Algorithm for Surfaces Profiles and Thickness Variation Measurement of a Transparent Plate Using a Fizeau Interferometer with Wavelength Tuning
Round 1
Reviewer 1 Report
The manuscript of Dr. T. Sun et al. demonstrates the methodology of the interferometric measurement of the interface profiles and thickness of the optical elements when the wavelength tuning is applied during measurements. Generally, the manuscript is quite clearly written and easy to follow but the style of writing is not suitable in some places. The motivation and aims are well stated in the manuscript. The abstract and discussion need to be corrected prior to publication. Additional information is required in the manuscript to make it more clear.
The following issues need to be addressed prior to publication:
1. The Abstract should concisely demonstrate what has been done. The current style of the abstract text is not suitable. Please, rewrite it.
2. Line 42: ‘measurement modulation’ – remove repetition.
3. Line 57 – it would be good to include here the references of the phase step methods
4. Lines 59-63 – the sentence is too long. Hard to follow what the authors wanted to say.
5. Line 64 – ‘single signal detection’ ? Please be more specific.
6. Introduction – please, try to include 1-2 sentences summarizing the novelty of the proposed approach.
7. Line 72 – please, remove the word ‘superimposed’.
8. Eq.1 – k is not explained in the text
9. Line 83 – dlambda/dk - is it really the rate of change of wavelength per time unit?? (not wavenumber??)
10. Line 90 – it is better to use the terms ‘interface’ rather than ‘wavefront’.
11. Why actually the algorithm consists of 32 steps not the other number.
12. Line 121 – please revise the sentence.
13. Line 126 – change ‘improving’ to ‘improve’
14. Figure 3 – how would the Gaussian window work?
15. Line 161 – there is ‘x’ missing between ‘1024’
16. Line 193 – ‘title’ ???
17. Line 196 – ‘three-plate transparent plate’ ??
18. Line 196-197 – revise the sentence
19. Discussion should be extended
Author Response
Point 1: The Abstract should concisely demonstrate what has been done. The current style of the abstract text is not suitable. Please, rewrite it.
Response 1: We agree with the reviewer’s comment. We have revised the abstract completely, and we wish the revised abstract can concisely demonstrate what we has been done.
Point 2: Line 42: ‘measurement modulation’ – remove repetition
Response 2: We have removed the ‘measurement modulation’, and thanks a lot for checking our little mistake.
Point 3: Line 57 – it would be good to include here the references of the phase step methods
Response 3: Yes, it is a good advice, and we have add a reference of the phase step methods in the manuscript.
Point 4: Lines 59-63 – the sentence is too long. Hard to follow what the authors wanted to say.
Response 4: We have rewrite this sentence in the manuscript.
Point 5: Line 64 – ‘single signal detection’ ? Please be more specific.
Response 5: Yes, the single signal point to the signal of the surface to be tested, and we have revised it in the manuscript.
Point 6: Introduction – please, try to include 1-2 sentences summarizing the novelty of the proposed approach.
Response 6: “The 36-step algorithm not only realizes the separation of multi-surface superposition information, but also breaks through the traditional limitation of short air-gap length when measuring thin-plate components, thereby effectively avoiding the risk of collision of the reference mirror due to the cavity length being too small in the actual measurement process.” We have add the sentences in the bottom of the introduction.
Point 7: Line 72 – please, remove the word ‘superimposed’.
Response 7: Yes, we have remove the word ‘superimposed’ in the manuscript.
Point 8: Eq.1 – k is not explained in the text
Response 8: k is the number of the interferogram and explained below the Eq.1, please check it.
Point 9: Line 83 – dlambda/dk - is it really the rate of change of wavelength per time unit?? (not wavenumber??)
Response 9: dlambda/dk is the rate of change of wavelength per time unit, not the wavenumber. It can be write as Δλ in discretized expression.
Point 10: Line 90 – it is better to use the terms ‘interface’ rather than ‘wavefront’..
Response 10: Yes, it is a good advice, and we have changed the word ’wavefront’ as ‘interface’
Point 11: Why actually the algorithm consists of 32 steps not the other number.
Response 11: Thanks for your question, I think reviewer points to 36-steps. Actually, the number of the interferogram related to the phase-shift, we use the phase-shift as 2π/N=π/4, so N=8. Finally, we design the window function with 5N-4=36 according to the phase extraction design algorithm-characteristic polynomial method [27]. The value of the 36-step window function obtained by the Eq.(5)(6)(7)(8)(9).
Point 12: Line 121 – please revise the sentence.
Response 12: Yes, we have revised the sentence carefully.
Point 13: Line 126 – change ‘improving’ to ‘improve’
Response 13: Yes, we have changed ‘improving’ to ‘improve’.
Point 14: Figure 3 – how would the Gaussian window work?
Response 14: We have test the performance of the Gaussian window, however, its sidelobe exceeded 5%, much higher than Hanning windows and 36-steps window.
