Tunable, Nonmechanical, Fractional Talbot Illuminators

Round 1

Reviewer 1 Report

Tunable, nonmechanical, fractional Talbot illuminators.

The purpose of present article is threefold:

First, the authors try to a scale changes generate quadratic phase factors, resulting in Talbot images of arbitrary fractional order.

Second, the authors try to discuss an optical technique that continuously increases the scale of the virtual Fourier spectrum without mechanical intervention.

Third, the authors try to design a tunable fractional Talbot illuminator that can be used for Talbot interferometry.

In fact the present manuscript in its present form is simple and easy to follow, however, it needs some little modification to be accepted for publication. The following points have to be addressed:

• In Fig. 1, the authors show the setup used for observing Luxmoore for varying the spatial frequency of a master grating. Can the authors give details about the resolution of the point source along distance xo and the minimum distance of the grating (d) grating constant?

• In Fig. 2, the authors add three lenses to the setup. Can the authors give more details about the difference between these two setups?
• Can the author’s comments on the effect of the diffraction on the image plane (Fourier spectrum)
• Equations 1,2,3 contain some typo errors.
• Most of the references used are very old; please use up-to-date references.
• The English needs careful revision.

With my best regards

• The English needs careful revision.

Author Response

Reply to the Reviewers:

Tunable, nonmechanical, fractional Talbot illuminators.

Cristina M. Gómez-Sarabia ¹, and Jorge Ojeda-Castañeda ^2, *

Reply to the Reviewer number one.

We have merge Figures 1 and 2 for improving our description. And a new figure caption was in order for discussing the difference between the two setups. The new figure caption reads:

“Schematics of the optical setups for varying the spatial frequency of a master grating. In (a) the arrangement described by Luxmoore. In this arrangement, the master grating moves along the optical axis, for scaling its Fourier spectrum. And a fixed optical power lens implements a Fourier trans-form, of the scaled Fourier spectrum. In (b), our proposed apparatus. Instead of moving the master grating, two varifocal lenses magnify the Fourier spectrum; which remains at fixed axial position.”

Moreover, in the main text, we have indicated that:

“We observe, in Figure 1 (a), that the separation z₀ is variable, for scaling the Fou-rier spectrum. For evading this motion, in Figure (b), the separation z₀ is fixed. In our proposed apparatus, the axial motion, of the master grating, is substituted by the use of two varifocal lenses. These lenses magnify the Fourier spectrum, with-out changing its axial position.  In both cases, the position of the point source defines the input plane. In both setups, we employ a lens, whit fixed optical power K₃ = 1/f.”

2. To comply with the request, from Reviewer number one, we have added a comment on the practical aspects of the depicted setups, we have added the following text.

“Our previous discussion was no intended for arguing on the favor of Luxmoore technique. But rather for given the necessary background for the following method. However, before that, some practical considerations may be in order. The master grating can be a Ronchi ruling with an area of 50 (mm) x 50 (mm); and with 40 lines per millimeter. Then, the total number of lines is two thousand. If the dis-tance, between the point source and the master grating, is z₀ = - 1 (m), the diffrac-tion orders are practically Dirac´s deltas. For fully illuminating the master grat-ing, the angular spread of the wavefront is about 3. 2 degrees.”

3. We were unable to identify any typo in equations 1, 2 and 3. We believe that the Reviewer comment was due to . Another possibility is that we have a noncommon notation. If this is the case, we kindly ask to bear our notation based on geometrical optics.
4. In our list of references, there are now only 4 papers that were published before 2019. These 4 papers are relevant to our discussion, and they can not be substituted. The remaining 19 papers are rather recent. And, out of the 23 listed papers, only 3 papers are citations to our previous contributions.
5. To improve the clarity of our descriptions, we have rephrased several sentences in our script.

We express our sincere gratitude to the Reviewer for her/his valuable advice.

Author Response File: Author Response.pdf

Reviewer 2 Report

Journal: Optics

Manuscript Number: optics-2694011  

Title: Tunable, nonmechanical, fractional Talbot illuminators

In this work, the authors have investigated inserting a varifocal system for magnifying continuously the frequency of a grating. As the magnification M varies, without mechanical intervention, the Fourier spectrum remains at the same location. And, also at a fixed detection plane, one can generate Talbot images of any fractional-order.

It is an interesting paper, and I think it is of interest to the readers of Optics Journal. I have the following comments:    

My comments

1.      There are some typos. I give some examples: “And of course, the technique requires of a mechanical device for” should be “And of course, the technique requires a mechanical device for”;               “delay is responsible for generating Talbot images, of any fractional-order” should be “delay is responsible for generating Talbot images, of any fractional order”;                        “Second, we discuss an optically technique for magnifying continuously” should be “Second, we discuss an optical technique for magnifying continuously”;   There are other typos. Please go through the manuscript, and correct it.

