Moiré Reduction Technique for Near-Virtual-Image-Mode Light Field Displays via Aperture Array Modification

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please kindly see the attachment.

Comments for author File: Comments.pdf

Author Response

Overall comment: In this manuscript, the authors have proposed a zigzag-aperture-based moiré reduction technique. By changing the aperture arrays from straight to zigzag, the deformation of virtual subpixel images is suppressed, leading to the reduction of moiré fringes in panel display. By the employment of the proposed technique, the moiré contrast decreased from 0.0263 to 0.00916 in simulations, while from 0.0639 to 0.0169 in experiments. In summary, the proposed moiré reduction technique is a beneficial attempt in the field of light field display. The simulations and experiments can support the authors’ statement. The manuscript is logically coherent, and the figures in the manuscript illustrate the authors’ concept. Considering all the above factors, I think this manuscript is suitable for publication in APPLIED SCIENCES. Before publication, some concerns listed below should be addressed:

Answer: Thank you for reading our manuscript carefully and understanding our technique. We revised our manuscript following your comments.

Comment 1: [Line 75, Page 2] The authors note that the zigzag-based method has been previously proposed in Ref. [20]. What is the innovative point of the proposed technique in this manuscript compared to that in Ref. [20]? Does the method in Ref. [20] directly applied in the proposed technique, or some modifications have been made to adjust the near virtual-image mode light field display? The authors are suggested to clarify it in the section of Introduction.

Response1: Thank you for your comment. To apply the zigzag aperture technique described in Ref. [21], we modified the zigzag aperture shape to match the subpixel geometry of the liquid crystal display. We revised our manuscript to highlight this modification.

Fifth paragraph in Sec. 1:

… Introducing unevenness into slit apertures allows them to act as Gaussian low-pass filters. We apply the idea of modifying the aperture shape of the aperture array to the near virtual-image mode light field displays to suppress high-frequency components arising from the pixel structure. To apply the zigzag apertures to the near-virtual-image mode, we modified the design such that the zigzag aperture shape matches the subpixel geometry of the liquid crystal display. Compared with diffuser-based techniques, this aperture-deformation approach may suppress blur in 3D images.

Comment 2: [Figure 2, Page 4] The information conveyed by Figure 2 is limited, lacking sufficient contents.
(1) The difference between ‘convexed’ virtual pixel image and ‘concaved’ virtual pixel image is difficult to understand from this figure. The authors are suggested to magnify related areas, to make the difference clear to understand.
(2) There are no obvious moiré patterns in the presented figure. Therefore, this figure is not intuitive for me. The authors are suggested to modify this figure to make the manuscript understood.

Response 2: Thank you for your suggestions. We modified Figure 2 by adding enlarged images of virtual pixel images and a moiré pattern image.

Comment 3: [Section 3, Page 4] When the zigzag-aperture is applied, the blocked areas of different colored subpixels have different size. Thus, the zigzag-aperture might cause discrepancies between the actual emitted intensity and the designed emitted intensity for different colors. Could this potentially lead to chromatic aberration? The authors are suggested to consider this issue.

Response3: Thank you for your comment. According to the simulation results, despite the difference in size of the blocked areas in the zigzag aperture shown in the color-coded subpixels, no noticeable chromatic aberration was observed. We added Figure 10 to present the fluctuations in RGB light intensity and revised our manuscript accordingly.

A new paragraph has been added in Sec. 4:

Figure 10 shows the RGB light intensities for the zigzag slit in the simulation results over one moiré period. Although the block size by zigzag patterns differed slightly across RGB subpixels, the intensity fluctuations were uniformly suppressed. While the absolute intensity differences across the red, green, and blue channels persisted, they could be compensated by adjusting the display intensity.

Comment 4: [Figure 7, Page 7] In this figure, the moiré patterns are also not very obvious, which are difficult to recognize. The authors are suggested to use dashed lines or other markers to indicate the location of the moiré patterns.

Response 4: Thank you for your comment. We modified Figure 8 by adding red boxes to indicate the one moiré period and enlarged the corresponding regions.

Comment 5: [Section 5] The authors only provide the parameters of the zigzag-slit. The parameters of the straight slit are not given. The authors are suggested to provide the parameters of the straight slit in Section 5.

Response 5: Thank you for your comment. The parameters of the straight slits are the aperture width and slanted angle. Thus, we added the explanation of the slanted angle of the straight slit.

At the end of fourth paragraph in Sec. 4:

… For comparison, moiré artifacts were simulated using a straight slit without zigzag shapes, which corresponds to the conventional aperture shapes used in the previous prototype. The aperture width of the straight slit was determined from the prototype we previously developed [10] as 0.355 mm. The straight slit was also slanted at the same angle for the lenticular lens.

