Study on Aided Optical Alignment by Programmable Spots Array Generated by Off-Axis Parabolic Phase Based on LCoS-SLM
Round 1
Reviewer 1 Report
The authors in the paper entitled “Study on Aided Optical Alignment by Programmable Spots Array Generated by Virtual Off-Axis Parabolic Phase Based on LCoS-SLM”, to find a new cost-effective approach to overcome the difficulty in off-axis optical alignment and measurement, conduct a study on using a programmable optical system to generate a space position controllable focus light spots array to aid the alignment process. The authors exploited the liquid crystal on silicon spatial light modulator (LCoS-SLM) to generate a virtual off-axis light spots array.
Results verify the feasibility and effectiveness of the method. Moreover the authors describe an interferometer method to calibrate and compensate the phase nonlinear and non-uniformity due to the cutting and polishing operation in the LCoS-SLM manufacture procedure.
The paper is clear and can be accepted for publication.
Author Response
Dear Editors and Reviewers:
We would like to express our sincere thanks for your constructive and positive comments on our manuscript. We have studied comments carefully and have made correction which we hope meet with approval. Revised portions are marked in red for easy tracking. The main corrections in the paper and the responds to the reviewer’s comments are as following:
Reviewer #1
Thank you for your careful review and comments in the manuscript. Firstly, thank you for your recognition of our research. We have provided more discussion in the introduction to enrich the background research. Then, based on the editor’s suggestion, we thought about it carefully and responded and revised them.
Comment.1: The authors in the paper entitled “Study on Aided Optical Alignment by Programmable Spots Array Generated by Virtual Off-Axis Parabolic Phase Based on LCoS-SLM”, to find a new cost-effective approach to overcome the difficulty in off-axis optical alignment and measurement, conduct a study on using a programmable optical system to generate a space position controllable focus light spots array to aid the alignment process. The authors exploited the liquid crystal on silicon spatial light modulator (LCoS-SLM) to generate a virtual off-axis light spots array.
Response: Thank you for your kind comments.
Comment.2: Results verify the feasibility and effectiveness of the method. Moreover the authors describe an interferometer method to calibrate and compensate the phase nonlinear and non-uniformity due to the cutting and polishing operation in the LCoS-SLM manufacture procedure.
Response: Thank you for your careful work about this issue. We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the main content and framework of the paper and be marked in red in the revised paper.
We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Corresponding authors:
Xiaodong Zhang, [email protected]
Author Response File: 
Author Response.docx
Reviewer 2 Report
I believe that the concept is to use a phase only SLM to focus spots from a collimated beam on an object. The object is aligned by moving the object until all the spots are in focus. This overall method on alignment is not clearly explained. Some tolerance or accuracy considerations should be discussed. Especially in regards to the depth of focus, which varies depending on the distance to the object and the width of the fresnel pattern on the SLM. Ultimately, what is the depth and horizontal positioning resolution that is possible by observing laser spots on an object? This needs to consider viewpoint of the observing camera that would be viewing the object. (As opposed to the experiment that places a camera at the object plane.
Also, the problem being overcome by tilting seems to be undersampling of the wavefront by the SLM. However, it is possible to include a focusing lens in series with the SLM to eliminate quadratic phase (other than fine adjustments on focal depth.) A comparison of object positioning accuracy with and without a focusing lens is well worth adding to the study.
A ray trace for an undeviated ray and for a ray from the quadratic phase modulation that includes the variables in the optics formulas would make the equations more understandable. The ray trace can probably be shown with a single optical axis, rather than two axes at an angle of theta.
The figure that shows the SLM not tilted and then tilted has two problems. i) It looks like the tilt angle of the SLM should be half the angle of the reflection angle. The reflected beam is shown as perpendicular to the SLM in the tilted drawing. The angle looks ok in a later drawing. ii) The coordinate system shown on the same figure is a left handed,rather than right handed coordinate system.
Author Response
Dear Editors and Reviewers:
We would like to express our sincere thanks for your constructive and positive comments on our manuscript. We have studied comments carefully and have made correction which we hope meet with approval. Revised portions are marked in red for easy tracking. The main corrections in the paper and the responds to the reviewer’s comments are as following:
Reviewer #2
Thank you for your careful review and comments in the manuscript. Firstly, thank you for your recognition of our research. In view of the language problem you pointed out, we have checked the writing grammars in detail throughout the article and revised them. Besides, we have provided more discussion in the introduction to enrich the background research. Then, based on the three amendments you suggested, we thought about it carefully and responded and revised them.