2.      Please give a new paragraph at the end of the introduction section to illustrate the novelty.

3.      Please show clearly the main aim of this manuscript.

4.      What does your work add to the field?  

5.      Some of the references are not so recent. To keep the reader updated, I advise the authors to cite some recent references on Talbot phenomenon. I recommend the following citations:  doi :10.1088/1755-1315/128/1/012047 ; doi:10.1016/j.tsf.2010.04.067

6.      In the PDF file, equations 1, 2 and 3 are not clear.

7.      Please cite references for the equations presented in section 2.

Journal: Optics

Manuscript Number: optics-2694011  

Title: Tunable, nonmechanical, fractional Talbot illuminators

In this work, the authors have investigated inserting a varifocal system for magnifying continuously the frequency of a grating. As the magnification M varies, without mechanical intervention, the Fourier spectrum remains at the same location. And, also at a fixed detection plane, one can generate Talbot images of any fractional-order.

It is an interesting paper, and I think it is of interest to the readers of Optics Journal. I have the following comments:    

My comments

1.      There are some typos. I give some examples: “And of course, the technique requires of a mechanical device for” should be “And of course, the technique requires a mechanical device for”;               “delay is responsible for generating Talbot images, of any fractional-order” should be “delay is responsible for generating Talbot images, of any fractional order”;                        “Second, we discuss an optically technique for magnifying continuously” should be “Second, we discuss an optical technique for magnifying continuously”;   There are other typos. Please go through the manuscript, and correct it.

2.      Please give a new paragraph at the end of the introduction section to illustrate the novelty.

3.      Please show clearly the main aim of this manuscript.

4.      What does your work add to the field?  

5.      Some of the references are not so recent. To keep the reader updated, I advise the authors to cite some recent references on Talbot phenomenon. I recommend the following citations:  doi :10.1088/1755-1315/128/1/012047 ; doi:10.1016/j.tsf.2010.04.067

6.      In the PDF file, equations 1, 2 and 3 are not clear.

7.      Please cite references for the equations presented in section 2.

Author Response

Reply to the Reviewers

Tunable, nonmechanical, fractional Talbot illuminators.

Cristina M. Gómez-Sarabia ¹, and Jorge Ojeda-Castañeda ^2, *

Reply to the Reviewer number two.

1. We thank the Reviewer for the grammar corrections. For improving the clarity of our descriptions, now, we have amended several sentences in our script.
2. At the end of the introduction, for describing the novelty of our contribution, we have added the following text:

“Here, we claim novelty on three results: (a) we offer analytical descriptions of two techniques that control the spatial frequency of a master grating; (b) we unveil the use of a two varifocal lenses for implementing a motionless method, which tunes the spatial frequency of a master grating; (c) we propose a technique for generating a structural beam, which can illuminate a sample without occluding regions. This type of illumination can be useful for Talbot interferometry.”

3. In the introduction and in the conclusions, we have rephrased the three goals of our typescript.
4. At the end of every section, now, we are indicating our additions to the field of Talbot interferometry.
5. We are grateful to the Reviewer, number two, for suggesting the reference of the nonlinear Talbot effect. We were not aware of this publication. However, we decline including the second recommended paper, since we believe that the second recommendation is not relevant to our current discussion.
6. We will check that the amended version will have a proper PDF document.
7. Now, we have included the references associated to the discussion on the use of varifocal lenses.

We express our sincere gratitude to the Reviewer for her/his valuable advice.

Author Response File: Author Response.pdf

Reviewer 3 Report

Cristina et al. focused on tunable illuminators and highlighted the significance of scale variation in inducing a quadratic phase factor. This factor, in turn, generates Talbot images of arbitrary fractional order. The author also discussed an optical technique that allows for continuous magnification of the virtual Fourier spectrum scale without the need for any mechanical intervention. The author has successfully developed a tunable fractional Talbot illuminator, specifically designed for Talbot interferometry applications.  This paper is well written and has been accepted for publication. Please consider the following suggestions.

1.       The author should consider merging Figure 1 and Figure 2 in order to highlight the proposed setup.

2.       The author should consider moving some of the equations and appendix A to the supporting data section. Additionally, it would be beneficial to only highlight the important equations in comparison to the figures.

Author Response

Reply to the Reviewers

Tunable, nonmechanical, fractional Talbot illuminators.

Cristina M. Gómez-Sarabia ¹, and Jorge Ojeda-Castañeda ^2, *

Reply to the Reviewer number three.

1. We thank the Reviewer, number three, for suggesting to join the initial figures. We have followed that suggestion.
2. We have considered bringing material from the appendix to the main text. However, the main text is already large. For a proper discussion on geometrical optics, readers are kindly addressed to references 19 and 20.

We would like to express our sincere gratitude to the Reviewer for her/his valuable advice.

Author Response File: Author Response.pdf