The Algorithm for Recognizing Superposition of Wave Aberrations from Focal Pattern Based on Partial Sums
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsMajor issues
The authors say in the introduction (page 2) and in the conclusion that "In adaptive optics, Zernike functions are used to correct distortions" and that the incorrect approximation of the phase by Zernike polynomials can decrease the correction efficiency. It is not always the case. Generally, the Zernike polynomials are used only to represent the wavefront, either before or after correction. For example, when you use Shack-Hartmann device, the real correction is made by minimizing the displacements of the focal spots on the sensor. The less the displacements — the better the correction.
Please, clarify this statement.
I would assume that this algorithm could be helpful for the wavefront measurements applications rather than for the wavefront correction ones. If it is not the case, please, explain it in the introduction.
The phase map at Fig. 3a (and Fig. 5a) looks like it has discontinuities. Is it the phase map to reconstruct with the SLM? If not, the phase map (or fringes map) should look smooth, without discontinuities.
Please, also add the color bar with the range values correspond to min and max values for each of sub-figures.
I did no find the time consumptions of the proposed algorithm and considered optimization cases. Please, provide those estimations.
Minor issues
What is the measurement unit of the RMS = 0.3 in the introduction?
At Page 2, section 2.1 - "Functions Zernike have next view [25-27]:" - please, rephrase the sentence, it is incorrect.
Page 5, section 3.1 - it is better to provide the formula for the aberrated wavefront once more rather than make the reader to go back 3 pages to find it.
Fig. 4 could be upgraded, and the minimizing functional could be added right to the graphics for better readability.
For the sake of similarity, it is better to provide the phase map for the case considered in section 3.1.
Please, rephrase the sentences with the duplicated words, i.e. "Let us define an aberrated wavefront (5), defined..."
Author Response
We are thankful to Reviewer for useful comments and suggestions, which allow us to improve the quality of the manuscript making it more clear for readers. All changes in the manuscript are highlighted by yellow color.
The authors say in the introduction (page 2) and in the conclusion that "In adaptive optics, Zernike functions are used to correct distortions" and that the incorrect approximation of the phase by Zernike polynomials can decrease the correction efficiency. It is not always the case. Generally, the Zernike polynomials are used only to represent the wavefront, either before or after correction. For example, when you use Shack-Hartmann device, the real correction is made by minimizing the displacements of the focal spots on the sensor. The less the displacements — the better the correction.
Please, clarify this statement.
I would assume that this algorithm could be helpful for the wavefront measurements applications rather than for the wavefront correction ones. If it is not the case, please, explain it in the introduction.
Answer 1.
The reviewer is basically right. We have added a corresponding clarification in the Introduction.
“In adaptive optics, there are several approaches to wavefront correction. In particular, when a Shack-Hartmann device is used, the wavefront correction is made by minimizing the displacements of the focal spots on the sensor [34]. When analyzing a picture in the focal plane, the size of point spread function (PSF) is minimized [35] and/or the Strehl ratio is maximizing [36]. Also, for interferograms, it is possible to track the deviation of the ideal distribution from the distorted one [37]. In addition, methods of adaptive wavefront corrections using the modal decomposition of correlation filter method are considered [38]. A similar approach is possible using filters matched to Zernike functions [27, 28, 30, 32]. However, generally, the Zernike polynomials are used only to represent the wavefront, either before or after correction.”
Point 2.
The phase map at Fig. 3a (and Fig. 5a) looks like it has discontinuities. Is it the phase map to reconstruct with the SLM? If not, the phase map (or fringes map) should look smooth, without discontinuities.
Please, also add the color bar with the range values correspond to min and max values for each of sub-figures.
Answer 2.
Thank you for your valuable comment. No, the phase map at Fig. 3a (and Fig. 5a) is a visualization of the phase in the simulation. We have added min and max values ​​for sub-figures.
Point 3.
I did no find the time consumptions of the proposed algorithm and considered optimization cases. Please, provide those estimations.
Answer 3.
Thank you for your suggestion. In terms of time, the phase restoration result takes less than a minute. On the one hand, the time can be significantly reduced by using additional optimization of calculations and more advanced computing resources. But, on the other hand, we do not claim a real implementation in this work, but demonstrate the capabilities of the proposed algorithm.
Minor issues
Point 4.
What is the measurement unit of the RMS = 0.3 in the introduction?
Answer 4.
RMS is root mean square. We have replaced the abbreviation in the abstract.
Point 5.
At Page 2, section 2.1 - "Functions Zernike have next view [25-27]:" - please, rephrase the sentence, it is incorrect.
Answer 5.
Thank you for your recommendation. We rephrase the sentence “Zernike functions are defined as follows [25-27]:”».
Point 6.
Page 5, section 3.1 - it is better to provide the formula for the aberrated wavefront once more rather than make the reader to go back 3 pages to find it.
Answer 6.
Thank you for your suggestion. We have added the provide the formula for the aberrated wavefront in section 3.1.
Point 7.
Fig. 4 could be upgraded, and the minimizing functional could be added right to the graphics for better readability.
Answer 7.
Thank you for your recommendation. We have added the minimizing functional to Figures 4 and 6.
Point 8.
For the sake of similarity, it is better to provide the phase map for the case considered in section 3.1.
Answer 8.
Thank you for your comment. We have added phase distribution figures to Tables 1, 2, 3 and 4.
Point 9.
Please, rephrase the sentences with the duplicated words, i.e. "Let us define an aberrated wavefront (5), defined..."
Answer 9.
Thank you! We rephrase the sentence “Let us consider an aberrated wavefront (5), defined by the superposition of three wave aberrations (6)” and “Let us consider an aberrated wavefront (5), defined by a superposition of five wave aberrations (6)”.
