Liquid Lens Optical Design for Adjustable Laser Spot Array for the Laser-Based Three-Dimensional Reconstruction of Vocal Fold Oscillations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a method for generating a spatial two-dimensional spot array in three-dimensional endoscopy. The authors propose an optical lens device consisting of two liquid lenses and a DOE. The first liquid lens controls the size of the focused spots, while the second liquid lens controls the size of the spot array. The authors provide a theoretical derivation of the imaging process, construct an optical experimental setup to validate the modulation of the projected spot array, and analyze the uniformity of the generated spot array. Although the results have not yet been applied to three-dimensional endoscopy, the optical design method for realizing the spot array provides valuable insights for the field. I recommend the publication of this article with the following specific suggestions:

1. The manuscript uses a DOE device to create a 21×21 spot array. Is this device a micro lens array? It is recommended to provide a brief description of this device.
    
2. The authors analyze the standard deviations of distance between adjacent spots, spot diameter, and amplitude. Do the current deviations meet the requirements for three-dimensional endoscopic imaging?
    
3. According to Table 1, is the spatial distribution of relative standard deviations in the generated spot array random or ordered? if it is an ordered distribution, it means that some aberrations occur.  The authors also mention "potential aberrations" on page 6, line 205. What specific aberrations are they referring to?
    
4. Should the depth of field of the generated spots be considered? In three-dimensional structured light imaging, the three-dimensional contour of the object can cause variations in the shape and size of the projected spots.

Author Response

This manuscript presents a method for generating a spatial two-dimensional spot array in three-dimensional endoscopy. The authors propose an optical lens device consisting of two liquid lenses and a DOE. The first liquid lens controls the size of the focused spots, while the second liquid lens controls the size of the spot array. The authors provide a theoretical derivation of the imaging process, construct an optical experimental setup to validate the modulation of the projected spot array, and analyze the uniformity of the generated spot array. Although the results have not yet been applied to three-dimensional endoscopy, the optical design method for realizing the spot array provides valuable insights for the field. I recommend the publication of this article with the following specific suggestions:

1. The manuscript uses a DOE device to create a 21×21 spot array. Is this device a micro lens array? It is recommended to provide a brief description of this device.

We thank the reviewer for the comment. The device is a diffractive optical element, i.e. a hologram that generates the beamlet pattern through diffraction effects on a specifically designed grating. There are no lenses involved. For furhter information on DOEs and the therein-involved working principles the reader should start at [Gabor Holography 1948-1971 and Goodman Introduction to Fourier Optics].

We added now (rows 70-74): “In this paper, as a proof-of-principle, we present a free space optical system for non-mechanical beam manipulation using two liquid-lenses and a static diffractive optical element (DOE). A DOE is basically a type of a holographic grating that allows for a lens-free generation of arbitrary intensity patterns through diffraction, see [15] and [16] for further reading. The specific DOE used here, generates a laser spot array consisting 21x21 individual beams and is placed between two electro-wetting liquid lenses so that the combination of the static DOE and the varioptic lenses functions as a dynamic spot array generator.”

2. 
   The authors analyze the standard deviations of distance between adjacent spots, spot diameter, and amplitude. Do the current deviations meet the requirements for three-dimensional endoscopic imaging?
   
   

We thank the reviewer for the comment. Yes, the deviations are small enough to meet the requirements. The aim is to have especially uniform distribution for the spot diameters and their amplitude, because if there would be large deviations, than this might lead in the worst case to intensities at individual beamlets that exceed laser safety regulations for tissue, while some other spots are too weak or too diluted to provide a sufficient signal for the camera. With the low deviations measured this is not a problem. The distance between spots is necessary for the estimation of adjacent beamlets so that a corresponding pair “beamlet”-“bright spot in the camera”-pair can be reproducibly identified. Nonlinear changes of the spot distance during refocusing or zooming caused by aberrations would impair the ability to find the corresponding pairs. We additionally write now at the end of Chapter 3.4 Uniformity: “With the standard deviations for beamlet distances below 1.2%, the beamlet’s size below 5.2 % and the beamlet’s amplitude below 10.8 % the system easily meets the requirements for three-dimensional endoscopic imaging at different working distances and magnification settings.”

