Simple Method of Light Field Calculation for Shaping of 3D Light Curves

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

We are thankful to reviewers for their useful comments and suggestions, which allow us to improve the quality of the manuscript making it more clear for readers. We believe the corrections made address the Reviewer’s concerns making the manuscript suitable for publication in the journal.

All changes in the manuscript are highlighted by green color.

Reviewer 1

This manuscript proposed a method for generating three-dimensional light fields with given intensity and phase distributions using purely phase transmission functions. The results seem interested, and the experimental results are in good agreement with the simulation results. Thus, in my opinion, the manuscript could be published in photonics. In addition, there are some problems should be clarified in the manuscript. They are summarized as follows:

1. Does the distributions of the amplitude and phase in figures 2 to 10 refer to the light field in the source plane or the SLM plane? It is better to give the corresponding expressions.

Reply:

In fact, the amplitude and phase distributions refer to the source plane (z = 0 mm). For experimentally obtained intensity distributions shown in these figures, we used purely phase transmission functions in the SLM plane. In order to get these pure phase transmission functions, an amplitude encoding technique was used as we mentioned in section “2.2 Experimental setup”: “Amplitude encoding was used to encode the calculated amplitude-phase distributions into pure phase transmission functions of the elements realized using the SLM [41-43].” We added the corresponding text to the figure captions.

2. In the 2.2 section “Experimental setup”, “designed amplitude-phase transmission functions were first encoded into pure phase masks”. It is better to briefly explain the conversion process or give corresponding references.

Reply:

We added the description:

Amplitude encoding was used to encode the calculated amplitude-phase distributions into pure phase transmission functions of the elements realized using the SLM [41-43]. In this case, the complex amplitude-phase field Aexp(iφ) at each point was defined as the sum of two pure phase fields u and ν: Eq. (19).

The phase values u and ν are displayed in adjacent samples of the designed phase element. Phase samples u and ν are in a 2×2 sub-matrix along two diagonals. The phases u and ν can be calculated from the known amplitude and phase of the encoded light field as follows: Eq. (20).

Author Response File: Author Response.doc

Reviewer 2 Report

This manuscript proposes to introduce a weighting function in the calculation of the CGH for generating various laser beam patterns, and amplitude encoding is used for generating CGH. The demonstration of the result looks promising, but the description of the concept and methodology is not quite clear. Some comments are given as follows for the authors’ reference.

 

1.      The description from line 13-15 and 168-170 is a bit confusing. “Using amplitude encoding to calculate purely phase transmission function” looks self-contradicted. If the SLM is a phase modulation device, the phase transmission function of the CGH can be directly encoded as a phase modulation pattern on the SLM. If the SLM is an amplitude modulation type as used in reference 37, the complex encoding method can be used, i.e. with both amplitude and phase modulation. According to the result of low efficiency, it should be the latter case. More description on the SLM hardware and the complex encoding method to be used is required.

2.      It is claimed that the iteration process is not required, which makes the method “simple” as the title claims. However, due to the SLM being a digital device and the modulation value being quantized, the iteration process does help to optimize the modulation on SLM. For example, if the required modulation is 0.18, and the SLM can only make 0, 0.25, 0.5, 0.75 and 1.

3.      One major feature of the proposed method would be the weighting function and it is related to the derivative of the phase variation along the laser pattern, according to the manuscript. How does the introduction of this weighting function make a difference could be elaborated to further highlight the contribution of this manuscript.

Moderate editing of English language required

Author Response

We are thankful to reviewers for their useful comments and suggestions, which allow us to improve the quality of the manuscript making it more clear for readers. We believe the corrections made address the Reviewer’s concerns making the manuscript suitable for publication in the journal.

All changes in the manuscript are highlighted by green color.

Reviewer 2 

This manuscript proposes to introduce a weighting function in the calculation of the CGH for generating various laser beam patterns, and amplitude encoding is used for generating CGH. The demonstration of the result looks promising, but the description of the concept and methodology is not quite clear. Some comments are given as follows for the authors’ reference.

