Measured and Predicted Speckle Correlation from Diffractive Metasurface Diffusers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The comments are in a PDF attachment that you can download.

Comments for author File: Comments.pdf

Author Response

1. In 94 lines, the lower limit of the speckle contras is 5%. However, at a working wavelength of 940 nm, what is the lower limit of the speckle contras?

Reply:

We don’t have a set measure for what an imaging processing algorithm would require since it varies by application but as a rule of thumb, it’s related to what can be observed by the human eye. The definition of speckle contrast is independent of wavelength though we know that speckle sizes scale with wavelength. For completeness, we know that light at 940nm is invisible to the human eye. A clearer explanation of this has been added to the manuscript.

2. In Line 116, the manuscript lacks a supplement to the definition of U ((x, Y)) in Formula

Reply:

A definition of U(x,y) has been added to the manuscript which states that U(x,y) is defined as: U is the electric field in the near-field with its amplitude and phase interpolated by the pillar diameter according to the phase table as depicted in Fig. 2.1(a) (a new figure added to the manuscript giving a more detailed description of the diffuser design)

 

3. In Lines 118-123, the author's introduction to the diffuser pattern model may be too brief. In line 63, the model is also not FDTD. Adding some detail may increase readability.

Reply:

It is correct, that the model used in this paper is not FDTD, the reference to FDTD is to explain the challenges involved with designing meta-optical elements for divergent light sources, and therefore highlights the need to understand the impact on the profile of the diffuser, including the speckle pattern when illuminating with a light source which the diffuser is not optimized for. This has now been clarified in the introduction of the manuscript.

More detail on the design and simulation method of the diffuser discussed in this manuscript has been added to section 2.4 to improve readability.

4. At Line 152, the author mentions that the light source is linearly polarized at emission. Especially when there are multiple light sources, the polarization characteristics will become more complex. Can the author add a linear polarizer to the optical path and then rotate the principal axis of the linear polarizer to explore the effect of the polarization direction of the light source on the speckle contrast?

Reply:

An extra measurement study was conducted after the initial data collection for this manuscript where the collimated light source in this investigation was controlled for polarization. Measurements of the diffuser profile were taken with two linear polarizations, orthogonal to each other and circular polarization.  For the two orthogonal polarizations, a difference of approximately 10% was found as for one polarization the speckle contrast was found to be 62.7% with a standard deviation of 1.8% and for the other it was found to be 51.4% with a standard deviation of 2.06%.  Text has been added to the manuscript addressing these new findings.

 

5. The author should carefully explain what is the Innovation of the manuscript? Is a model constructed or an optimized structural light source?

Reply:

The innovation of the manuscript derives from the lack of experimental data associated with the use of meta-optical elements for flood illumination particularly with VCSEL being used as the light source for example for applications like 3D sensing. The data that this manuscript presents is of particular interest for mobile applications, where there is a lot of recent interest in using more compact optics modules within the phones to decrease the thickness of the mobile phone as currently, the bulky refractive lenses used are the limiting factor in determining the dimensions of the mobile phone.  There are also other applications such as endoscopy where having a compact illumination module, is of great interest and therefore the data presented in the paper can also help to understand the advantages of using a meta-optical element such as the diffuser presented in this study compared to other options which this manuscript compares it to in the discussion section.

This manuscript also uses cross-correlation to try and understand how different illumination conditions including the location of the light source compared to the center of the diffuser element as well as the divergence angle, which in itself is not a novel way of studying speckle as it has been used in previous papers, but the application of it in the context of this manuscript to try and link the simulated and measured speckle pattern to demonstrate if it is deterministic as well as using it to explain why we do not see that it is the case in this manuscript is in itself new to the best of our knowledge.

 

The main contributions listed therefore are:

1. Quantitative characterization of metasurface diffusers that are important for many practical applications
2. Experimental quantitative demonstration of speckle reduction by increasing divergence
3. Experimental quantitative demonstration of speckle reduction by VCSEL illumination
4. Simulated speckle patterns with qualitative correlation with the measurements.
5. Simulated prediction of an asymptotic approach to a finite speckle limit at increasing number of emitters

6. It is best to add a table to compare the advantages and disadvantages of mechanical motion, random vibration, large divergence angle and the number of the VCSEL, and integration with MEMS

Reply:

Table to outline advantages and disadvantages of the different methods to reduce speckle has been added to the manuscript, but direct comparison is difficult due to speckle contrast being defined differently across papers.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript ID photonics-3148473 mainly presents a study about a speckle correlation from particular diffractive metasurface diffusers. Please see below some points to the authors:

