Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner
Round 1
Reviewer 1 Report
The paper has a proper structure and is well written. The content is well balanced between revealing the mathematical apparatus applied and experiment procedure description. I think it would be good to provide some explanation for choosing the second order Tikhonov regularization. Did the other regularization methods were taken into account (e.g iterative techniques like - truncated SVD or non-quadratic methods like total variation). Another thing worth explaining (in the future) is taking into account only the data taken from the limited region.
I have found a typo in Table 1 (Opertating).
All in all, the mentioned suggestions do not lower the quality of the paper that can be published in the present form.
Author Response
We thank the reviewer for his/her highly constructive and valuable suggestions. We addressed all the issues and changed the text in the revised manuscript accordingly.
Reviewer comments:
I think it would be good to provide some explanation for choosing the second order Tikhonov regularization. Did the other regularization methods were taken into account (e.g iterative techniques like - truncated SVD or non-quadratic methods like total variation). Another thing worth explaining (in the future) is taking into account only the data taken from the limited region.
Answer:
Total variation priors promote closed shapes of constant value in the reconstruction and, thus, do not comply with the expectation (nor prior knowledge) of the profiles in the counterflow burner.
Truncated SVD promotes a similar behavior to zeroth order Tikhonov [https://doi.org/10.1007/BF01937276], biasing the whole reconstruction to a low norm. As this contradicts our expectations and prior knowledge of the profiles (monotonic function of the radius with nonzero gradient), it is not regarded in this work.
For choosing the order of Tikhonov regularization we follow the following reasoning. The most important values of the reconstruction for model validation are the maximum values found on the centerline of the burner. As explained previously, a zeroth order Tikhonov regularization would bias the solution to low values in general and would not be explained by the diffusive transport in the gas. The first order Tikhonov regularization biases the solution to low gradients and, hence, also to a low range between minimum and maximum value of the expected monotonic profiles. The important maximum values at the center are therefore again biased low. The second order Tikhonov regularization promises to not bias first derivatives and therefor minimum and maximum values. Only a distortion in shape (biased to linear) is to be expected in the case of over regularization. Furthermore, second order Tikhonov was proven successful in previous work in chemical species tomography. Of course, these effects only become dominant in the case of overregularization or very high noise levels. Hence, evaluations conducted with first and second order Tikhonov regularization and properly chosen regularization parameters yielded very similar results. Nonetheless, for the reasons discussed above we limit the results presented in this work to second order Tikhonov regularization.
I have found a typo in Table 1 (Opertating).
Answer: We corrected the manuscript.
Reviewer 2 Report
The Manuscript ‘Axisymmetric linear hyperspectral absorption spectroscopy and residuum-based parameter selection on a counter flow burner’ by Johannes Emmert, Martina Baroncelli, Sani v.d. Kley, Heinz Pitsch and Steven Wagner demonstrate the recently introduced linear hyperspectral absorption tomography (LHAT) on an axisymmetric counterflow burner used for speciation studies of Oxyfuel combustion. This research is well aimed and it may positively influence the environment-friendly combustion.
This work is well written and organized; good quality figures are being used. Details of used procedure are very well presented, and the methods are described thoroughly. There can only minor shortcomings be found in the present version, and a revision (minor) is needed prior to publication.
1. The primary thought which comes to one’s mind is would it be feasible to evaluate the applicability of Lorentzian profile – as the Authors consider the broadening models in S.3.1. As recently demonstrated, Lorentzian profile results from CDHO model, and it has limitations originating from the assumptions made. Perhaps this would be helpful for the future considerations.
Thomas Mayerhöfer and Jürgen Popp. Quantitative Evaluation of Infrared Absorbance Spectra - Lorentz profile vs. Lorentz oscillator. Chem.Phys.Chem. 20 (2018) DOI: 10.1002/cphc.201800961
2. Other than that, some minor remarks may be helpful in the revision. The operating points are not explained (e.g. in Table 1). This is a surprising incosnistency, seeing as some textbook terms are being explained (e.g. FWHM, SNR). Last remark, not based on scientific evaluation of the manuscript. The reference suite is a bit short, and the work mostly appeals to a narrow readership.
Author Response
We thank the reviewer for his/her highly constructive and valuable suggestions. Their feedback helped us to improve the clarity of our manuscript. We addressed all the issues and changed the text in the revised manuscript accordingly.
Reviewer comments:
1. The primary thought which comes to one’s mind is would it be feasible to evaluate the applicability of Lorentzian profile – as the Authors consider the broadening models in S.3.1. As recently demonstrated, Lorentzian profile results from CDHO model, and it has limitations originating from the assumptions made. Perhaps this would be helpful for the future considerations.
Thomas Mayerhöfer and Jürgen Popp. Quantitative Evaluation of Infrared Absorbance Spectra - Lorentz profile vs. Lorentz oscillator. Chem.Phys.Chem. 20 (2018) DOI: 10.1002/cphc.201800961
Answer:
We are working solely on weak rovibrational transitions in the gas phase with Lorentz profile widths in the order of Doppler widths. As other homogeneous gas phase water measurements in ambient pressure flames did not show significant deviations from a Voigt profile [Diemel et al. Proceedings of the Combustion Institute, 2018, doi:10.1016/j.proci.2018.06.182].we assume the described effects can be neglected. However, we thank the reviewer for bringing this to our attention and the analysis of other gas phase species might benefit from the exact CDHO solution.
2. Other than that, some minor remarks may be helpful in the revision.
The operating points are not explained (e.g. in Table 1). This is a surprising incosnistency, seeing as some textbook terms are being explained (e.g. FWHM, SNR).
Answer: We added an explanation of the operation point in table 1.
Last remark, not based on scientific evaluation of the manuscript. The reference suite is a bit short, and the work mostly appeals to a narrow readership.
Answer:
We tried to reference only publications which support the statements or are related to it closely. Therefore, we avoided referencing applications in medical tomography or the use of tomography in civil engineering. We believe that the reference list already includes all relevant work. Nevertheless, we added two textbook references for absorption spectroscopy and TDLAS.