3. 
   According to Table 1, is the spatial distribution of relative standard deviations in the generated spot array random or ordered? if it is an ordered distribution, it means that some aberrations occur.  The authors also mention "potential aberrations" on page 6, line 205. What specific aberrations are they referring to?

We thank the reviewer for the comment. Table 1 is ordered only by the working distance and then, secondly, by the refractive power at Lens 2, which sets the magification factor. It is the numerical list of deviations that were used to construct Fig. 9. As one can see in Fig. 9 there is no trend for the deviations to increase or decrease depending on the parameter setting. The values appear to be random, which is good, because this shows that there is no systematic effect of the parameters on the uniformity of beamlets.

With “potential aberrations” we mean aberrations that are introduced in Section 3.4, where we already write: “… Thus, refractive aberrations, such as cushion/barrel distortions might cause a varying in-ter-spot distance across the spot array, while other types of aberrations, e.g. coma, spherical aberrations etc. might change the spot shapes and certainly decrease the available maximum intensity at aberrated spots. Therefore, they would heavily depend on the zoom factor, as the zoom factor is effectively set by controlling the curvature of the liquid in the lens. …” We have now added on page 6 line 205 the reference to Section 3.4: “…This way it was possible to investigate the action of the liquid lenses on both the spot size, spot array magnification and any potential aberrations (see Section 3.4) and uniformity deviations of all beamlets generated by the DOE…”

4.  
   Should the depth of field of the generated spots be considered? In three-dimensional structured light imaging, the three-dimensional contour of the object can cause variations in the shape and size of the projected spots.

We thank the reviewer for the comment. Because the generated beamlets follow very closely a Gaussian distribution, the spot sizes in front and behind the working distance range can be described by Gaussian beam propagation. That this is a valid assumption is shown by Fig. 6 in Chapter 3.3. The minimum spot sizes widen with increasing working distance, meaning that the focal spot must lie at a closer positions, i.e. closer to the LPUs exit facet than the range of the working distances (40 -70 mm). The monotone increase of the spot size shows that the desired working distances lie in the far field of the Gaussian, when the beamlet sizes increase (nearly) linearly with the distance. Hence, for longer working distances the spot size will become only larger.

Yes, 3D contours will have an effect on the perceived spot shape and intensity. However, vocal fold vibrations do not cause steep enough surface normals so that the center of mass based spot detection algorithm would break. Otherwise, the 3D vocal fold movement estimation would not have been possible in the case of a just static beamlet array: https://doi.org/10.3390/app7060600

Reviewer 2 Report

Comments and Suggestions for Authors

The paper "Liquid lens optical design for adjustable laser spot-array for laser-based three-dimensional reconstruction of vocal fold oscillations" focuses on developing an optical system with liquid lenses designed for dynamic adjustment of a laser spot array to improve imaging accuracy compared to traditional laser endoscopy for analyzing vocal fold oscillations. The introduction sufficiently explains the motivation of the authors, but the subsequent sections raise concerns regarding both the methodological and practical significance of the proposed approach.

 

The main technical part of the paper presents an engineering solution with a well-described methodology for calculating the dynamic factor. However, the final system does not surpass existing alternatives and largely replicates known scaling solutions using dual liquid lenses. Notably, the described system closely resembles the Varioptic liquid lens approach presented in [1], which also achieves a zoom factor of 1.8. The absence of a reference to this study is a significant omission, as the publication by Zhang provides a more comprehensive approach.

 

[1]  W. Zhang, D. Li, X. Guo, Optical Design and Optimization of a Micro Zoom System with Liquid Lenses // Journal of the Optical Society of Korea 17, 447–453 (2013).

 

Some novelty is introduced by the inclusion of a diffractive optical element. However, the entire setup has not been integrated into an endoscopic system, which could be expected based on the paper's title.

 

Additionally, the authors did not sufficiently proofread the text. For example, Section 3 ("Results") begins with a placeholder template text, which was likely left unintentionally. Similarly, Table 1 has formatting errors—values in the first column ("zWD in mm") are written with a comma but lack decimal precision.

 

According to the journal's guidelines, the article should include a Discussion section where the authors explain their results in the context of previous studies and working hypotheses, as well as define directions for future research. The current "Conclusion and Outlook" section is not mandatory and instead resembles a brief summary that would be more appropriate within a proper Discussion section.