1. From the text is not clear how were selected the parameters associated with the diffusers proposed. Please justify.
2. Please comment if the speckle correlations can be dependent on incident polarization in metasurfaces.
3. Advantages and disadvantages of the use vertical-cavity-surface-emitting laser illumination to reduce the speckle contrast should be described with better details in the discussion section.
4. In the text the expression MOE diffuser should be defined.
5. Perspectives related to the main findings can be presented in the discussion section to better see how this work can be a base for future research. The authors are invited to see for instance applications in random or dynamic speckle patterns: https://doi.org/10.1016/j.apacoust.2021.108384
6. The main findings must be confronted with alternatives provided by updated publications in the topic of diffusers and advanced materials. You can see for instance: https://doi.org/10.1186/s43074-022-00080-2
7. A photo of the experimental setup would be welcome.
8. Experimental error bar must be provided.
9. The font size in figure 3.8 and 4.1 must be enlarged.
10. It is suggested to split some of the citations presented in collective form. As a result, a better justification of the information individually presented by the references could be visualized.

 

Comments on the Quality of English Language

A proofreading is suggested

Author Response

1. From the text is not clear how were selected the parameters associated with the diffusers proposed. Please justify.

Reply:

This improved justification has been added to the manuscript: With a collimated light source, the target field of illumination of the diffuser design selected is 70x50 degrees which is a size relevant for 3D sensing applications and is also a size which requires design parameters which are not only easier to model, but also capture using the experimental setup described in section 2.5.

 

2. Please comment if the speckle correlations can be dependent on incident polarization in metasurfaces.

Reply:

Extra measurements were taken with a collimated light source where the polarization was controlled to investigate the effect of the polarization on the speckle correlation. When the cross-correlation of the two orthogonal polarizations was compared to the autocorrelation, for one of the polarizations, the magnitude of the cross-correlation was found to be within 5% of each other whereas for the other polarization there was a difference of 50% which suggests that polarization has a strong effect on the speckle pattern of the diffuser for the design that was tested in this manuscript. Text, addressing this finding has been added to the manuscript.

 

3. Advantages and disadvantages of the use vertical-cavity-surface-emitting laser illumination to reduce the speckle contrast should be described with better details in the discussion section.

Reply:

A table has been added to the discussion section which evaluates the advantages and disadvantages of the methods used in this paper, including VCSEL illumination, to reduce speckle compared to other methods used in other recent publications.

4. In the text the expression MOE diffuser should be defined.

Reply:

The definition of a MOE diffuser has been added to section two.

5. Perspectives related to the main findings can be presented in the discussion section to better see how this work can be a base for future research. The authors are invited to see for instance applications in random or dynamic speckle patterns:  https://doi.org/10.1016/j.apacoust.2021.108384

Reply:

Thank you for the suggestion, we unfortunately think that the gap between our study and the study in the article is too large to benefit from each other at present.

 

6. The main findings must be confronted with alternatives provided by updated publications in the topic of diffusers and advanced materials. You can see for instance: https://doi.org/10.1186/s43074-022-00080-2

 

Reply:

We do not see the methods in the article as a direct alternative for analysing diffuser speckle in the same method that we have done to understand the behavior of the speckle pattern between simulation and measurement, but we do see how diffusers could be interesting for non-invasive imaging techniques through opaque media. We have adresses this by citing the Bertolotti et al., Nature 491, 232–234 (2012). https://doi.org/10.1038/nature11578 article on the subject and stating how, in particular, a predictable speckle pattern from simulation would allow new applications.

To confront the method of speckle reduction with alternative approaches, a table has been added to the discussion section which evaluates the advantages and disadvantages of the methods used in this paper to reduce speckle compared to other methods used in other recent publications.

7. A photo of the experimental setup would be welcome.

Reply:

A photo of the setup has been added to the figure describing the experimental setup.

8. Experimental error bar must be provided.

Reply:

Error bars are visible for the plots for which direct measurements have been plotted. For figures which are not direct measurements, such as the pixel shift results which are derived from the cross correlation between two images error bars have not been added. Given more time, repeated measurements could be done under the same measurement conditions and the cross-correlation algorithm could be applied to a larger data set and the pixel shift obtained from each of these cross-correlations could be used to give a standard deviation of the pixel shift. A new figure has also been added to figure 3.7 in which error bars were added.

 

9. The font size in figure 3.8 and 4.1 must be enlarged.

Reply:

Font and figure size of Figures 3.8 and 4.1 have been increased.

 

10. It is suggested to split some of the citations presented in collective form. As a result, a better justification of the information individually presented by the references could be visualized.

Reply:

Citations have been modified to try to better visualize justifications of information from individual references.