Comment.1: I believe that the concept is to use a phase only SLM to focus spots from a collimated beam on an object. The object is aligned by moving the object until all the spots are in focus. This overall method on alignment is not clearly explained. Some tolerance or accuracy considerations should be discussed. Especially in regards to the depth of focus, which varies depending on the distance to the object and the width of the fresnel pattern on the SLM. Ultimately, what is the depth and horizontal positioning resolution that is possible by observing laser spots on an object? This needs to consider viewpoint of the observing camera that would be viewing the object. (As opposed to the experiment that places a camera at the object plane.
Response: Thank you for your careful work on this issue. In the experiment, the CCD camera we use is produced by AVT at 2448 × 2050 resolution with the pixel size of 3.45µm. The position and orientation of the tested surface sample or CCD camera could be adjusted according to the shape of the light spots array to align it to the optical axis. We used the captured image of the light spots array to explain the process better, but the camera is not necessary. It would need a careful observation of the focused light spots on measured surface by eyes. Its accuracy in the vertical direction (optical axis direction) is at sub-millimeter level, which is enough for primary optical alignment.
Comment.2: Also, the problem being overcome by tilting seems to be undersampling of the wavefront by the SLM. However, it is possible to include a focusing lens in series with the SLM to eliminate quadratic phase (other than fine adjustments on focal depth.) A comparison of object positioning accuracy with and without a focusing lens is well worth adding to the study.
Response: Thank you for your comments on the rigor of the article. We did some work on the use of focusing lens to help the alignment in the optical system consisting LCoS-SLM. However, we considered that the characteristic of the phase modulation ability of LCoS-SLM makes it will produce a nonlinear change when it is given an oblique incidence light. When the tile angle is small, the change is approximate to the cosine function. But when the Angle is larger, additional calibration work of this part of the nonlinear relationship is needed. In our proposed system, we hope to minimize additional optical devices, so we use LCoS-SLM itself to complete the alignment.
Comment.3: A ray trace for an undeviated ray and for a ray from the quadratic phase modulation that includes the variables in the optics formulas would make the equations more understandable. The ray trace can probably be shown with a single optical axis, rather than two axes at an angle of theta.
Response: Thank you for such valuable and thorough comments. In the optical simulation, we use the optical path shown in Figure 3, which represents the reflection of the parallel incident light by an off-axis parabolic (OAP) lens. After the reflection of this OAP, plane wavefront can become spherical wavefront and converge to its focus. It has computable the parent focal length as F, the off-axis magnitude as D, reflected focal length as L, and off-axis angles as θ. SLM can also perform a similar function after loading the phase pattern. This provides a basis for the application of LCoS-SLM to generate converging points and spot arrays at specific locations in space. Moreover, after SLM used in the alignment step, it does not need further adjustment and then the compensation phase diagram for the measured optical surface can be loaded directly to finish the measurement step, which is very convenient. Therefore, we propose the off-axis reflection model for optical alignment and optical surface interferometry measurement.
Comment.4: The figure that shows the SLM not tilted and then tilted has two problems. i) It looks like the tilt angle of the SLM should be half the angle of the reflection angle. The reflected beam is shown as perpendicular to the SLM in the tilted drawing. The angle looks ok in a later drawing. ii) The coordinate system shown on the same figure is a left handed, rather than right handed coordinate system.
Response: Thank you for pointing out our clerical error accurately. According to the theory of light reflection, the rotation angle of the reflecting surface is indeed half of the optical axis deflection angle. The compensating phase of the off-axis paraboloid function loaded on the LCoS-SLM we designed is distributed symmetrically, so the optical axis of the reflected spherical wave front is perpendicular to the plane of the LCoS-SLM. As for the identification of the coordinate system, we adjusted the coordinate indication in the correlation figures in the manuscript to correctly display the direction in the optical path and the direction in the calculated phase pattern.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the main content and framework of the paper and be marked in red in revised paper.