Comment 6: The results in Figure 8 and Figure 11 indicate that the intensity fluctuations caused by both the straight slit and the zigzag slit are small. Although the zigzag slit demonstrates better performance, the difference is not significant. The results in Figure 12 also confirm that Moiré patterns remain visible even when using the zigzag slit. The authors are suggested to provide a more detailed explanation on how the Moiré fringes are reflected in the intensity fluctuations. Appropriate analysis on potential strategies that could further suppress Moiré fringes are also suggested to discuss in a more detailed manner in the manuscript.

Response 6: Thank you for your valuable comment. We revised Section 6 by adding details on the reflection of the moiré fringes in the intensity fluctuations and included potential strategies to further suppress the fringes.

First paragraph in Sec. 6:

The designed zigzag slits yielded lower moiré contrast compared with the conventional straight slits. The minimum contrast perceivable by human eyes depends on spatial frequency and retinal illuminance level [27]. In the experiment, the spatial frequency of the moiré fringe and retinal illuminance were measured as 3.41 cycles/degree and 1,910 Td, respectively, corresponding to a theoretical minimum contrast perceivable by the human eye of 0.0020. Moiré artifacts with contrast below this value were assumed to be imperceptible. The measured moiré contrast reduced by varying degrees, from a factor of 32 compared with the minimum contrast for straight slits to a factor of 8.5 higher for the zigzag slit. However, it remained above the minimum value. In the simulation results, the moiré contrast of the zigzag slit also exceeded the threshold, suggesting the difficulty to reduce the moiré contrast below an imperceptible level when using the zigzag slits for a flat-panel display with the nonrectangular pixels considered in this study. To further reduce the moiré contrast, displays with more uniform subpixel geometries may be required. Although the zigzag slits suppressed moiré artifacts in near virtual-image mode light field displays, their moiré contrast remained above this minimum contrast value.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript proposes to use a zigzag aperture for reducing the moire contrast of a slanted lenticular light field display. The idea is new and the work is quite complete, including design, analysis and experiment. However, there are some fundamental issues to be clarified so as to make the argument more convincing. Some comments are given as follows for the authors’ reference.

 

1. The reason why the distortion of subpixel as shown in Figure 2 is considered as the source of the moire is not clear, because the moire pattern exhibits dark fringes rather than distorted pattern. The parameters which matter for the moire should be the pitch of pixel, the pitch of lenticular array and the tilt angle of the lenticular array.
2. As the moire pattern appears on the plane of the panel, the validity of the analysis based on diffraction in section 4 could be questionable. Ray tracing from the LCD pixel through the lenticular array to the eye could be more straightforward to demonstrate the dark fringe effect of the moire. Figure 5 does not show clear result regarding to moire pattern.
3. There is no explanation on why the zigzag pattern of the aperture was proposed. The idea itself is novel but the scientific reason behind it is not clear. In addition, how the dimension of the zigzag pattern was determined is not clear neither. The function of the zigzag aperture could be somewhat similar to that of a diffuser.
4. Figure 10 does show an improvement of moire contrast reduction with the zigzag aperture. However, Figure 12 shows that the moire pattern still seriously disturbs the picture quality even with zigzag aperture. The question becomes how much contrast of moire pattern can be considered acceptable? Could the proposed idea be considered sufficiently effective for moire reduction, or which parameters of the zigzag aperture can be tuned to make the moire contrast sufficiently low so as to be not visible.

Comments on the Quality of English Language

N/A

Author Response

Overall comment: This manuscript proposes to use a zigzag aperture for reducing the moire contrast of a slanted lenticular light field display. The idea is new and the work is quite complete, including design, analysis and experiment. However, there are some fundamental issues to be clarified so as to make the argument more convincing. Some comments are given as follows for the authors’ reference.

Answer: Thank you for reading our manuscript carefully and providing us with valuable comments. We have revised our manuscript following the reviewer’s comments.

Comment 1: The reason why the distortion of subpixel as shown in Figure 2 is considered as the source of the moire is not clear, because the moire pattern exhibits dark fringes rather than distorted pattern. The parameters which matter for the moire should be the pitch of pixel, the pitch of lenticular array and the tilt angle of the lenticular array.

Response 1: Thank you for your comment. Typically, the moiré pattern in light field displays primarily arises from the mismatch between the pitches of the pixel and lenticular array. However, in light field displays with near-virtual-image mode, the moiré artifacts are caused by a different essential reason. Specifically, they originate from the periodic distortion of virtual subpixel images. We revised the manuscript to clarify the different causes of moiré artifacts.

