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Abstract
A horopter screen has been popularly studied since its curvature reduces the parallax between two eyes and the immersive displays with a horopter-curved screen are regarded to provide vivid impression of depth and stereopsis. But, the projection on a horopter screen causes some practical problems that the image is hard to be focused on the entire screen and its magnification is partially different. An aberration-free warp projection has a great potential to solve these problems, which changes the optical path from an object plane to an image plane. Since the variation of the curvature is severe in the horopter screen, a freeform optical element is required for an aberration-free warp projection. In comparison with the traditional fabrication method, the hologram printer has the advantage of rapidly manufacturing free-form optical devices by recording the desired wavefront phase on the holographic medium. In this paper, for a given arbitrary horopter screen, the aberration-free warp projection is implemented with the freeform holographic optical elements (HOEs) fabricated by our tailor-made hologram printer. We experimentally demonstrate that the distortion and defocus aberration are effectively corrected.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Horopter-curved display has been studied actively since it provides a vivid impression of depth and stereopsis in field of immersive displays. The horopter is a curved surface which contains all points allocated at the same empirical distance of the fixation point and a horopter screen reduces the parallax between the eyes [1–4]. However, the shape of a horopter screen causes some practical problems when an image is projected on it through a conventional projection optical system. One is the distortion of projected image on the screen such as the keystone, the pincushion, or the barrel distortion. The other is the defocus aberration on the projected image because the screen is not flat. Therefore, the correction of the distortion and defocus aberration are significant issues in the fabrication of projection optics.
In other studies, the distortion of a projected image is corrected computationally [5–8]. The computational method measures a horopter surface and then deforms the image before projection. This deformation method tricks the observer into believing that the image is undistorted. However, pixel density of the projected image becomes ununiformed resulting from the deformation process. Moreover, it is hard to compensate for the aberration such as the defocus. To solve these problems, it is necessary to design the projection optical system for compensating aberration and distortion. The method using such a projection optical system optically warps the three-dimensional space considering the optical axis, unlike the method of simply deforming the two-dimensional image.
Horopter screen is not flat and tilted off-axis from the optical axis, so the image is hard to be focused on the entire screen and its magnification is partially different. Therefore, a freeform optical element is required for a projection lens [9–12]. Various methods for designing freeform optical elements have been proposed. Among these methods, the geometrical method calculates the optical path length to obtain the optical phase from the freeform optical element, and the phase profile is usually decomposed into the Zernike polynomials to analyze its properties. The freeform optical elements are generally fabricated using diamond-turning machines [13,14]. However, although this machine has high precision, it is difficult to manufacture freeform optical elements with complex and steep surface gradients because they are machined using rotating a diamond tip. In addition, there is a practical problem that it takes a long time to manufacture the freeform optical system.
The hologram printer has the advantage of rapidly manufacturing free-form optical devices by recording the desired wavefront phase on the holographic medium. Various types of hologram printers have been studied according to the method of recording the wavefront [15–17]. In hologram printers, wavefronts are recorded in units of hogels, so in order to record high spatial frequency of the wavefront, the interval between hogels, that is, the sampling interval, must be reduced. Recently, in order to quickly record a large-area hologram with high spatial frequency, methods of recording each hogel by changing the direction of two parallel lights have been proposed. However, in this method, the wavefront is represented as a polygonal surface because two parallel lights interfere, and the only prism phase is recorded in one Hogel. Hogel’s wavefront has no curvature, and the piecewise phase information does not represent a wavefront with smooth curvature. So, there is a critical problem that the wavefront is divided during propagation.
In this paper, we propose an aberration-free warp projection method on a horopter screen using a freeform HOE. The freeform HOE for the aberration-free warp projection is conducted with three steps. First step is calculation of grating vectors through geometric ray analysis. Next step is extraction of the phase profile from grating vectors with inverse gradient algorithm. In the final step, the phase profile is recorded by the tailor-made hologram printer. Our hologram printer has the large degree of freedom to fabricate the freeform HOE for an arbitrary shape of a screen. Figure 1(a) shows problems in conventional projection on a horopter screen. The projected image is distorted and defocused on the screen because of the curved horopter screen. This problem is solved by applying the HOE for compensation as shown in Fig. 1(b). The projection beam is reflected on the freeform HOE, it changes the direction to compensate distortion and focus on a proper position on the horopter screen. This paper is organized into four additional sections. Section 2 discusses the configuration of projection environments to estimate image distortion without the HOE. Section 3 describes the proposed k-vector analysis based on diffraction theory [18] and discusses the results obtained using phase profiles. Section 4 analyzes the obtained phase profile with the Zernike decomposition in the hogel unit. In last section 5, we propose a hologram printer to fabricate HOEs. The experimental result is provided with correcting the image distortion using the fabricated HOE in full color. The proposed method is validated by correcting the distortion without degrading the resolution of the image projected on the horopter screen.
Fig. 1. Scheme of horopter displays with (a) a conventional off-axis projection and (b) an aberration-free warp projection with a freeform HOE.