 

I recommend that the authors rename this section to "Discussion" and expand it by addressing the following points:

 

- How and why do the obtained results reconstruction accuracy of of vocal fold oscillations compared to traditional laser-based endoscopic method?  

- Is the achieved zoom factor of 1.8 sufficient for practical applications?  

- A more detailed analysis of the role of the first lens is needed, as it is given little attention compared to the second lens. For example, data in Figures 5 and 7 suggest that using a fixed lens with an optical power of approximately 20 m⁻¹ could be a viable alternative instead of the first liquid lens.

 

It is also strongly recommended to change the colormap in Figures 5 and 7, replacing the rainbow color scheme with a perceptually uniform colormap, as discussed in [2] and "Color Map Advice for Scientific Visualization" (https://www.kennethmoreland.com/color-advice/). Additionally, ticks should be added to the axes to improve data readability.

[2] K. Moreland, Why We Use Bad Color Maps and What You Can Do About //Electronic Imaging, 28, 1–6 (2016).

Overall, the paper has potential but requires significant improvements to the discussion section to better define the scientific novelty and practical advantages of the proposed system.

 

Author Response

• The paper "Liquid lens optical design for adjustable laser spot-array for laser-based three-dimensional reconstruction of vocal fold oscillations" focuses on developing an optical system with liquid lenses designed for dynamic adjustment of a laser spot array to improve imaging accuracy compared to traditional laser endoscopy for analyzing vocal fold oscillations. The introduction sufficiently explains the motivation of the authors, but the subsequent sections raise concerns regarding both the methodological and practical significance of the proposed approach.

We thank the reviewer for the comment. We have now subsumed certain parts from Conclusion and Outlook into a Discussion chapter, and are reiterating the methodological and practical significance of the work in the new Conclusion Chapter:

“In this work, we introduced a dual-liquid-lens optical design that flexibly adjusts the spot size and spot distance in a laser grid generated from a static DOE. Our experiments demonstrated a dynamic zoom factor of approximately 1.8 across clinically relevant working distances and confirmed that this adaptable configuration maintains optimal coverage of the vocal folds and minimal optical aberrations. These findings establish that using tunable liquid lenses for laser-based 3D laryngoscopy can effectively address inter-patient variability, such as differing vocal fold sizes and variable laryngoscope-to-larynx distances, thereby paving the way for improved 3D reconstructions of vocal fold oscillations.

Although our proof-of-concept system has not yet been incorporated into a fully miniaturized endoscope, it serves as a conceptual foundation for future integration demonstrating the feasibility of liquid lenses in laser projection. We have shown that the combination of a static DOE with two variable-focus liquid lenses offers the flexibility needed to adapt illumination parameters in real time, an essential step toward truly personalized and optimized laryngoscopic 3D imaging. By enabling precise control of both the laser spot-array size and individual spot diameters, our approach promises to enhance reconstruction accuracy and clinical utility, and ultimately addresses many of the practical and methodological concerns surrounding next-generation endoscopic imaging systems. We anticipate that further engineering for miniaturization and control systems will facilitate the application of this design in a clinical setting, thereby offering a valuable advance over existing fixed-geometry laser projection unit for endoscopy.”

• The main technical part of the paper presents an engineering solution with a well-described methodology for calculating the dynamic factor. However, the final system does not surpass existing alternatives and largely replicates known scaling solutions using dual liquid lenses. Notably, the described system closely resembles the Varioptic liquid lens approach presented in [1], which also achieves a zoom factor of 1.8. The absence of a reference to this study is a significant omission, as the publication by Zhang provides a more comprehensive approach.

 [1]  W. Zhang, D. Li, X. Guo, Optical Design and Optimization of a Micro Zoom System with Liquid Lenses // Journal of the Optical Society of Korea 17, 447–453 (2013).