Third paragraph in Sec. 1:

However, moiré artifacts on the display surface disrupt the 3D perception of observers. In light field displays, these artifacts are typically caused by differences in spatial frequency between the pixel structure and the lens or aperture array [12,13] (e.g., mismatch between the pitches of the pixel and lens). In contrast, in the near-virtual-image mode, the moiré artifacts essentially arise from the periodic distortion of the virtual subpixel images induced by the nonrectangular pixel structure of the flat-panel display. This study specifically addresses moiré artifacts caused by pixel structures in near virtual-image mode light field displays.

Comment 2: As the moire pattern appears on the plane of the panel, the validity of the analysis based on diffraction in section 4 could be questionable. Ray tracing from the LCD pixel through the lenticular array to the eye could be more straightforward to demonstrate the dark fringe effect of the moire. Figure 5 does not show clear result regarding to moire pattern.

Response 2: Thank you for your comment. In this study, we performed diffraction-based analysis because it allows to evaluate the blurring effect caused by the eye pupil and intensity distribution determined by light going through the aperture shape. Hence, diffraction-based analysis is more appropriate than ray-tracing-based analysis. Furthermore, the deformations of the virtual subpixel images obtained in the simulation closely match the experimental results, supporting the validity of the diffraction-based analysis. As you point out, Figure 6 does not show clear results regarding the moiré pattern. Therefore, we revised Figure 6 to depict three moiré periods.

We revised our manuscript as follows.

Second paragraph in Sec. 4:

Figure 6(a) shows the simulated moiré image obtained by calculating the diffraction for the pixel structure shown in Figure 3. The simulation result provides three moiré periods. …

Comment 3: There is no explanation on why the zigzag pattern of the aperture was proposed. The idea itself is novel but the scientific reason behind it is not clear. In addition, how the dimension of the zigzag pattern was determined is not clear neither. The function of the zigzag aperture could be somewhat similar to that of a diffuser.

Response 3: Thank you for your comment. The original technique proposed by Date et al. Ref. [21] used a zigzag aperture, whose parameters were determined using a Gaussian function, because their study addressed the moiré problem in light field displays with flat-panel displays having rectangular pixels. In contrast, our approach requires determining the parameters of the zigzag apertures based on the actual geometry of the pixels in the liquid crystal display because the light field display with the near-virtual-image mode employs nonrectangular pixels. We revised the manuscript to clarify the scientific reason underlying our proposal. In addition, we added an explanation on the dimension of the zigzag pattern.

Second paragraph in Sec. 3:

Unlike conventional moiré reduction techniques that rely on blurring via diffusers [14,15] or lens defocusing [16], the proposed technique blurs the subpixel structures using the apertures. Date et al. [21] also proposed a moiré reduction technique by deforming the aperture shape in light field displays. We applied this approach to near virtual-image mode light field displays using a zigzag aperture. The difference between the technique by Date et al. [21] and ours is that the former determines the parameters of the zigzag aperture using a Gaussian function, whereas our technique determines the parameters based on the subpixel geometry. The near virtual-image mode light field displays employ both the lens and aperture arrays, and the proposed technique gives the role of suppressing moiré to the aperture array, which was originally used to limit ray divergence.

Fourth paragraph in Sec. 4:

Figure 7 shows the designed zigzag slit. The zigzag width was determined by measuring the differences in the horizontal shapes of the virtual subpixel images considering the liquid crystal display shown in Figure 3 and setting it equal to their average value. As a result, Tthe zigzag width was 0.113 mm, and the average aperture width was 0.413 mm. …

Comment 4: Figure 10 does show an improvement of moire contrast reduction with the zigzag aperture. However, Figure 12 shows that the moire pattern still seriously disturbs the picture quality even with zigzag aperture. The question becomes how much contrast of moire pattern can be considered acceptable? Could the proposed idea be considered sufficiently effective for moire reduction, or which parameters of the zigzag aperture can be tuned to make the moire contrast sufficiently low so as to be not visible.

Response 4: Thank you for your comment. Figure 12 shows results from a selected region of the display, where the moiré pattern was suppressed, whereas Figure 14 shows the entire display screen, in which moiré artifacts remained visible in certain areas. As described in Section 6, the acceptable contrast level of the moiré pattern is 0.0020, despite the experimental results still exceeding this threshold. We revised the manuscript to clarify the difference between Figures 12 and 14. In addition, our revisions include a discussion of a possible solution to minimize the moiré contrast such that it was not visible.