Point 15: Line 161 – there is ‘x’ missing between ‘1024’
Response 15: Thanks for checking it carefully, we have add the ‘x’ in the manuscript.
Point 16: Line 193 – ‘title’ ???
Response 16: We made a mistake in spelling, we have changed the ‘title’ to ‘tilt’.
Point 17: Line 196 – ‘three-plate transparent plate’ ??
Response 17: We want to express is that the three phase maps generated from reference surface and front-rear surface of transparent plat. We have revised the sentence in the manuscript completely.
Point 18: Line 196-197 – revise the sentence
Response 18: We have revised the sentence in the manuscript completely.
Point 19: Discussion should be extended
Response 19: Thanks for your advice, we have extended the discussion with a figure and explanation to make the manuscript more understandable. The figure shows that relationship between phase error coefficients of different order-ε0,ε1,ε2,and ε3 phase shift error.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper introduces a novel method for the measurement of the surface profile of the transparent plate based on the Fizeau interferometer. Simultaneous measurement of the surface profile and thickness is really unique, and this method is also expected to contribution in the industrial fields. However, English language and style are not enough for the publication. So, I suggest English language revision by native speaker.
My questions and comments are shown in the below.
1. The authors have proposed 36-step algorithm in that manuscript. Please explain why the step was set to be 36 in that study? It is difficult to understand the step number is enough or not. If the authors can, please describe the optimization process of the step number.
2. In equation 10, how did the author determine the parameters of the window function? Furthermore, is it necessary to redefine or reset of the parameters of the window function when the measuring instrument or light source wavelength is changed?
3. I cannot understand the view of Table 2 well. What is the number at the bottom of each lines?
Author Response
Point 1: The authors have proposed 36-step algorithm in that manuscript. Please explain why the step was set to be 36 in that study? It is difficult to understand the step number is enough or not. If the authors can, please describe the optimization process of the step number..
Response 1: Actually, the number of the interferogram related to the phase-shift, we use the phase-shift as 2π/N=π/4, so N=8. Finally, we design the window function with 5N-4=5x8-4=36 according to the phase extraction design algorithm-characteristic polynomial method [27]. The value of the 36-step window function obtained by the Eq. (5)(6)(7)(8)(9). We also have extended the explanation in the manuscript about the how calculate the number of the phase step.
Point 2: In equation 10, how did the author determine the parameters of the window function? Furthermore, is it necessary to redefine or reset of the parameters of the window function when the measuring instrument or light source wavelength is changed?
Response 2: As the response 1 above. We obtained the parameters of the window function according to the role of phase extraction design algorithm-characteristic polynomial method [27] and the Eq. (5)(6)(7)(8)(9). In another word, the parameters of the window function need to satisfied to the Eq. (5)(6)(7)(8)(9). The parameter is not necessary to refine or reset when the measuring instrument or light source wavelength is changed.
Point 3: I cannot understand the view of Table 2 well. What is the number at the bottom of each lines?
Response 2: The table 2 maybe make the reviewer misunderstanding. Actually, the number at the bottom of the lines belong to the number in the unit of the table. We have changed the format of the table to make it understandable.
Author Response File: Author Response.docx
Reviewer 3 Report
Content
The authors present a new approach to the separation of overlapping interferograms. These are generated with the help of a Fizeau interferometer by the reflection of the measuring light beam at the front and back of transparent rectangular objects. The method presented here forms the basis for determining the thickness variation of the measured objects.
Comments (exemplary)
• Abstract, first sentence: „It can separate the front and rear surfaces profiles…” What do the authors mean by "it"?
• Abstract, second sentence: “However, the measured thickness of the transparent plate is limited, for example greater than 10mm.” What is the reason for this limitation? Shouldn´t interferometric methods be able to differentiate interferograms generated by surfaces that are much closer to each other?
• Abstract, third sentence: “The 36-step algorithm is based…” What kind of algorithm is meant? What is the algorithm for?
• Abstract, second last sentence: The authors use "um" as symbol for the unit "micrometer", correct is the symbol "µm".
• The abstract is not understandable in its present form and must be completely revised.
• Introduction, second sentence: “There are three fundamental characteristics of a transparent plate – the surface profiles and optical thickness.” The authors name only two characterisitics instead of three.
• Introduction: What is the advantage of WTI compared to Low Coherence Interferomtry (LCI)? White light interferometry (WLI) is suitable for measuring the thickness variation of thin samples. Therefore, LCI should be suitable for measuring the thickness variation of samples with greater thickness (>1mm).
• Chapter 2, first paragraph: “When a beam of light is incident on a transparent plate, superimposed interference pattern is obtained by multiple reflections at the plate surfaces.” What do the authors mean by "multiple reflections"? Where exactly is the light reflected on the surfaces of the transparent plate?
