Three-Dimensional Transfer Functions of Interference Microscopes

Round 1

Reviewer 1 Report

The paper aim to define a mathematical approach to calculate the 3D TF for Coherent Scanning Interferometry. Extensive mathematical description is  done along the texy. Some examples of how the results affect the NA of the instrument as well 3D representations of the TF are shown.

The authors, however, could elaborate more some of the details ennumarated in the following lines, specially in the discussion. 

1. Specular and scatteing surface, do they referers to single point and more-dimensional analysis?
2. Page 3 line 66, numerical aperture depending on the instruments are very different, could the author give a range of NA where the diffractive far-field low pass is still valid for the calculations?  Also the NA is 0.55 and 0.9 in page 6, are these normal NA for CSI?
3. Page 9, the authors claim to use lambda=550nm from there on, why they did not use it before?
4. Section 2.3, I am not sure if I understood the aim of this section, is to give the equations and tools to understand why a 3D TF can affect the mirror surface measurements instead of the 2D? Also the section uses f for fringes in the equations, which is usually used for focal length. It may be confused
5. page 15 line 208 Aluminum instead of Aliminum.
6. The discussion about the previous paper is unnecesary in Sec. 3. However, some words about the final goal of developing 3D FT needs to be mention, being for example if the calculations will be used for a new software to run the Mirau CSI and in that case which code will be use, i.e., Python, Matlab, etc..

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Summary

In this paper, the authors describe a novel approach to derive an analytical description of the 3D transfer function (TF) for coherence scanning interferometry (CSI) in the acquisition of specular surfaces. The case of monochromatic illumination is considered first, before the approach is extended to the more general case of broadband illumination. It was shown that the surface reconstruction is highly dependent on the spectral bandwidth and also, as expected, on the numerical aperture (NA). The respective derivations are presented in a well comprehensible and mathematically sound manner. Furthermore, the authors present an approach to explain different transfer characteristics in the reconstruction of surfaces of different periodicity based on the detection of the coherence maximum of CSI signals.

 

Comments

The subject of the paper agrees very well to the topics covered by Metrology. The authors are not engaged in any kind of plagiarism or unethical academic practices. There is no possibility, that the manuscript could cause political or social issues. The linguistic quality of the paper is very high, a revision by a native speaker is not necessary. The quality of the figures is very high.

The individual chapters of the article build very well on each other. The problem definition, the mathematical methods used and the conclusions drawn are presented in great detail and are easy to understand.

 

Conclusion

Summarizing the high relevance and the very high quality, the paper should be accepted for publication in Metrology.

Author Response

Dear Reviewer, thank you very much for your positive comments on our manuscript.

Reviewer 3 Report

This is a 3rd paper on this group work on 3D Transfer functions for interference microscopes.
Here the authors address theoreticaly the particular problem of specularly reflecting surface. This is a rather difficult task with inherent complications. The approach is sound. The contribuition is of significance and the authors identify and stress the major limitations of this approach, that in any case has some advantages and the paper provides valid insights and should be published.
Please check the titles and distribution of the different chapters and include a Conclusion one, at the end, to sumarize the results.

Author Response

Dear Reviewer, thank you for your positive feedback. As you requested, we included a Conclusions chapter at the end of the manuscript. Unfortunately, the titles and the order of the different chapters are specified by the MDPI template, so that we cannot change them.