Fifth paragraph in Sec. 5:

Figure 14 shows 3D images of a human upper body displayed using straight and zigzag slits. The 3D model was generated by capturing an actual person with a depth camera and an RGB camera. Figure 14 includes enlarged images at the cheek regions of the 3D images. While Figure 12 shows a region of the display screen with clear moiré pattern reduction, Figure 14 shows the entire display screen. …

First paragraph in Sec. 6:

The designed zigzag slits yielded lower moiré contrast compared with the conventional straight slits. The minimum contrast perceivable by human eyes depends on spatial frequency and retinal illuminance level [27]. In the experiment, the spatial frequency of the moiré fringe and retinal illuminance were measured as 3.41 cycles/degree and 1,910 Td, respectively, corresponding to a theoretical minimum contrast perceivable by the human eye of 0.0020. Moiré artifacts with contrast below this value were assumed to be imperceptible. The measured moiré contrast reduced by varying degrees, from a factor of 32 compared with the minimum contrast for straight slits to a factor of 8.5 higher for the zigzag slit. However, it remained above the minimum value. In the simulation results, the moiré contrast of the zigzag slit also exceeded the threshold, suggesting the difficulty to reduce the moiré contrast below an imperceptible level when using the zigzag slits for a flat-panel display with the nonrectangular pixels considered in this study. To further reduce the moiré contrast, displays with more uniform subpixel geometries may be required. Although the zigzag slits suppressed moiré artifacts in near virtual-image mode light field displays, their moiré contrast remained above this minimum contrast value.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The submitted manuscript proposes the use of a zigzag aperture array as a moiré reduction technique for near virtual-image mode light field displays. The work is supported by both simulation and experimental results and shows measurable improvements in moiré suppression. However, before the manuscript can be considered for publication, several critical issues must be addressed.

1. Moiré effects are highly dependent on both the pixel geometry and the precise alignment between the display panel and optical components. The authors validate their method using only a single LCD panel (Dell 8K) and one lens–aperture configuration. While the results are promising, such a limited evaluation weakens the generalizability of the conclusions. To strengthen the claims, the authors are encouraged to test their technique with multiple display panels.
2. The manuscript reports moiré contrast values to demonstrate performance improvements. However, no explicit definition or formula for “moiré contrast” is provided. Without a rigorous and transparent definition, it is difficult for readers to interpret the reported numbers or reproduce the analysis. The authors should clearly describe how moiré contrast is calculated, including the mathematical expression and the specific regions of the images used for measurement.
3. In Figures 8 and 11, intensity profiles are presented to compare the performance of zigzag versus straight slits. However, no error bars or statistical analysis are shown. It is unclear whether the reported data represents single measurements or averages over multiple trials/regions. Including error bars or confidence intervals would provide insight into the repeatability and uncertainty of the measurements.
4. The introduction acknowledges that diffusers, defocusing, and slanted arrays have been proposed as alternative moiré reduction methods. However, the experimental results only compare zigzag and straight apertures. As a result, it remains unclear whether the proposed method provides superior performance relative to other established approaches.
5. Figure 7 and Figure 12: The differences between zigzag and straight slit results are not immediately clear to the reader. The authors should consider adding zoomed-in regions or annotated markers to highlight the observed differences.
6. Figures 2, 3, 5, 9, etc.: Scale bars are missing, which makes it difficult to assess the dimensions and relevance of the presented structures and images. Scale bars should be added wherever appropriate.
7. The diffraction-based equations (Eqs. 1–3) form the theoretical foundation of the proposed analysis. However, they are presented without referencing prior literature or textbooks.

Author Response

Overall comment: The submitted manuscript proposes the use of a zigzag aperture array as a moiré reduction technique for near virtual-image mode light field displays. The work is supported by both simulation and experimental results and shows measurable improvements in moiré suppression. However, before the manuscript can be considered for publication, several critical issues must be addressed.

Answer: Thank you very much for reading our manuscript carefully and providing us the valuable comments which can improve our manuscript. We have revised the manuscript following the reviewer’s comments.

Comment 1: Moiré effects are highly dependent on both the pixel geometry and the precise alignment between the display panel and optical components. The authors validate their method using only a single LCD panel (Dell 8K) and one lens–aperture configuration. While the results are promising, such a limited evaluation weakens the generalizability of the conclusions. To strengthen the claims, the authors are encouraged to test their technique with multiple display panels.

Response 1: Thank you for your valuable comment. We appreciate your positive feedback on our study. Unfortunately, due to time constraints, we could not test multiple display panels and optical configurations in this study. Nevertheless, the simulation and experimental results suitably agreed for the evaluated prototype configuration. Therefore, we believe that these results likely validate our approach.

Comment 2: The manuscript reports moiré contrast values to demonstrate performance improvements. However, no explicit definition or formula for “moiré contrast” is provided. Without a rigorous and transparent definition, it is difficult for readers to interpret the reported numbers or reproduce the analysis. The authors should clearly describe how moiré contrast is calculated, including the mathematical expression and the specific regions of the images used for measurement.

