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Article
Peer-Review Record

Phase Mask Design Based on an Improved Particle Swarm Optimization Algorithm for Depth of Field Extension

Appl. Sci. 2023, 13(13), 7899; https://doi.org/10.3390/app13137899
by Zeyu Huang 1, Fei Li 1, Lina Zhu 1, Guo Ye 2 and Tingyu Zhao 1,*
Reviewer 1: Anonymous
Reviewer 2:
Appl. Sci. 2023, 13(13), 7899; https://doi.org/10.3390/app13137899
Submission received: 22 June 2023 / Revised: 30 June 2023 / Accepted: 3 July 2023 / Published: 5 July 2023
(This article belongs to the Collection Optical Design and Engineering)

Round 1

Reviewer 1 Report (Previous Reviewer 3)

The article " Phase Mask Design based on an Improved Particle Swarm Optimization Algorithm for Depth of Field Extension " deals with the comparison between three optimization algorithms, two belonging to the state of the art (but rather old one) and a third proposed by the authors as an improvement of the state of the art. It is applied to the case of the optimization of a cubic phase mask, in the context of wavefront coding for depth of field extension. 

The article is clear and well written. With this new version, the authors have taken great care to meet the requirements of certain reviewers, notably by adding an experimental section. Nevertheless, some other issues have been little discussed by the authors, either in response to the reviewers, or by adding elements of precision in the text (if only in perspectives). As it stands, I think the article corrected with the suggestions below might be suitable for publication in MDPI's Applied Sciences, at the discretion of the other reviewers and the editor's final decision. Below are some comments and questions.

*** General questions/comments ***

(1)   Perhaps the first version of the PSO algorithm [8] was very velocity-dependent, but today the algorithm is still widely used (as mentioned by the authors) and often gives good results. Could the authors consider adding to the text other bibliographical examples of poor PSO results than those shown in Table 3?

(2)   L274 : How was the conversion between 90.23 and 0.2 made? Please consider adding this explanation to the text and adding the appropriate units to keep equation (8) homogeneous.

(3)   A wavefront is defined for a wavelength, which, unless I'm mistaken, is not defined in the text. What wavelength is used for the calculations (the conversion) and has particular attention been paid to the illumination spectrum? Please consider adding this in the text.

(4)   How was Fig6 obtained? Please consider adding this in the text.

*** Typos & other remarks ***

(1)   The quality of the images doesn't seem to have improved (in particular, Fig1 and Fig A1). Perhaps this is a problem specific to the .pdf conversion of the journal, which keeps the quality low for proofreading, but if not, I'd suggest saving the images as .pdf or .eps.

(2)   L154 : one dot missing

(3)   L162: one verb missing (before T=0.15)

(4)   L245: "k" should be capitalized

(5)   L338: “mage” -> “image” ?

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report (Previous Reviewer 2)

Due to the authors‘ good revisions to the questions raised by the reviewers, the manuscript can be accepted for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.


Round 1

Reviewer 1 Report

In this work authors propose the modification of a known optimization algorithm (PSO) to calculate the strength of a cubic phase plate for its use in wavefront coding.

Not being an expert in optimization algorithms, I do not doubt that the proposed algorithm is faster than other minimization algorithms and if the improvement of the algorithm is novel, I think it should be published in a mathematics or statistics journal. For the optimization of a single parameter of a WFC phase plate I do not find the utility of the method since the authors have not taken into account very important facts :

Optimization in one dimension is an initial approximation to the value of the plate strength. It is well known that for a cubic phase the shape of the pupil can introduce artifacts in the form of 45 degree fringes as well as other artifacts in the form of replicas [1]  that worsen the  image quality. Artifacts together with the presence of the noise indicate that providing an optimal strength parameter value with 5 digits is of no practical value, and thus the other optimization methods do not differ appreciably in both accuracy and speed for a value given with, say, two decimal places (in fact average value of proposed strength value is close to 10^-2 ). In addition, it is not clear without an optical design software that a cubic phase plate can be manufactured under an accuracy of 5 decimal places (or even 2) since the carving of the plate can leave other residual aberrations [2] and therefore the quality of image will be also affected.

But even for the straightforward optimization of a cubic phase, the optimization based on the invariance of the MTF does not optimize the image quality due to the presence of artifacts [3], and the PTF [3] or/and differences between images is a better merit function.

Therefore, I do not consider this work to be publishable material in this journal.

