Round 1

Reviewer 1 Report

In the paper, Hartmann wavefront sensor with different lenslet arrangement is investigated. And valuable results are obtained. Some suggestions are listed as follows:

1) The arrangement of lenslets as shown in figure 2(c) and (d) are not practically producable. It increase the cost because of its special structure. In addition, the two arrangements shown in figure 2(c) and (d) are given directly without any optimization.

2) The precison of the reconstructed wavefront as shown in figure 3 are not high. 

3) The numbers in figure 8 are not clear.

4) It seems that the designed 25 and 31 lenslet arrangement are only for "sparse". And it waists most of the incident light, which should be avoided especially in astronomical observations. 

There are many grammar errors that affect its clear presentation. for example,

1) In the line 83, "In the experiment" should be changed to "In the simulationi".

2) In the line 98, "D and 0 r are the aperture 98 and atmospheric coherence length of the telescope respectively" should be changed to "D and 0 r are the aperture of the telescope  and atmospheric coherence length,respectively"

Author Response

Response to Reviewer 1 Comments

Point 1: The arrangement of lenslets as shown in figure 2(c) and (d) are not practically producable. It increase the cost because of its special structure. In addition, the two arrangements shown in figure 2(c) and (d) are given directly without any optimization..

Response 1: The lens arrangements in Fig. 2, c and d, were generated directly by simulation in order to facilitate comparison with the uniform type of lens array arrangement.

Point 2: The precison of the reconstructed wavefront as shown in figure 3 are not high.

Response 2: The data in Fig. 3 are mainly used to verify the reconstruction accuracy of different lens arrangements and different numbers of sub-lens units for each order of aberration. However, the reconstruction accuracy is low due to the number of lenses in different arrangements and the space utilization..

Point 3: The numbers in figure 8 are not clear.

Response 3: Thanks for your careful checks. We have adjusted accordingly.

Point 4: It seems that the designed 25 and 31 lenslet arrangement are only for "sparse". And it waists most of the incident light, which should be avoided especially in astronomical observations.

Response 4: The sparse arrangement of 25 and 31 lenslet that we have mentioned is to analyze the reconstruction performance of this arrangement on the wavefront, and then go on to compare it with the traditional uniform arrangement.

Point 5: In the line 83, "In the experiment" should be changed to "In the simulation".

Response 5: Thanks for your careful checks. We have changed experiment to simulation.

Point 6: In the line 98, "D and 0 r are the aperture 98 and atmospheric coherence length of the telescope respectively" should be changed to "D and 0 r are the aperture of the telescope and atmospheric coherence length, respectively".

Response 6: Thanks for your careful checks. We've made corrections.

Reviewer 2 Report

In this work, the authors model the recovery of the expansion coefficients of the phase function using Zernike polynomials. The phase function (wavefront aberrations) is specified using the deviations of the focal point from the center in a system of several spherical lenses in a Shack-Hartmann type sensor. Each lens had a diameter of 2.5 cm, a focal length of 1.2 m, and a wavelength of 1064 nm. The maximum number of lenses in the Schack-Hartmann sensor was 31. It was shown that if there are 31 lenses, then the restoration efficiency is 36. Unfortunately, the work does not indicate the turbulence parameters that lead to strong aberrations that can be restored with an efficiency of 36. And what is this the parameter is: recovery efficiency? The work can be published if the authors relate in more detail the parameters of optical turbulence with the parameters of wavefront aberrations and with the RMSE of reconstruction of such aberrations.

Comments

1. The work does not define the recovery efficiency, there is no definition of the parameter β and there is no abbreviation PV.

2. What is Quantity in Table 2?

3. What were the parameters of the turbulence that led to the aberration of the 28 Zernike polynomials that were reconstructed in RMSE in Fig. 3?

4. From Table 2 it follows that a scheme consisting of 31 lenses restores best. But this is understandable, since to restore 28 unknown numbers (coefficients in (1)) it is necessary to have more measurements (31 lenses and 31 measurements of the deviation of the wave front from the focus center). And 3 other schemes have fewer lenses than unknown ones - 19, 25, 25.

Author Response

Response to Reviewer 2 Comments

Point 1: The work does not define the recovery efficiency, there is no definition of the parameter β and there is no abbreviation PV.