1. The description from line 13-15 and 168-170 is a bit confusing. “Using amplitude encoding to calculate purely phase transmission function” looks self-contradicted. If the SLM is a phase modulation device, the phase transmission function of the CGH can be directly encoded as a phase modulation pattern on the SLM. If the SLM is an amplitude modulation type as used in reference 37, the complex encoding method can be used, i.e. with both amplitude and phase modulation. According to the result of low efficiency, it should be the latter case. More description on the SLM hardware and the complex encoding method to be used is required.

Reply:

In our study, the initially calculated transmission functions are complex amplitude-phase functions – this can be seen from Eq.(10). All presented figures show the amplitude and the phase distributions of the calculated transmission functions in the source plane (z = 0). The SLM we used in the experiments was a phase only SLM and it was necessary to encode the complex amplitude-phase transmission functions into pure phase transmission functions. We added a description of the used encoding method.

2. It is claimed that the iteration process is not required, which makes the method “simple” as the title claims. However, due to the SLM being a digital device and the modulation value being quantized, the iteration process does help to optimize the modulation on SLM. For example, if the required modulation is 0.18, and the SLM can only make 0, 0.25, 0.5, 0.75 and 1.

Reply:

We used a phase SLM, which has enough gradations (256 gray levels) to not worry about the influence of the quantization effect. Therefore, iterations for the purpose of optimization are unnecessary, which is confirmed by the results of the experiment.

 

3. One major feature of the proposed method would be the weighting function and it is related to the derivative of the phase variation along the laser pattern, according to the manuscript. How does the introduction of this weighting function make a difference could be elaborated to further highlight the contribution of this manuscript.

Reply:

Thank you for this suggestion, we have added relevant explanations to the Discussion section.

Author Response File: Author Response.doc

Reviewer 3 Report

Please see attachment.

Comments for author File: Comments.pdf

Author Response

We are thankful to reviewers for their useful comments and suggestions, which allow us to improve the quality of the manuscript making it more clear for readers. We believe the corrections made address the Reviewer’s concerns making the manuscript suitable for publication in the journal.

All changes in the manuscript are highlighted by green color.

Reviewer 3

 In this paper by Khonina et al, the authors have investigated the issue on the light field calculation for shaping of three dimensional light curves. The authors proposed a method for generating three-dimensional light fields with given intensity and phase distributions using purely phase transmission functions. This method is based on a generalization of the well-known approach to the design of diffractive optical elements that focus an incident laser beam into an array of light spots in space. The authors considered various types of contour intensity distributions and the possibility of controlling their 3D structure is demonstrated. The results of the experimental formation of the calculated curves are in good agreement with the simulation results. The proposed approach can be used to control the three-dimensional structure of the intensity and phase of shaped light fields along the propagation axis. The format of this paper is standardized, the structure of the paper is reasonable, and the results obtained in this paper have certain scientific significance and reference value. Therefore, I can recommend accepting this paper after a minor revision.

In order to demonstrate various types of contour intensity distributions and experimental results, the authors provided some figures to vividly demonstrate these different characteristics of 3D intensity and phase distributions. However, the description of the figures is not detailed enough. It is recommended that the authors analyze the figures in detail, especially figures 10-12.

Reply:

Thank you for this suggestion, we have added relevant explanations to the end of Section 3.

 

On the other hand, the control and shaping of three-dimensional beams have important scientific significance. In order to expand the readability and universality of this paper, it is recommended that the author can cite papers from different research directions in this field, for example, articles on beam arrays include Chin. Opt. Lett. 2022, 20: 022602 and Commun. Nonlinear Sci. Numer. Simlat. 2021, 103: 106005; articles on 3D beam control and shaping include Opt. Lett. 2019, 44: 3917 (2019) and Appl. Math. Lett. 2020, 102: 106114.

Reply:

We added these references.

Author Response File: Author Response.doc

Round 2

Reviewer 2 Report

The authors have addressed the issues raised in the previous review and the manuscript can be considered for the publication in Photonics

N/A