We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions
Best regards,
Corresponding authors:
Xiaodong Zhang, [email protected]
Author Response File: Author Response.docx
Reviewer 3 Report
Please see my comments in the attached file.
Comments for author File: 
Comments.pdf
Author Response
Dear Editors and Reviewers:
We would like to express our sincere thanks for your constructive and positive comments on our manuscript. We have studied comments carefully and have made correction which we hope meet with approval. Revised portions are marked in red for easy tracking. The main corrections in the paper and the responds to the reviewer’s comments are as following:
Reviewer #3
Thank you for your careful review and comments in the manuscript. Firstly, thank you for your recognition of our research. In view of the language problem you pointed out, we have checked the writing grammars in detail throughout the article and revised them. Besides, we have provided more discussion in the introduction to enrich the background research. Then, based on the nine amendments you suggested, we thought about it carefully and responded and revised them.
Comment.1: Coordinate axes. Figure 1 is missing the coordinate basis, In Figure 2 there are only Y and Z coordinate axes(not critical as such). The coordinate axes in Figure 4 are defined differently to Figure 3. Also axes in Figures are given with capital letters and in the text are in small letters. Do they correspond one to another? Is “Z” in Equation 3 a coordinate? And what is “Phi” in Figure 4?
Response: Thank you for your careful work on this issue. We apologize for the improper use of these coordinate axes. The coordinate axes in Figure 1,3 and 4 have been adjusted to illustrate the direction in the optical path and the direction in the calculated phase pattern better. At the same time, we have modified the Equation 3. “Z” in Formula 3 refers to the vector height of the off-axis paraboloid surface in equivalent calculation, which is specially marked as ZOAP. “Phi” in Figure 4 refers to the angle between the optical axis of the reflected light and incident parallel light. Both optical axes are marked with dashed lines in the figure.
Comment.2: Color bars. Could you provide the information to what the white and black correspond in Figure 4, and color in Figure 8? For example, in Figure 8 “zero” should not change its color from green to blue. Mind also that in Figure 8 there are 18 grayscale intervals, and not 15 as written in the text.
Response: Thank you for your good suggestion on this problem. Figure 4 contains the calculated phase pattern. The white and black pattern, which is a grayscale pattern ranging from 0 to 255, refer to the calculated phase. The interval of one black and white fringe is a 2 PI period, representing the distance of one wavelength. The multiple periods of the phase pattern is due to the use of a phase truncation algorithm with a period of 2 PI in the phase calculation.
In Figure. 8, MATLAB is used to draw the phase diagrams for sequence calibration. We have modified the relevant text about the number of phase intervals and steps. What we want to explain is that there are 18 step phase diagrams are generated at an interval of 15 gray values between 0 and 255 to calibrate LCoS-SLM's phase modulation capability.
Comment.3: Figure 9 has almost no description in the text. So, for me it is hard to comment it. What are X(greylevel) and Z(lambda)?
Response: Thanks for your kind advice. We added the description text for Figure 9. We correspond the 256 gray levels (0-255) of the grayscale image to the 2PI phase. That is the meaning of X(greylevel) and Z(lambda). Figure 9a shows the curve of the measured value with the given gray scale image on the LCoS-SLM, and the straight line is the theoretical value. Figure 9b shows the error of them. The calibrated SLM has a modulation phase precision of 0.025λ (1/40λ). So that it can already be considered as a high precision phase modulation.
Comment.4: Could you comment on the role of the interferometer as the light source, why cannot it be simply a laser?
Response: Thanks for your valuable question. The Interferometer plays an important role in the whole optical system. Our idea is to replace the role of optical compensators in the interferometry of aspheric surface and free-form surface by using LCoS-SLM with compensating phase modulation. Therefore, the interferometer provides the light source for the whole measuring system with its laser and is also the measuring instrument for the phase data. As the phase of the virtual off-axis parabolic function is loaded on the LCoS-SLM, we can observe the spots array and measure the phase by the interference pattern. The alignment precision using the interferometer of the light array and its interference patterns is much more accurate than that on the paper target or the tested surface which is observed by the human eye. This is of great significance for accurate alignment of interferometric optical system.
Comment.5: Could you comment on the role of the “transmission sphere” and the polarization state mentioned in the sketches?