Response 2: Thank you for your valuable comment. We agree that the definition of the moiré contrast should be explicitly described. Thus, we revised the manuscript to define this contrast, its calculation, and specific regions of the images used for measurement.

Sixth paragraph in Sec. 4:

Figure 9 shows the light intensities of virtual subpixel images obtained from the specific regions indicated in Figure 8. the simulation results. These values were obtained by averaging the intensities of the virtual pixel images aligned vertically along the cylindrical lens, excluding the black regions of the aperture. The intensity variation for the zigzag slit was smaller than that for the straight slit. The moiré contrast was calculated using the light intensities shown in Figure 9 as follows:

Cmoiré = (Imax - Imin) / (Imax + Imin)

(4)

where I_max and I_min denote the maximum and minimum light intensities within one moiré period, respectively. …

We also modified Figure 8 to add the regions of the images subjected to measurement.

Comment 3: In Figures 8 and 11, intensity profiles are presented to compare the performance of zigzag versus straight slits. However, no error bars or statistical analysis are shown. It is unclear whether the reported data represents single measurements or averages over multiple trials/regions. Including error bars or confidence intervals would provide insight into the repeatability and uncertainty of the measurements.

Response 3:Thank you for your valuable suggestion. We revised the manuscript to include error bars in Figure 13.

Fourth paragraph in Sec. 5:

Figure 13 shows the measured light intensities of virtual subpixel images for one moiré period, as indicated in Figure 12. The intensities are shown as averages over five trials, and the error bars indicate their standard deviations. …

Comment 4: The introduction acknowledges that diffusers, defocusing, and slanted arrays have been proposed as alternative moiré reduction methods. However, the experimental results only compare zigzag and straight apertures. As a result, it remains unclear whether the proposed method provides superior performance relative to other established approaches.

Response 4: Thank you for your comment. Unfortunately, we did not compare the performance of diffusers, defocusing, and slanted arrays with the proposed approach. Defocusing achieves moiré reduction by increasing the divergence of rays. However, this technique is unsuitable for light field displays with the near-virtual-image mode because it also increases blurring in 3D images. Meanwhile, diffusers suppress moiré artifacts by uniformly blurring pixel structures. However, the blurring degree is difficult to control. In contrast, the proposed zigzag-aperture-based technique allows controlling the blurring effect through aperture design. Therefore, we adopted zigzag-aperture-based moiré reduction for the light field displays with near-virtual-image mode. However, the superiority of the proposed method compared with the other technique remains unclear without experimental verification.

Comment 5: Figure 7 and Figure 12: The differences between zigzag and straight slit results are not immediately clear to the reader. The authors should consider adding zoomed-in regions or annotated markers to highlight the observed differences.

Response 5: We revised Figures 8 and 14 by adding zoomed-in regions of the moiré fringe.

Comment 6: Figures 2, 3, 5, 9, etc.: Scale bars are missing, which makes it difficult to assess the dimensions and relevance of the presented structures and images. Scale bars should be added wherever appropriate.

Response 6: Thank you for your valuable comment. We added scale bars to our Figures 2, 3, 6, and 11.

Comment 7: The diffraction-based equations (Eqs. 1–3) form the theoretical foundation of the proposed analysis. However, they are presented without referencing prior literature or textbooks.

Response 7: Thank you for your comment. We added references to prior literature and textbooks to support the equations.

At the beginning of first paragraph in Sec. 4:

The zigzag aperture was designed using the diffraction-based moiré analysis [24,25]. …

Following reference has been added to the reference list and the reference numbers have been revised accordingly.

24. Goodman, J.W. The Fresnel Approximation. In Introduction to Fourier Optics, 2nd ed.; Director, S. W., Ed.; McGraw-Hill: New York, NY, USA, 1996; pp. 66-73.
25. Ozaktas, H.M.; Yüksel, S.; Kutay, M.A. Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.  Opt. Soc. Am. A 2002, 19, 1563-1571.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Please see attached review report.

Comments for author File: Comments.pdf

Author Response

Overall comment: In this manuscript, the authors proposed a method to reduce moiré in near virtual image-mode light-field displays by changing aperture slits from straight to zigzag, which blurs the peripheral differences among non-rectangular RGB subpixels. A diffraction-based design shows moiré contrast drops from 0.0263 to 0.00916 in simulation, and in experiment on an 8K LCD prototype it drops from 0.0639 to 0.0169 while increasing the average intensity. The measured moiré frequency (3.41 cycle/degree) and retinal illuminance (1910 Td) imply a 0.002 detection threshold. Although the zigzag slits suppressed moiré artifacts, their contrast remains above this level. This manuscript can be accepted for publication after following questions and comments have been addressed.

Answer: Thank you for reading our manuscript carefully and providing us the valuable comments. We revised our manuscript following reviewer’s comments.

