Half-Period Gray-Level Coding Strategy for Absolute Phase Retrieval

Round 1

Reviewer 1 Report

(1) From line 43, the authors start saying that "the phase map recovered by both FTP and PSP ranges from 0 to 2π with 2π discontinuities, known as the wrapped phase." The introduction should concretely state the disadvantages of such discontinuities. And why the authors' work is excellent in this aspect. 

(2) A color bar for Fig. 6(f) is recommended. 

(3) It can be seen from Fig. 8 and 9, nGL is not better than the traditional phase shifting method. What is the reason? Why are there black lines in Fig. 9b 8b?

(4) What are the difference between the proposed method and the nGL?

(5) The last sentence says " this method has the ability to reconstruct objects in defocused scene". What are the quantified results in defocused scenes? What are the performances comparison of the methods in defocused scenes? In fig. 10 and 11, to what level the image has been defocused (blurred)? Are there any limits of such defocusing scenario on the different methods?

Author Response

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Reviewer 2 Report

Major remarks:

This paper proposes modifying a gray-level coding strategy for absolute phase retrieval in fringe projection profilometry. The paper has great academic merit, however, the novelty is marginal. The claim of improvement from Ref [29] seems to be to reduce the number of projected patterns while maintaining the same phase quality. Nevertheless, the comparison is not carried out by comparing against [29], but the standard nGL coding method. 

Moreover, the errors which the experiments manifest (both for the complex shape and the sphere) seem to be somewhat exaggerated–especially for the sphere–and, to some extent, fixable with a median filter and reassigning the fringe order [7]. 

Finally, the conclusions are misleading since the authors indicate that only one pattern is required. This should be stated as “only one additional pattern” to the three phase-shifting patterns. 

Minor remarks:
- Line 13: “a lot of” -> many
- Line 19: n2 -> n^2
- Line 59: “is therefore developed” -> was developed?
- Line 63: “Lots” -> many
- Sec. 2.1. I don’t see that superscript C is really necessary. Also, fix the latex \cos function. 
- Eq (9): fix latex for \mod symbol
- Eq (10) use \mathrm{code} for Latin text in equation.
- Equations are considered part of a sentence and should be punctuated accordingly.
- Line 268: “only requires to project only” -> only requires to project one …

Author Response

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Round 2

Reviewer 1 Report

In the revised version, the authors have addressed my concerns. I have the following minor suggestion:

1. In Line 83 "Besides, the proposed method requires to project only one additional pattern to unwrap the wrapped 84 phase comparing to other temporal unwrapping methods, which has the potential to be applied in high-speed measurement". How much can the method improve the unwrapping speed compared to other temporal methods?

Thank you!

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Reviewer 2 Report

The authors have appropriately addressed most critiques. The results have improved, especially now that they are compared to a state-of-the-art method. The improvement is marginal, but it provides an alternative approach to the existing methods. I recommend the paper be accepted.

Author Response

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