Response: Thank you for pointing out such a serious misnomer. We apologize for the improper expression. This part is a transmission plane lens which is used to transmit the plane wave front of the interferometer. We have modified both the text and the graphics. The polarization direction is labeled in the figures. The reason is that LCoS-SLM is an optical device sensitive to the polarization state of light. The light emitted by the interferometer is circularly polarized and becomes linearly polarized after passing through a linear polarizer. The polarization direction of the obtained linearly polarized light must be adjusted according to the polarization direction of LCoS-SLM so that it can correctly modulate the incident polarized light.
Comment.6: Could you mention why the focus spots images should be oversaturated?
Response: Thanks for your valuable question. The light spots in the figures are captured by the camera or the interferometer. They are oversaturated a little in order to show the shape of the spots better.
Comment.7: Figure 17 seems to contain a lot of information and has very few descriptions. For example, I can only guess that “obvious spherical aberration fringe” must be seen in the central and right part of Figure 17a.
Response: Thank you for your careful work on this issue. More detailed descriptions are added to illustrate Figure 17. It is very useful to observe the image of the spot array with interferometer and to align the light path. If there is a shift or tilt in the path, the shift of the spot and the change in the spot shape on one side will be observed. At the same time, using the phase measurement function, the phase of the light spots array can be obtained. In the defocused state, a phase pattern similar to a spherical wave is observed. And the other group of phase pattern could be observed with less phase data due to less reflection of light. In optical alignment, you can precisely align the optical path by observing the location of these spots and their phase patterns.
Comment.8: Could you comment on why the parabolic phase is the prime choice? Why the array of light spots is better then, for example a grid?
Response: Thanks for your kind suggestion. The off-axis parabolic (OAP) phase was chosen because it can convert parallel light into a spherical wavefront and produce a focused spot of light at a specific location in space. At the same time, the returned light can be received and measured by interferometers. These two points are very advantageous for visual coarse adjustment and precise alignment by interference fringe and phase. Compared with that, light grids can only be coarsely observed by eyes.
Comment.9: Also, the last sentence on the page 2 is summarizing the whole article and describes the Figure 2. But unfortunately, it is badly formulated. Consider rewriting it. And also, in the caption of the Figure 1 it must be “positioning” and not “poisoning”.
Response: Thank you for your careful review and comments. We have rewritten this part for better understanding. And thank you for point out the grammar problem in Figure 1.We also examined other relevant parts of the manuscript.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the main content and framework of the paper and be marked in red in revised paper.
We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions
Best regards,
Corresponding authors:
Xiaodong Zhang, [email protected]
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
This manuscript is significantly improved and much more understandable.
One minor revision that should be considered is the use of the word "virtual". While the parabolic phase front can be referred to as a "virtual parabolic mirror" the phase itself and the resulting spots are not "virtual". Just dropping these inappropriate uses of "virtual" will avoid a lot of confusion by readers.
Author Response
Dear Editors and Reviewers:
We would like to express our sincere thanks for your constructive and positive comments on our manuscript. We have studied comments carefully and have made correction which we hope meet with approval. Revised portions are marked in red for easy tracking. The main corrections in the paper and the responds to the reviewer’s comments are as following:
Reviewer #2
Thank you for your careful review and comments in the manuscript. Based on the comments you suggested, we thought about it carefully and responded and revised them.
Comment.1: This manuscript is significantly improved and much more understandable. One minor revision that should be considered is the use of the word "virtual". While the parabolic phase front can be referred to as a "virtual parabolic mirror" the phase itself and the resulting spots are not "virtual". Just dropping these inappropriate uses of "virtual" will avoid a lot of confusion by readers.
Response: Thank you for your careful work on this issue. The word “virtual” means that the LCoS-SLM could be used as a real off-axis parabolic mirror with the calculated parabolic phase loaded. The light spots array is visual to eyes and could be captured by CCD camera or the Interferometer as mentioned in the manuscript. We have reduced or changed the use of “virtual” to other words for better understanding. The revised parts are at Line 40, Line72, Line 85, Line 111 and Line 209.And the word “virtual” in the title of the paper is also removed.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the main content and framework of the paper and be marked in red in revised paper.
We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions
Best regards,
Corresponding authors:
Xiaodong Zhang, [email protected]
Author Response File: Author Response.pdf