Comment 1: Introduction
Presently, LCD, OLED, and micro-LED are three major flat panel display technologies. Their basic operation principles and performance have been analyzed by Y. Huang, Light Sci. Appl. 9, 105 (2020). This reference will help readers to better understand the background information.

Response 1: Thank you for telling us the information. We added the paper to our references in the revised manuscript.

First paragraph in Sec. 1:

Light field displays [1–5] generate three-dimensional (3D) images by reconstructing light rays from 3D objects, allowing observers to view them without glasses or other devices. Flat-panel-type light field displays, implemented by combining a liquid crystal display or organic light-emitting diode display [6] with optical elements such as lens or aperture arrays [67–89], have enabled practical 3D display applications due to their thin structure. …

Following reference has been added to the reference list and the reference numbers have been revised accordingly.

6. Huang, Y.; Hsiang, E.; Deng, M.; Wu, S. Mini-LED, Micro-LED and OLED displays: present status and future perspectives. Light Sci. Appl. 2020, 9, 105.

Comment 2: Figure 2: Distinction between convex and concave virtual pixel images
The distinction between “convex” and “concave” virtual pixel images is not visually evident at the provided resolution. If the resolution of the image could be higher, then readers can spot the difference between them. If applicable, please provide a calculation or estimate of the deformation period visible in the figure.

Response 2: Thank you for your comments. The image resolution was limited because the moiré pattern should be captured at 1.2 m by a single-lens reflex camera. The deformation period was visually estimated according to Figure 2. We revised the manuscript and modified Figure 2 by adding enlarged images of convex and concave virtual pixel images, ensuring that the distinction can be clearly visualized.

Second paragraph in Sec. 2:

… Figure 2 shows an enlarged image of moiré fringes when a white image is displayed on the light field display. The moiré fringes were captured using a single-lens reflex (SLR) camera equipped with a 250-mm lens positioned 1.2 m away from the display surface. The virtual images of subpixels were observed through a lenticular lens, and the shapes of virtual subpixel images were periodically changed in the horizontal direction. At the center area of the figure, virtual subpixel images with a concave shape are visible and convex-shaped images are observed in the neighboring area. This deformation of virtual pixel images continues periodically in the entire display, primarily generating moiré fringes in the near virtual-image mode light field display. The deformation period was estimated by identifying repeating shapes of virtual pixel images, which extended over approximately 10 cylindrical lenses.

Comment 3: Figures 7 and 10: Zoom in to show the difference
Simulation/experimental results for the straight slit and zigzag slit aim to provide a difference between these slits. However, the reader must zoom in yet barely sees the difference. Please provide enlarged pictures (with stated magnification factors) and highlight the difference clearly between these two slits.

Response 3: Thank you for carefully examining our figures. We revised Figures 8 and 12 and added enlarged views with a magnification factor of 6. We revised the manuscript accordingly.

Fifth paragraph in Sec. 4:

Figure 8 shows the simulation results obtained using straight and zigzag slits, along with enlarged pictures of one moiré period at a magnification factor of six. The simulation results were calculated considering distance l = 1.2 m and a pupil diameter of 7.8 mm. Compared with the straight slit, the deformation of virtual subpixel images was mitigated by the zigzag slit. As shown in Figure 8 (a), the straight slit caused periodic light intensity changes in the horizontal direction and generated moiré artifacts. In contrast, the zigzag slit weakened the moiré in Figure 8(b). The period of moiré artifacts was approximately 10 lenses in both results, corresponding to the results discussed in Section 2.

Third paragraph in Sec. 5:

Figure 11 presents the experimental results obtained by displaying a white image on the light field display using straight and zigzag slits. The moiré images were captured at 1.2 m from the display surface using an SLR camera with a pupil size of 7.8 mm. Enlarged pictures of one moiré period under magnification with a factor of six are also shown. The deformation of virtual pixel images was also suppressed. Compared with straight slits, zigzag slits reduced moiré artifacts. The measured moiré periods were approximately 10 lenses in both cases.

Comment 4: Figure 12(b): The moiré effect is still noticeable when using zigzag slits
Please give a more in-depth explanation on why there is still a moiré effect on not only the cheek and neck but also on the hoodie, and especially, the moiré effect is more severe on the background than that on the straight slit. Furthermore, what is the possible solution to mitigate the moiré effect when using zigzag slits?

Response 4: Thank you for your comment. Accordingly, we revised the explanation for the still moiré effect on the cheek, neck, hoodie, and background. In addition, a possible solution to mitigate the moiré effect was outlined.