Reviewer 2 Report
Comments and Suggestions for AuthorsReview of Photonics manuscript # 3633502 titled “The algorithm for recognizing superposition of wave aberrations from focal pattern based on partial sums” by Volotovskym Khorin, Dzyuba and Khonina.
The manuscript presents a technique to retrieve wavefront aberrations from the aberrated Point Spread Function (PSF) recorded in the focal plane of an imaging system.
The manuscript has several issues that the authors should address before becoming suitable for potential publication.
The manuscript needs to be edited carefully there are several grammatical errors.
A couple of example:
Introduction: “the recognizing the superposition of such..” should be “the recognizing of the superimposition of such..”
Page 3: “A set of simplest superpositions” should be changed or add an article “A set of the simplest superpositions”
Page 4: figure 1 covers eq 14.
From the technical point of view, I also have several issues.
The area of phase retrieval from intensity distribution in the focal plane is an area of research with a rich history and a large body of literature. None of such literature is mentioned by the authors.
The authors mention adaptive optics as a justification of their algorithm but fail to demonstrate that their algorithm could be used in real time, I strongly doubt given the iterative nature, or that their algorithm performs better than current wavefront sensors. They show via simulations that they can retrieve the superposition of a handful of Zernike modes by their algorithm. Modern adaptive optics systems can demonstrate Strehl ratios in closed loop operation up to 80%, see for example results from the Large Binocular Telescope adaptive optics system, and this while measuring and removing several tens of modes.
In the Discussions, issue number 2, the authors mention energy loss. I suspect that they mean digital quantization and not energy as number of photons per pixel.
Comments on the Quality of English Language
See above
Author Response
We are thankful to Reviewer for useful comments and suggestions, which allow us to improve the quality of the manuscript making it more clear for readers. All changes in the manuscript are highlighted by yellow color.
Review of Photonics manuscript # 3633502 titled “The algorithm for recognizing superposition of wave aberrations from focal pattern based on partial sums” by Volotovskym Khorin, Dzyuba and Khonina.
The manuscript presents a technique to retrieve wavefront aberrations from the aberrated Point Spread Function (PSF) recorded in the focal plane of an imaging system.
The manuscript has several issues that the authors should address before becoming suitable for potential publication.
Point 1.
The manuscript needs to be edited carefully there are several grammatical errors.
A couple of example:
Introduction: “the recognizing the superposition of such..” should be “the recognizing of the superimposition of such..”
Page 3: “A set of simplest superpositions” should be changed or add an article “A set of the simplest superpositions”
Page 4: figure 1 covers eq 14.
Answer 1.
Thank you! We rephrase some sentences in page 1, 2, 3, 8, 9, 12. Unfortunately, figure 1 covers eq 14. due to a layout error in the article.
From the technical point of view, I also have several issues.
Point 2.
The area of phase retrieval from intensity distribution in the focal plane is an area of research with a rich history and a large body of literature. None of such literature is mentioned by the authors.
Answer 2.
Although the first version of the article already provided references to significant works in this area, we have added text to the Introduction with additional literature.
“In adaptive optics, there are several approaches to wavefront correction. In particular, when a Shack-Hartmann device is used, the wavefront correction is made by minimizing the displacements of the focal spots on the sensor [34]. When analyzing a picture in the focal plane, the size of point spread function (PSF) is minimized [35] and/or the Strehl ratio is maximizing [36]. Also, for interferograms, it is possible to track the deviation of the ideal distribution from the distorted one [37]. In addition, methods of adaptive wavefront corrections using the modal decomposition of correlation filter method are considered [38]. A similar approach is possible using filters matched to Zernike functions [27, 28, 30, 32]. However, generally, the Zernike polynomials are used only to represent the wavefront, either before or after correction.”
Point 3.
The authors mention adaptive optics as a justification of their algorithm but fail to demonstrate that their algorithm could be used in real time, I strongly doubt given the iterative nature, or that their algorithm performs better than current wavefront sensors. They show via simulations that they can retrieve the superposition of a handful of Zernike modes by their algorithm. Modern adaptive optics systems can demonstrate Strehl ratios in closed loop operation up to 80%, see for example results from the Large Binocular Telescope adaptive optics system, and this while measuring and removing several tens of modes.
Answer 3.
We do not claim in this work a real implementation, but demonstrate the capabilities of the proposed algorithm. Thus, comparing our method with existing ones in terms of performance or speed does not make sense. However, we have performed some measurements. The result of phase reconstruction takes less than a minute. It is worth noting that we propose a new approach to data transformation for known optimization methods, which in turn can already be applied to existing wavefront sensors. Moreover, there are special degenerate aberrations that are difficult to detect with a conventional iterative algorithm, and additional studies are needed for comparison with other sensors, which go beyond the scope of this article.
Point 4.
In the Discussions, issue number 2, the authors mention energy loss. I suspect that they mean digital quantization and not energy as number of photons per pixel.
Answer 4.
Thank you for your valuable comment. We have replaced this paragraph with the following explanatory text:
“With an increase in the aberration level, the size of the formed PSF pattern is expanding, so the peripheral part of the analyzed pattern may not fall into the recorded/observed area, which will lead to incorrect results. Therefore, one more analyzed integral characteristic, corresponding to the total intensity value, can be used. Taking into account the standard deviation, it will be of decisive importance if such a characteristic does not match in the reference and current images.”
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAlmost all the issues have been addressed.
Concerning the RMS in the introduction — I believe the authors got me wrong. RMS has the measurement unit. If you measure the wavefront in microns, it will be in microns. If you measure the wavefront in waves, RMS will be in waves. Please, place the measurement units you used.