Response 1: We sincerely appreciate the valuable comments. We have modified the paper accordingly. In this paper, we mainly use the reconstruction accuracy for different wavefronts under different lens array arrangements as the evaluation criterion, and the specific calculation method is given in lines 158-168 of the paper. The parameter β is an important parameter used to describe the quality of a laser beam. It is usually used to measure the degree of similarity between a laser beam and an ideal Gaussian beam, and can also be used to compare the quality difference between different laser beams, defined as the ratio of the actual far-field divergence angle to the reference far-field divergence angle, or the ratio of the actual focused spot radius to the ideal spot radius. The abbreviated PV refers to the peak-to-valley.

Point 2: What is Quantity in Table 2?.

Response 2: The quantity here refers to the amount of data involved in the calculation of statistical data, which is 25.

Point 3: What were the parameters of the turbulence that led to the aberration of the 28 Zernike polynomials that were reconstructed in RMSE in Fig. 3?

Response 3: The reconstruction accuracies of 28 orders of single aberration in front of different lens arrangements are shown in Fig. 3, and the influence of turbulence factors on the reconstruction accuracy of the wavefront is not involved, and this part of the analysis can be used to obtain the accuracy of the recovery of each order of aberration for different lens layouts and lens arrays with different numbers of lenses, as well as the highest order of the aberration wavefront that can be reconstructed effectively.

Point 4: From Table 2 it follows that a scheme consisting of 31 lenses restores best. But this is understandable, since to restore 28 unknown numbers (coefficients in (1)) it is necessary to have more measurements (31 lenses and 31 measurements of the deviation of the wave front from the focus center). And 3 other schemes have fewer lenses than unknown ones - 19, 25, 25.

Response 4: Yes, in general, as the number of sub-lens units in the lens array increases the reconstruction accuracy of the wavefront improves accordingly, so from the results the scheme consisting of 31 lenses has the best restoration.

Reviewer 3 Report

Brief summary

The manuscript entitled “Simulation Analysis of Atmospheric Turbulence Wavefront Measurement System” shows an analysis of simulated data utilizing phase front sensors such as Hartmann sensor. Four different layout of lens-arrays are studied, divided in two subgroups: regular and sparse.

The paper tries to explain the topic to the reader. It provides a brief introduction to the mathematical background such as reconstruction matrix and only sketches the phase reconstruction. The four different lens array arrangements are sufficiently described. Simulation results are shown by the RMS errors for four different lens layouts. Single aberration analysis and turbulent / randomized wavefronts are analysed.

This work could be suitable for publication in Photonics, answering the comments below.

Major comments:

1. In the case of the turbulent wavefront analysis, it is not clear what parameter are randomized in what range and distribution. Please explain more carefully how a random wavefront is obtained.

2. What about aberrations originating from the optical setup? What are typical main contributions to aberrations in a optical system?

3. What are typical or possible applications of the found results?

Minor and still important comment that should be addressed:

1. Please explain the abbreviation PV (Peak-Valley?)

Author Response

Response to Reviewer 3 Comments

Point 1: In the case of the turbulent wavefront analysis, it is not clear what parameter are randomized in what range and distribution. Please explain more carefully how a random wavefront is obtained.

Response 1: Thank you for your suggestions, we have made changes in this paper. From Equations ( 2 ) to ( 4 ), the covariance matrix of Zernike polynomial coefficients of any order can be obtained, and there is a correlation between Zernike polynomial coefficients. To obtain the turbulent wavefront, Zernike polynomials need to be converted. In the simulation, the K-L function is used to expand the wavefront. The polynomial coefficients are statistically independent, and the Zernike polynomial coefficient matrix can be obtained by conversion. The random wavefront that does not conform to the statistical law of turbulence can be directly generated by Equation ( 1 ). The Zernike coefficient is a pseudo-random number uniformly distributed between (-1, 1).

Point 2: What about aberrations originating from the optical setup? What are typical main contributions to aberrations in a optical system?.

Response 2: Aberrations in optical systems are mainly out-of-focus, with some coma, spherical and astigmatic aberrations. The causes of these aberrations are divided into the focusing performance of the system and on-axis and off-axis calibration issues. In this paper, we mainly discuss the turbulence-induced aberrations, so we do not elaborate much on the aberrations caused by the optical system itself.

Point 3: Please explain the abbreviation PV (Peak-Valley?)

Response 3: We apologize for not indicating the PV when it first appears in this paper; PV denotes peak-valley values.

Round 2

Reviewer 1 Report

The  authors revised the manuscipt in detail. And all of the questions are addressed. I suggested that the manuscript could be accepted.

Reviewer 2 Report

The authors took into account all my comments and I recommend publishing this work