We have changed all ‘Data File 1’ to ‘Supplementary Materials’ in the article.
Comment 4: It is necessary to explain the letters in Figure caption in the Figure 7. Because some letters were used earlier for other values (L, c), some captions are presented at first time (Ma (Is it Mach number?), X). Then the δ in Fig 7a is the dimension marked in figure, but in 7b it is the difference of two dimensions, etc.
Response: We have added an explanation of the letters in Figure 7 to the article.
Comment 5: The blue line in the top parts of Figure 8 (the left top, especially) is almost invisible. And it is not clear that the black solid lines (Voight fit 1) are coincided with other lines (red lines, possibly) in the bottom part of Figure 8, isn’t it?
Response: We amend Figure 8 to make it clearer. At the bottom of Figure 8, the black solid line does not completely overlap with the red line. In fact, the black solid line is the result of fitting the red line. The red line at the top of Figure 8 is the residual of the two.
The relevant content has been added in section 4.1 in the revised manuscript.
Comment 6: There are small captions in all legends in the Figure 9, and the caption of X-axis in these figures (“δ/L) are
Response: Thanks to the reviewer’s suggestions, we have modified Figure 9.
Comment 7:There are some typos in the manuscript, e.g., “Guass” instead of “Gauss” (Figure 6 left top part); there is writing the “FADF“, though in all previous cases the Fadf fitting was written without Caps Lock.
Response: The mistake has been corrected in the revised manuscript.
Comment 8: Authors presented results of their simulations but there are not in the text or in conclusion any comparison with results of applications of other algorithm of fitting carried out by other scientific groups.
Response: The fitting algorithm also has an important influence on the IA error, so we discussed it in Section 3.4. It focuses on comparing four different fitting methods. Many different approximate Voigt line shape algorithms have been applied in the past research. However, the evaluation of the fitting algorithm is beyond the scope of this paper. The four fitting methods compared in the article are already sufficiently representative.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Thank you for improving your manuscript, which now, to my opinion is ready to get published.