We thank the reviewer for the comment. While Zhang et al. focus on the theoretical optical design and optimization of a liquid-lens-based micro zoom system for IMAGING, our work specifically targets laser grid PROJECTION for endoscopic 3D reconstruction of vocal fold oscillations. Zhang et al. do not report building or experimentally testing a physical prototype. In contrast, we perform an experimental proof-of-concept. We employ a diffractive optical element in conjunction with two liquid lenses to adapt both the spot distance and spot size, thereby addressing the unique clinical constraints of laryngoscopy. We have now added in the introduction, before describing our laser based light projection system, a text portion referring to imaging with varioptic liquid lenses:

“Various liquid-lens-based zoom systems have been explored for compact imaging applications [Ref: https://doi.org/10.1364/OE.432290 ; doi: 10.3390/s16010045;  DOI: 10.1088/1748-3190/abfc2b]. For instance, Zhang et al. present a theoretical design and optimization of a micro zoom system employing liquid lenses for general imaging purposes [Ref Zhang]. In contrast, our approach specifically targets laser spot-array generation for endoscopic 3D reconstruction.”

• Some novelty is introduced by the inclusion of a diffractive optical element. However, the entire setup has not been integrated into an endoscopic system, which could be expected based on the paper's title.

We thank the reviewer for the comment. However, as mentioned above, the novelty in our manuscript is not the introduction of the DOE, but the application of the dual-liquid-lens setup for laser grid projection and an experimental demonstration of its feasibility.

• Additionally, the authors did not sufficiently proofread the text. For example, Section 3 ("Results") begins with a placeholder template text, which was likely left unintentionally. Similarly, Table 1 has formatting errors—values in the first column ("zWD in mm") are written with a comma but lack decimal precision.

We thank the reviewer for finding these errors. We have corrected them.

• According to the journal's guidelines, the article should include a Discussion section where the authors explain their results in the context of previous studies and working hypotheses, as well as define directions for future research.

We thank the reviewer for the comment. We have divided now the previous sections “Results” and “Conclusion and Outlook” into “Results“, “Discussion” and “Conclusion”. Now we write in the Discussion section that:

“So far, all previous studies in the field of 3D imaging of the human larynx were based on a fixed geometry of the laser projection unit. There are setups with one or more laser lines as well as regular laser dot grids. There are approaches with microlens arrays or DOEs (George et al. (2008), Phys. Med. Biol., 53(10):2667–2675, Luegmair et al. (2015), IEEE Trans. Med. Imaging, 34(9), Semmler et al. (2016), IEEE Trans. Med. Imaging, 35(7):1615–1624, Semmler et al. (2017), Applied Sciences, 7(6): 600). However, none of the previous approaches allow the laser projection to be adapted to the anatomical conditions of the subject during the recording.”

• How and why do the obtained results reconstruction accuracy of vocal fold oscillations compared to traditional laser-based endoscopic method?  

We thank the reviewer for the comment. We added in the discussion section the following text: “As the distance from endoscope to larynx as well as the vocal fold length vary depending on gender and age of the test subjects, in a fixed laser spot array without the proposed liquid lens design, the laser grid can only be optimized for a certain spot-to-spot distance and an average vocal fold length. Due to the necessary divergence of the laser beams between the exit window (2 mm) at the endoscope and the vocal folds in the larynx (10-20mm), the laser points could unnecessarily hit the laryngeal tissue around the vocal folds or, conversely, the points could to be so close that they overlap with each other. Compounding the problem further, the diameter of the laser spots can, in a static case, only be adjusted to lie within a certain spot size range, which means that the laser spots may be too large for exact detection. By adjusting the spot distance and spot diameter, we are able to tailor the laser grid for each larynx size so that the vocal folds are completely covered while the points can still be clearly distinguished from each other.”

• Is the achieved zoom factor of 1.8 sufficient for practical applications?  

We thank the reviewer for the comment. Yes, our complete design is specifically matched to the dimensions and recording situation during human in vivo laryngoscopy including the distance from the oral cavity to the vocal folds (30-80mm) as well as the vocal fold length (10-20mm). We write now in the discussion section: “With the achieved zoom factor of 1.8, compare Section 3.1, the design is matched to the recording situation during human in vivo laryngoscopy including the distance from the oral cavity to the vocal folds (30-80mm) as well as the vocal fold length (10-20 mm).”

 

• A more detailed analysis of the role of the first lens is needed, as it is given little attention compared to the second lens. For example, data in Figures 5 and 7 suggest that using a fixed lens with an optical power of approximately 20 m⁻¹ could be a viable alternative instead of the first liquid lens.

