Adaptive Gradient Estimation Stochastic Parallel Gradient Descent Algorithm for Laser Beam Cleanup

Round 1

Reviewer 1 Report

In this paper the authors propose and investigate Adaptive Gradient Estimation Stochastic Parallel Gradient Descent (AGESPGD) algorithm for beam cleanup (wavefront correction) of solid-state lasers. The results of this advanced algorithm are compared with results of classical Stochastic Parallel Gradient Descent (SPGD) algorithm, and advantages of AGESPGD are demonstrated. The numerical results are interesting, useful and seem to be reliable. Experimental results are also obtained and presented also reflecting the excellence of the developed algorithm over SPGD. I suggest to the authors to improve the following points in their manuscript.

1. In the introduction, the authors describe algorithms for a wavefront correction, but the physical reasons for wavefront distortions are not mentioned. I suggest to expand the introduction and discuss the physical mechanisms, mainly thermally induced aberrations. The corresponding papers should be cited [Zelenogorsky V.V. et al., Applied Optics 2006, 45, 4092-4101, https://doi.org/10.1364/AO.45.004092]; [Antipov O.L. et al., Quantum Electronics 2009, 39, 1131-1136, https://doi.org/10.1070/QE2009v039n12ABEH014160]; [Slezak O. et al, IEEE Journal of Quantum Electronics 2013, 49, 960-966], etc.
2. What is the typical computational time for 100 simulations using AGESPGD and SPGD?
3. In Figures 5 and 9, colorbars should be given. Here far-field intensities of the initial beams should be presented in more detail (may be using the normalization to maximum). In the present version, it is difficult to understand the structure of the beams.
4. In Section 4, experimental details should be provided (what is the laser used, its power, optical signal-to-noise ratio, etc).

Author Response

Thank you for your precious comments and advice. Those comments are all valuable and very helpful for revising and improving our paper. We have revised the manuscript accordingly，and our point-by-point responses are presented above. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear authors, the introduction of the gradients second derrivatives in gradient descent is very nice and i find this is usefuly for optical problem you postulated. However, there are plenty of unclear things that have to be improved. I am sending the document with my remarks. 

Comments for author File: Comments.pdf

Author Response

Thank you for your precious comments and advice. Those comments are all valuable and very helpful for revising and improving our paper. We have revised the manuscript accordingly，and our point-by-point responses are presented above. Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear authors, the quality of the artuicle improved significantly. Althogh some improvements are needed from my point of view for publishing. The main problem is the merit function. You do not provide any description or explanation what it is. Please, ass the information inside. Also, the simulations in Eq.12 are not clear (their correspondence with the real life situation is not clear at all, but this is because the merit function is not defined in the article). Also, please, check the englihs once more. A lot of redundancy like application scenarios (scenario can go away in this case), long sentences are heavy for reading (for example lines 32-34) etc.

 

Author Response

Dear Editors:

Thank you for your precious comments and advice. We have studied comments carefully and have made correction.

Dear Reviewer,

Thanks very much for taking your time to review this manuscript again. We really appreciate all your generous comments and suggestions! Please find my revisions in the re-submitted files. According to your advice, we amended the relevant part in manuscript. All of your questions were answered one by one.

Point 1: The main problem is the merit function. You do not provide any description or explanation what it is. Please, ass the information inside. 


Response 1: We are extremely grateful to you for pointing out this problem. We have added relevant content (lines 84-85).

Point 2: The simulations in Eq.12 are not clear (their correspondence with the real life situation is not clear at all, but this is because the merit function is not defined in the article).

Response 2: Thank you very much for your comments. We have revised the Eq.12 in the manuscript (lines 132-134). Eq.12 is a multi-extreme unary function constructed by us to verify the AGESPGD method, which has nothing to do with the merit function of the wavefront-free beam purification system. In order to avoid ambiguity, we modified the expression of Eq.12.

Point 3: Check the englihs once more. A lot of redundancy like application scenarios (scenario can go away in this case), long sentences are heavy for reading (for example lines 32-34) etc.

Response 3: Thank you for correcting the English expression errors in the manuscript. We have checked and corrected the errors we found. For details, please refer to the content marked by the horizontal line in the manuscript.