Fifth paragraph in Sec. 5:

… However, as shown in Figure 14(b), the moiré pattern was particularly noticeable in some areas, such as the right cheek, and neck, and hoodie. This effect These residual moiré artifacts likely occurred because the display panel, slit array, and lenticular lens were not adhered together. In these regions, the gap between the lens array and display increased slightly, altering the magnification of the virtual subsspixel images and undermining the suppression of moiré artifacts. By adhering the display panel, slit array, and lenticular lens together, the moiré effect could be mitigated. Furthermore, at the edges of the screen (background regions), the moiré effect with zigzag slits was more severe than that with straight slits because of slight misalignments between the lens and aperture arrays. , allowing small gaps to form in those regions.

Comment 5: Figure 13: Wavelength-dependent intensity
The red light exhibits the lowest intensity, while the blue light is the highest. Please explain the origin of this wavelength dependence (e.g., source spectra, panel transmittance, slit diffraction efficiency, or sensor spectral sensitivity).

Response 5: Thank you for your comment. The differences in absolute intensities across RGB channels are primarily attributed to the white balance adjustment of the camera used for measurement. We revised our manuscript to clarify the wavelength dependence observed in Figure 15.

At the end of second paragraph in Sec. 6:

… These results indicate that the zigzag slit reduced each moiré contrast in RGB, revealing that the proposed technique also suppressed the color moiré. The absolute intensity differences across RGB channels were mainly attributed to the white balance setting of the camera used for measurement.

Comment 6: Simulation part
- The reader needs to draw a schematic diagram to understand the position of each of the different planes. Provide a schematic showing all computational planes and parameters (lens plane, observation plane, distances, eye/pupil position), with symbols mapped to equations.

Response 6: Thank you for your comment. We added a schematic diagram to provide all computational planes and parameters with symbols formulated as equations.

First paragraph in Sec. 4:

The zigzag aperture was designed using the diffraction-based moiré analysis [24,25]. Figure 5 shows computational planes and parameters for diffraction-based moiré analysis. …

Comment 6: - Lines 193 to 195: “The captured image appears more blurred than the simulated image because calculations were conducted for only a single wavelength in each RGB subpixel during the simulation.” Putting the captured and simulated images side-by-side is more straightforward so that readers can understand how blurred the captured image is compared to the simulation image.

Response 6: Thank you for your suggestion. We revised Figure 6 to put the captured and simulated images side-by-side.

Comment 6: - Lines 212 and 213: “…the requirement in the fabrication process that the minimum line width was limited to 0.03 mm.” Can you quantify how the minimum line width (≥0.03 mm) and rounded tips impact performance?

Response 6: Thank you for your comment. In our design, the vertical zigzag pitch was set to 0.0908 mm, which was higher than twice the minimum line width of 0.03 mm. This ensured that the minimum line width did not affect fabrication. Regarding the rounded tips, we simulated the moiré contrast without rounding. The simulated moiré contrast without rounding (0.00912) was almost equal to that with rounding (0.00916).

Comment 6: - What design rules govern the relationship between the LCD subpixel geometry and optimal zigzag amplitude/pitch?

Response 6: The amplitude of the zigzag width was determined from differences in the horizontal shapes of virtual subpixel images derived from the LCD subpixel geometry. In this study, the average of the measured differences was set to the zigzag width. We revised our manuscript to clarify the relationship between the LCD subpixel geometry and optimal zigzag width.

Fourth paragraph in Sec. 4:

Figure 7 shows the designed zigzag slit. The zigzag width was determined by measuring the differences in the horizontal shapes of the virtual subpixel images considering the liquid crystal display shown in Figure 3 and setting it equal to their average value. As a result, Tthe zigzag width was 0.113 mm, and the average aperture width was 0.413 mm. …

Comment 7:  Experiment part
- What is the tolerance and manufacturability of the film-based photomask technique? Please discuss the tolerance and manufacturability of the film-based photomask process, including the inspection metrics that confirm the fabricated features of the design.

Response 7: Thank you for your comment. Unfortunately, because the fabrication of the film-based photomask was outsourced to an external company, we cannot provide details about manufacturability, including the inspection metrics. According to the fabrication specifications, the minimum line width was 0.03 mm with a tolerance of ±3 mm. To assess the effects of this tolerance, we conducted additional simulations of the moiré contrast by varying the zigzag width within ±3 mm. The results showed that when the zigzag width increased by 3 mm, the moiré contrast was 0.00569, whereas when it decreased by 3 mm, it was 0.0129. We revised the manuscript by adding a discussion of the tolerance of the film-based photomask technique.