We thank the reviewer for the comment. We clarify now in the Discussion section: “However, just adjusting the size or edge length of the spot array by lens 2 only would lead to problems as illustrated by Figure 7. This is because at higher refractive powers of Lens 1 and 2, i.e. especially when Lens 2 is used for getting shorter edge lengths of the beamlet array, there is a chance to achieve a beam spot below 100 µm as depicted by the dashed line. This poses the risk of exceeding laser safety regualtions for tissue (which is still far from tissue damage threshold). As this must be safe-guarded against, lens 1 needs to be set to smaller diopters, even below zero, in order to increase the spot size. On the other hand, when Lens 2 is used to generate large array sizes, the divergence of the beamlets increases significantly. In order to have for the high speed camera sufficiently bright beamlets their spot size must be smaller than their size if only Lens 2 would be involved.”

 

• It is also strongly recommended to change the colormap in Figures 5 and 7, replacing the rainbow color scheme with a perceptually uniform colormap, as discussed in [2] and "Color Map Advice for Scientific Visualization" (https://www.kennethmoreland.com/color-advice/). Additionally, ticks should be added to the axes to improve data readability.

[2] K. Moreland, Why We Use Bad Color Maps and What You Can Do About //Electronic Imaging, 28, 1–6 (2016).

We thank the reviewer for the suggestion. We have changed both Figures to a brightness based color scheme and added ticks.

Overall, the paper has potential but requires significant improvements to the discussion section to better define the scientific novelty and practical advantages of the proposed system.

Thank you for the constructive suggestions. We have now set up a Discussion section that addresses all the points you mention above.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for submitting the article “Liquid lens optical design for adjustable laser spot-array for laser-based three-dimensional reconstruction of vocal fold oscillations” to MDPI optics.

The article presents a formal and practical description of the liquid lens optical design technology for endoscopy.  

Please respond to the following comments and corrections:

1.      Please further characterise the material properties of the lens, principal functioning of the technology and the practical advantages and disadvantages.

2.      Is the article a review or an original article?

3.      Rewrite the conclusion. The conclusion should pertinently summarise the article (keypoints) and potentially address further research questions, gaps and future developments.

Author Response

1. Please further characterise the material properties of the lens, principal functioning of the technology and the practical advantages and disadvantages.

We thank the reviewer for the comment. We are already stating the model type and manufacturer as well the properties of said lenses in section 2: “…two liquid lenses from Corning Inc., Type A-25HX-D0, whose focal lengths can be varied by adjusting the input voltage, between -35 m^-1 to +35 m^-1 with 7.75 mm outer diameter and 2.5 mm clear aperture”. We have added additionally a brief description of the working principle: “In electro-wetting liquid lenses, a focus variation can be induced by changing the curva-ture of the liquid-liquid interface between two immiscible transparend liquids with dif-fering refractive indexes through applying a voltage via electrodes to the conductive liquid (DOI: 10.1163/156856111X599562)”.

Unfortunately, an extensive explanation is out of scope for this paper and is also not necessary for comprehension of the works novelty. Nevertheless, quoting wikipedia, the working principle of the lenses can be explained by the electrowtting effect: “The electrowetting effect has been defined as "the change in solid-electrolyte contact angle due to an applied potential difference between the solid and the electrolyte". The phenomenon of electrowetting can be understood in terms of the forces that result from the applied electric field.”

2. Is the article a review or an original article?

This is an original article.

3. Rewrite the conclusion. The conclusion should pertinently summarise the article (keypoints) and potentially address further research questions, gaps and future developments.

 

We thank the reviewer for the suggestion. We have now rewritten the Sections Discussion and Conclusion, where all these points are addressed accordingly.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,
 
I have carefully read the last version of the manuscript. All the comments made earlier, including the inclusion of the Discussion section, correction of the formatting of tables and figures, as well as a more detailed justification of the methodological and practical significance of the proposed system, have been taken into account. 
 
However, on line 265 there is a reference to Section 3.4, which is missing from the article. This reference should be corrected, most likely to Section 4.1.
 
Given the changes made, I recommend that the article be accepted for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for improving the manuscript.