[1] Demenikov et al A technique to remove image artefacts in optical systems with wavefront coding

August 2009Proceedings of SPIE - The International Society for Optical Engineering 7429

DOI: 10.1117/12.825923

[2]  Arines et al, "Wavefront-coding technique for inexpensive and robust retinal imaging," Opt. Lett. 39, 3986-3988 (2014)

[3] Mo et al Phase transfer function based method to alleviate image artifacts in wavefront coding imaging system

September 2013Proceedings of SPIE - The International Society for Optical Engineering 8907:89074H

DOI: 10.1117/12.2034741

Reviewer 2 Report

In this paper, phase mask design based on an improved particle swarm optimization algorithm for depth of field extending is investigated. Based on some equations, the corresponding numerical simulations are performed. However, the theoretical analyses are not enough in-depth. Moreover, this research is not supported by any convincing experimental results. This paper may be too concise due to the lack of content materials. Therefore, the present manuscript is not suitable for publication in this journal.

In this paper, phase mask design based on an improved particle swarm optimization algorithm for depth of field extending is investigated. Based on some equations, the corresponding numerical simulations are performed. However, the theoretical analyses are not enough in-depth. Moreover, this research is not supported by any convincing experimental results. This paper may be too concise due to the lack of content materials. Therefore, the present manuscript is not suitable for publication in this journal.

Reviewer 3 Report

The article "Phase Mask Design based on an Improved Particle Swarm Optimization Algorithm for Depth of Field Extending" deals with the comparison between three optimization algorithms, two belonging to the state of the art and a third proposed by the authors as an improvement of the state of the art. It is applied to the case of the optimization of a cubic phase mask, in the context of wavefront coding for depth of field extension. 

The article is clear and well written, but several points could be detailed or improved to better prove the benefits of using the proposed algorithm. Below are some comments and questions.

*** General questions/comments ***

(1)   The authors have chosen to apply their algorithm to the optimization of an optical criterion for MTF equalization. It is known that the phase masks used for the extension of the depth of field strongly reduces the image quality. This is why a digital processing is often used to enhance the contrast a posteriori (see these articles and similar works on end-to-end design/ co-design strategies -Javier Portilla and Sergio Barbero, "Integrated analysis of industrial limitations and image quality: an end-to-end design approach," Opt. Express 31, 16897-16908 (2023) ; Alice Fontbonne, Hervé Sauer, Caroline Kulcsár, Anne-Lise Coutrot, François Goudail, "Experimental validation of hybrid optical–digital imaging system for extended depth-of-field based on co-optimized binary phase masks," Opt. Eng. 58(11) 113107 (27 November 2019))

a.      Why didn't the authors consider an image quality criterion for optimization?

b.      The proposed optimization algorithm uses the definition of the threshold T, which has been set arbitrarily (as are the parameters of other algorithms). How to choose T and what is its influence on the good performance of the algorithm?

(2)   Only one parameter is optimized for performance demonstration.

a.      It would therefore seem interesting to me to plot the evolution of the optimization criterion as a function of the alpha parameter to account for the difficulty of the optimization landscape.

b.      Futhermore, it would (maybe?) explain the bad results obtain by PSO in Table 3. In all case, it would be interesting that the authors provide an explanation of these results.

*** Other comment ***

(1)   The quality of the all the figures is very bad, and prevents the reading of certain information. Please consider to upload in better quality

(2)   Fig.2 and Fig. 3 : the normalization value/criterion (Nyquist, cut-off frequency…) should be specified

(3)   Can the authors justify why there are so many significant digits ?

*** Typos and minor comments ***

(1)   The authors sometimes use “DoF Extending” (in the title), “Dof Extended” (keywords), “DoF expansion” (in the text). It seems to me that “DoF Extension” would be preferable in all these cases.

(2)   L14 : “(SA)” is not necessary here.

(3)   In all the text : From the moment "Depth of Field" has been replaced by "DoF", it could be done in all the text.

(4)   What is the purpose of L50-52 ?

(5)   L56 : please consider to replace “;” by “and”.

(6)   L60 : please consider to replace “;” by “and”. It seems that “j” does not appear.

(7)   L120 : please consider to remove.

(8)   L259 : please consider to add a “.” at the end.

(9)   L265 : why is the phrasing in the plural ?

It is well written !

Reviewer 4 Report

As a wish for future work, it is desirable to present the results of experimental testing of the proposed phase mask, and not just the simulation results

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