A new paragraph has been added in Sec. 6:

The tolerance of the film-based photomask technique is discussed. According to the fabrication specifications, the tolerance of the line pattern was ±3 mm. For the designed zigzag aperture shape, the zigzag width might vary by ±3 mm compared with the virtual subpixel width of 0.34 mm. The simulation results indicated moiré contrasts of 0.00569 and 0.0129, when the zigzag width increased and decreased by 3 mm, respectively. Although the tolerance of film-based fabrication process altered moiré suppression using zigzag apertures, its impact on moiré suppression was limited.

Comment 7: - Please add a scale bar to the microscopic image of the zigzag slit in Figure 9(b). In such a case, the real size of the fabricated slit can be estimated and not just based on the numbers in the description.

Response 7: Thank you for your comment. We added a scale bar to the microscopic image in Figure 11(b).

Comment 7: - For Figures 8 and 11, what are the viewing distance, eye box, and assumed pupil size in both simulation and measurement.

Response 7: Because the eye box was not defined in our simulation and experiment, we added the viewing distance and assumed pupil size in our manuscript.

Fifth paragraph in Sec. 4:

Figure 8 shows the simulation results obtained using straight and zigzag slits, along with enlarged pictures of one moiré period at a magnification factor of six. The simulation results were calculated considering distance l = 1.2 m and a pupil diameter of 7.8 mm. …

Third paragraph in Sec. 5:

Figure 11 presents the experimental results obtained by displaying a white image on the light field display using straight and zigzag slits. The moiré images were captured at 1.2 m from the display surface using an SLR camera with a pupil size of 7.8 mm. …

Comment 8: Conclusion part
Lines 304 and 307: “Simulation results showed that the moiré contrast…”
The authors did not mention how you defined the moiré contrast in the article, and readers will wonder how this metric was defined. Please outline the exact moiré contrast formula and averaging across lenses (~10 lens period) and include uncertainties/error bars and sample counts to analyze the moiré contrast between slits quantitatively.

Response 8: Thank you for your comment. We added the definition and formula of the moiré contrast. In addition, we added error bars in Figure 13, reflecting the variability across the five samples.

Sixth paragraph in Sec. 4:

Figure 9 shows the light intensities of virtual subpixel images obtained from the specific regions indicated in Figure 8. the simulation results. These values were obtained by averaging the intensities of the virtual pixel images aligned vertically along the cylindrical lens, excluding the black regions of the aperture. The intensity variation for the zigzag slit was smaller than that for the straight slit. The moiré contrast was calculated using the light intensities shown in Figure 9 as follows:

Cmoiré = (Imax - Imin) /

(4)

where I_max and I_min denote the maximum and minimum light intensities within one moiré period, respectively. …

Comment 9: Ref. 10 is incomplete. Please check.

Response 9: Thank you for your careful check. We revised the reference to add the article number.

11. Fukano, K.; Kudo, T.; Yura, T.; Takaki, Y. Resolution Improvement in Near-Virtual-Image-Mode Light-Field Display Using Resolution-Priority Technique.  Sci. 2024, 14, 9962.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have provided explanation and supplemented corresponding statement in the revised manuscript for the issues raised in the previous review. Although the moire resulted from the distortion of the virtual image pixel cannot be fully eliminated with the proposed zigzag aperture, the improvement is nontheless visible and the proposed approach can be a good reference for further work. This manuscript could be considered for the publication in Applied Sciences. Based on the authors' response, the mechanism of the moire to be resolved in this manuscript differs from that of the traditional one caused by the different pitch between display pixel and lenticular array. It is suggested to provide more statement to explain why the distortion of the image pixel can cause moire. A clear understanding on the mechanism can be helpful for further improving the corresponding moire effect.  

Author Response

Comment: The authors have provided explanation and supplemented corresponding statement in the revised manuscript for the issues raised in the previous review. Although the moire resulted from the distortion of the virtual image pixel cannot be fully eliminated with the proposed zigzag aperture, the improvement is nontheless visible and the proposed approach can be a good reference for further work. This manuscript could be considered for the publication in Applied Sciences. Based on the authors' response, the mechanism of the moire to be resolved in this manuscript differs from that of the traditional one caused by the different pitch between display pixel and lenticular array. It is suggested to provide more statement to explain why the distortion of the image pixel can cause moire. A clear understanding on the mechanism can be helpful for further improving the corresponding moire effect.  

Response: Thank you for your comments, and we appreciate your acceptance of our revision. Following your comment, we revised our manuscript to provide more statements to explain why the distortion of the image pixel can cause moiré.

Second paragraph in Sec. 2:

… This deformation of virtual pixel images continues periodically in the entire display, resulting in spatial fluctuations in the perceived light intensity. Consequently, these distortions of the virtual subpixel images are considered to primarily generategenerating moiré fringes in the near virtual-image mode light field display.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed the comments.

Author Response

Comment: The authors have addressed the comments.

Response: We greatly appreciate your acceptance and cooperation.