Phase-Shifting Projected Fringe Profilometry Using Binary-Encoded Patterns
Round 1
Reviewer 1 Report
The author proposed a phase unwarpping approach via encoding the fringe patterns used for phase-shifting method in FPP. But there remain some problems.
- Line 81-82 refer to Figure 4 (a) and (b), but Figure 4 is not marked (a) or (b) in the paper.
- Does the equation (3-6) consider the gamma nonlinear error [R1]?
- A calibration method is introduced on pages 5-7 in detail, but the proposed phase unwrapping method in this article is not used in the calibration method. As the topic of the article is to introduce the phase unwrapping method, so the purpose of introducing the calibration method is not clear. It is recommended to introduce the calibration method more briefly.
- What is the relationship between the threshold mentioned at line 221 and the one at line 115?
- Line 231, how to identity the point of phase discontinuities from the one of geometric discontinuities? Please describe the process in detail.
- From equation (2) and Figure 3, the amplitude of the coded fringe in some intervals is only half of the maximum one, which indicates that the signal-to-noise ratio in these intervals is much lower. Therefore, it is necessary to perform comparative simulation experiments with a controllable noisy to prove the effectiveness of the proposed method.
There are some confusions in the paper which need to be explained, the paper is not suitable for publication in present status.
Author Response
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Author Response.doc
Reviewer 2 Report
The manuscript introduces an unwrapping method for fringe projection by adding a binary distribution into the projection images. The binary distribution is then decoded from the acquired images. The main advantage is the combination of the unwrapping images and the high-frequency phase images. While I think that the method is useful within itself, I do not think it is innovative. Additionally, the proposed method increases the intrinsic phase noise of the fringe projection. However, I see the contribution of the manuscript on a scientific level. Nevertheless, I have some major and minor remarks.
Major remarks:
- Your method reduces the sine amplitude B (eq. (5)) of by half. The noise of the phase calculation is directly inverse proportional to the sine amplitude. Therefore, if you use your method you trade a lower projection time for a larger phase noise. However, I could not find any reference to this in the manuscript. Additionally, the reduced amplitude also reduces the measurement area.
- You add an evaluation based on a 3d measurement. However, you do not use the standard method based on the intersection of view rays. Therefore, your results cannot be compared to results from literature.
I suggest to compared your results of the phase reconstruction to a state-of-the-art algorithm, e.g., a multi-frequency phase-shift or heterodyne method. - Based on the remarks above, please greatly enhance your discussion section. You just state the benefits of your method without discussing the drawbacks, especially the potential scenarios in which your method fails to result in a correct unwrapping.
Minor remarks:
- Please cut down on the number of subfigures.
- Please increase the font size in your figures to a readable level.
- Generally, try to phrase your statements using ‘harder’ comparisons and use less, e.g., ‘not large enough’ etc.
- Please check your reference numbers. I think at least your [20] is actually [21], [22] or [23]
- Please explicitly state your unwrapping algorithm
- 80f / Fig. 2: please introduce ‘contrast’ and ‘phase’ before plotting those.
- 3: there are spikes in your plot but these spikes are not mentioned nor discussed.
- 4:
- Add subfigure captions
- Display the phase as multiplier of π
- (7): this equation is trivial. Using it complicates the reading.
- 109: Add equations for the decoding method explicitly. I cannot put ‘close to’ into a software algorithm.
- Results:
- Please add the resolution of both camera and projector and show an image of your real setup and add triangulation base and triangulation angle to that image.
- 5: fix typos
Author Response
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Reviewer 3 Report
The manuscript is presenting an interesting topic in phase unwrapping methods here to develop a profilometry with phase-shifting. However, a few comments and questions are due before we proceed with this manuscript:
- why there is no discontinued contrast distribution at the circled areas in Figure 5(f)?
-introduction should cite the image processing mentioned in DOI: 10.3390/nano11020505
-how the fluctuations on the phase-to-depth relationship in fig 6c.
-in fig. 11, could you clarify by looking at the previous images, how the “0” and “1” encoded fringes are still discernable? any correlation with other images relevant?
when authors take my comments in I can reconsider my decision.
Author Response
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Round 2
Reviewer 1 Report
The author made detailed modifications to the questions raised last time, such as adding gamma error calibration, explaining the method of identifying boundary points, explaining the relationship between the selected calibration method and the unwrapping method, discussing the relationship between SNR and unwrapping accuracy, and adding simulation experiments to drive the conclusion, etc.. In summery, the paper has reached the level of publication.
On the other hand, the supplementary method of identifying boundary points is so interesting that it would be great to briefly introduce the method with the future research plan in the fourth section, discussion.
Author Response
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Reviewer 2 Report
The authors have sufficiently answered to the remarks I had. The paper within itself is now suitable for publication. I would like to congratulate the authors on the enhancement of their discussion.
As requested, I would like to provide the DOI of a paper regarding the modelling of the phase noise corresponding the the acquired amplitude 10.1515/teme-2016-0059
On a stylistic point of view, I still would like the authors to present the measured 3d profiles as 2.5 heightmaps (figs. 10, 12, 18) and tighten the 2d plots to the acquired measurement data (figs. 8c, 15).
Author Response
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