A proofreading is suggested

Reply:

A proofreading of the paper has been done to improve English quality overall, the main changes to text have been highlighted in red, however, due to the number of minor changes in grammar and sentence construction, these have not been highlighted in red.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript "Measured and predicted speckle correlation from diffractive metasurface diffusers" presents a series of measurements with matching simulations on a 70 x 50 degrees diffractive diffuser to quantify the impact of speckles. The presentation is clear. There are some suggestions for authors to improve the completeness of the manuscript.

(1)    Please provide more details about diffractive metasurface diffusers, including the sizes and shapes of the meta-atoms. Please provide a detailed explanation of the role of metasurface diffusers in shaping optical fields, and the corresponding simulation results.

(2)    What are the reasons for failing to match the deterministic speckle pattern to the simulations? Please provide a more detailed analysis. Additionally, how can the experimental or simulation design be improved to achieve better agreement?

(3)    Make sure the style format of the references is consistent with each other. For example, in reference 6, the “Nat Commun” lacks a period “.”. Additionally, some journals use abbreviated forms, while others do not.

Comments on the Quality of English Language

The presentation is clear and the quality of English language is good.

Author Response

1. Please provide more details about diffractive metasurface diffusers, including the sizes and shapes of the meta-atoms. Please provide a detailed explanation of the role of metasurface diffusers in shaping optical fields, and the corresponding simulation results.

Reply:

More detailed description of diffractive metasurface diffusers and how they are used to shape optical fields has been added to section 2, including a new Figure (2.1) which shows the meta pillars library we are using in the design.

2. What are the reasons for failing to match the deterministic speckle pattern to the simulations? Please provide a more detailed analysis. Additionally, how can the experimental or simulation design be improved to achieve better agreement?

Reply:

The speckle pattern is extremely sensitive to even microscopic changes. To demonstrate successfully that the simulated speckle pattern of a diffuser profile can be captured in measurement, one could improve the simulation method so that takes into consideration fabrication tolerances such as angled side walls to see how this affects the speckle pattern and thus is the reason we fail to cross-correlate the simulated and measured speckle pattern in this paper. One could also try to further refine the measurement method to remove external sources such which could affect the speckle pattern such as mechanical vibrations in the setup as vibrations have been proven in other works to distort the speckle pattern and reduce speckle[20,21] Furthermore, one could also use a detector with a higher resolution to capture the sharper speckle peaks as from the simulation studies shown in Figure 3.8 and Figure 4.2, we have demonstrated that once a Gaussian filter is applied to the speckle pattern, the pixel shift that it undergoes under different illumination conditions becomes random, indicating that it is the loss of the sharp peaks which cause the loss in the predictability in the behavior of the speckle pattern.

If it is possible to correlate the specific experimental speckle pattern to simulation, it would also allow new understanding and potentially new applications for non-invasive imaging through opaque surfaces [42].

These comments have been added to the conclusion of the manuscript.

Despite the above, we have been able to obtain a qualitative correlation between speckle simulations and measurements. This is made more clear with the inclusion of figure 3.7 b

 

3. Make sure the style format of the references is consistent with each other. For example, in reference 6, the “Nat Commun” lacks a period “.”. Additionally, some journals use abbreviated forms, while others do not.

Reply:

References have been adjusted so that they all follow the same format

 

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All questions have been well answered, and I recommend publication of the manuscript.

Author Response

All questions have been well answered, and I recommend publication of the manuscript.

Reply:

The authors would like to thank the reviewers for their valuable feedback from the first round of reviews to improve the manuscript and the recommendation for publication from the second round. 

Reviewer 2 Report

Comments and Suggestions for Authors

I appreciate the effort of the authors to improve the presentation of their work by following the points raised in the initial review stage. However, a fundamental point seems to be still present in the manuscript, please see below:

*From the text is not still clear how were selected the parameters associated with the diffusers proposed. The authors should describe additional details within the text in order to see that the design of the diffuser is systematic instead of incidental.

Author Response

*From the text is not still clear how were selected the parameters associated with the diffusers proposed. The authors should describe additional details within the text in order to see that the design of the diffuser is systematic instead of incidental.

Reply

Thank you for the comment. We are unsure about which parameters are missing, but we have added more information on the diffuser profile as well as the meta-atoms used to design them. We now cover the relevance of the profile and FoV of the diffuser from an application point-of-view as well as for our investigations. We have furthermore added details on the metasurface design:

The parameters of the diffuser design selected for generating the phase-map such as the height of the pillars, lattice size, and pillar diameter range are selected to maximize the transmission of the meta pillars in the periodic lattice while covering a 2-pi change in phase across the pillar diameter range. The height, diameters and lattice constant of the diffuser design are already given in Figure 2.1.

We hope this covers the missing the details.