• Chapter 2: The authors should explain authors should explain the necessity of the reference plate in detail.
• Line 117: What exactly do the authors mean with “infection of the reflection coefficient”?
• Figure 1: The image inscription is blurred and too small. Parameter H is not explained in the text.
• Figures 2, 3, 5, 6: The axis labels have different sizes, are too small and blurred.
• Chapter “Conflicts of Interest”: The authors don't seem to have edited this chapter.
The linguistic quality of the paper is very low, a complete revision by a native speaker is mandatory. In its current state, the paper is very difficult to understand. There is room for improvement in the quality of the illustrations, particularly with regard to image and axis labelling.
Author Response
Point 1: Abstract, first sentence: „It can separate the front and rear surfaces profiles…” What do the authors mean by "it"?
Response 1: ‘It’ mean the 36-steps algorithm. However, we have rewrite the abstract completely to make the text more understandable.
Point 2: Abstract, second sentence: “However, the measured thickness of the transparent plate is limited, for example greater than 10mm.” What is the reason for this limitation? Shouldn´t interferometric methods be able to differentiate interferograms generated by surfaces that are much closer to each other?
Response 2: For two surfaces measurement, it can be much closer to each other. For the interference fringes generated from three surfaces (reference, front surface and rear surface of tested transparent plate), the air-gap (the distance between reference surface to front surface of tested transparent plate) was set as the shorter than the thickness of the tested transparent plate in traditional WTI method [18] to make sure the interference fringes can be separated. If the Thickness of transparent plate is smaller than 10mm, the air-gap must smaller than 10mm,the reference surface in interferometer will be in danger of being damaged by contact in the actual measurement. We have revised the sentence in the abstract to make the idea more understandable.
Point 3: Abstract, third sentence: “The 36-step algorithm is based…” What kind of algorithm is meant? What is the algorithm for?
Response 3: The algorithm is phase-shift algorithm and mainly for the surface profile measurement of transparent plate. We have revised the sentence to make the sentence more clear.
Point 4: Abstract, second last sentence: The authors use "um" as symbol for the unit "micrometer", correct is the symbol "µm"
Response 4: Yes, thanks for the reviewer’s advice. We have corrected to the ‘µm’.
Point 5: The abstract is not understandable in its present form and must be completely revised.
Response 5: Thanks for the advice. We rewrite the abstract completely to make it more understandable.
Point 6: Introduction, second sentence: “There are three fundamental characteristics of a transparent plate – the surface profiles and optical thickness.” The authors name only two characterisitics instead of three
Response 6: The three fundamental characteristics point to the front surface profile, the rear surface profiles and optical thickness, respectively. We have revised the sentence to make the sentence clearer.
Point 7: Introduction: What is the advantage of WTI compared to Low Coherence Interferomtry (LCI)? White light interferometry (WLI) is suitable for measuring the thickness variation of thin samples. Therefore, LCI should be suitable for measuring the thickness variation of samples with greater thickness (>1mm).
Response 7: WTI can measure the transparent plate with a larger aperture and higher measurement precision compared with LCI. Of course, LCI is suitable for measuring the thickness variation of samples with greater thickness, however, it not suitable for measure the surface profiles and variation of thickness simultaneously.
Point 8: Chapter 2, first paragraph: “When a beam of light is incident on a transparent plate, superimposed interference pattern is obtained by multiple reflections at the plate surfaces.” What do the authors mean by "multiple reflections"? Where exactly is the light reflected on the surfaces of the transparent plate?
Response 8: We have revised the sentence to make the sentence more understandable. "multiple reflections" points to the reflection beam from the reference surface, front surface and rear surface. Those refection beam will generated interference fringe pattern (Fig.5(a)) in the CCD, which include the information of front surface profile ,rear surface profile and the variation of thickness of transparent plate.
Point 9: Chapter 2: The authors should explain authors should explain the necessity of the reference plate in detail.
Response 9: Thanks for the reviewer’s advice. We have revise the sentence to explain the reference plate in detail, which as ideal surface with high plane accuracy (PV value less than λ/20 in general)
Point 10: Line 117: What exactly do the authors mean with “infection of the reflection coefficient”?..
Response 10: We have corrected the “infection of the reflection coefficient” to ‘effect of the reflection coefficient’.
Point 11: Figure 1: The image inscription is blurred and too small. Parameter H is not explained in the text.
Response 11: We have changed the image and make it clearer, and also add the explanation of the H, which is the length of air-gap.
Point 12: Figures 2, 3, 5, 6: The axis labels have different sizes, are too small and blurred.
Response 12: Thanks for the reviewer’s checking. We have changed the image with clear axis label and uniform size.
Point 13: Chapter “Conflicts of Interest”: The authors don't seem to have edited this chapter.
Response 13: Thanks for your reminder. We have edited this chapter.
Author Response File: Author Response.docx