2. Analysis of image distortion on a horopter screen
A horopter screen is a diffusive screen that forms an image on the trajectory without parallax between two eyes. The horopter screen in this study comes from the Hering-Hillebrand deviation adopted by Ogle [1,4] to describe the empirical horopter, and the equation is given by
where ${\alpha _l}\;$ and ${\alpha _r}$ represent the angles subtended at the rotation centers of the left and right eyes by a fixation point, respectively. ${R_0}$ is the amount described that the horopter curve is inclined at symmetrically the fixed point. The horopter curve is symmetrical about the fixed point when ${R_0}$ is 1. The H determines the horizontal curvature of the horopter screen. Several methods have been proposed to extend Eq. (1) vertically in two dimensions. In this paper, a horopter screen is chosen, whose H value changes with height as follow: where PD means the pupil distance between right and left eyes. H0 means the horizontal curvature at the horizontal plane containing two eyes. This horizontal curvature changes symmetrically in the vertical direction. So the first nonzero term is y squared. H1 is a coefficient representing the horizontal curve change along the vertical axis. In this paper, H0 and H1 are -7.06 × 10−6 and 1.26 × 10−3, respectively. The shape of the horopter screen is expressed as a quadratic polynomial $S({x,y} )$ as follow:
Table 1. Coefficients of quadratic polynomial $HS({x,y} )$ for the horopter screen
A conventional off-axis projection is shown in Fig. 2. The projection configuration was designed as an overhead projection with a projector tilted at an angle of ${\theta _p}$ (30°), as the observer might block the projected beam. The origin point O is the reference point of the camera and the point P is the reference point of the projector. For experiments, the projection configuration is scaled down to be five-times smaller than its actual size. So, the curvature of the horopter screen is designed with the pupil distance, PD of 14 mm where the screen width ${w_s}$ is 630 mm and its height ${h_s}$ is 373 mm. The distance from the camera, ${d_s}$ is set about $400\; mm$. The projector is located at a distance and height of ${d_p} = 463\; mm$ and ${h_p} = 500\; mm,$ respectively, from the origin. In this configuration, the field of view becomes 90 degrees.
Fig. 2. Conventional off-axis projection on horopter screen. (a) The horopter screen and (b) the geometric configuration (O - origin and observation point, P - projection point, HS - horopter screen).
Figure 3 shows the simulation results for two cases. One is an ideal case that an undistorted image is observed at the position of the camera. For simulation, the optical rays are traced reversely from the camera to the screen. The other is a real case that an image is distorted in the conventional off-axis projection. For simulation, the optical rays are traced forwardly from the projector to the screen. In this simulation, the vector calculation of chief rays is conducted using Matlab instead of using either Code V or Zemax. Figure 3(a) shows the foot prints of optical rays on the horopter screen for two cases. The blue diamond points are the footprint for the former case. Even though the observed view from the camera is not distorted, these blue points look out of alignment and the lines connecting the points are not straight. It is natural since the screen is not planar. On the other hand, the red circle points are the footprint for the latter case. The image projected from the projector is distorted. These red points are shifted from the blue points. Figure 3(b) shows the distortion vector from blue points to the corresponding red points. The size of the vector represents how the image distortion is severe. The upper part of the image is distorted mainly by about 10.9% in the horizontal direction, and the lower part of the image is mainly distorted by about 12.3% in the vertical direction. This distortion is possible to be corrected by a freeform HOE which is inserted to the projection configuration. From the distortion vector, the phase gradient of the HOE is obtained.
Fig. 3. (a) Footprints of projection images on the horopter screen. Red circles are the ideal projection in the viewpoint of the observer. Blue diamonds are projected from VP without distortion correction. (b) Distortion correction vectors on the horopter screen.
3. Phase profile of freeform holographic optical elements to correct image distortion
The phase profile of the freeform HOE is determined from the difference between the phases of the incident and modulated beams. Figure 4 shows the geometric parameters used for calculating the phase profiles of the freeform HOE. Point $P^{\prime}$ indicates the reference point of the projector mentioned in Fig. 4. The position of point $P^{\prime}$ is vertically 453 mm and horizontally 484 mm away from origin. The beam that starts from $P^{\prime}$ and propagates to point ${P_H}$ on the hologram material has a wave vector, $\overrightarrow {{k_p}} $. In this paper, the maximum angle of the $\overrightarrow {{k_p}} $ is 30-degrees tilted from normal of the freeform HOE, and the numerical aperture of the freeform HOE need more than 0.5. The point on the freeform HOE is constrained respectively as follows:
where ${d_H}$ and ${h_H}$ are the z-axis and y-axis positions of the freeform HOE, and they are set 654 mm and 613 mm, respectively. Similarly, $\overrightarrow {{k_d}} $ is a wave vector of the beam diffracted at the freeform HOE starting from point ${P_H}$ and directed to point ${P_S}$ on the screen. The point on the horopter screen is constrained as follows:Fig. 4. Aberration-free warp projection on horopter screen with a freeform holographic optical element.
The diffracted beam from the freeform HOE appears to converge in the area indicated by the dotted circle in Fig. 4. This dotted circle is located around the projector reference point P in Fig. 2. However, it should be noted that the curvature of the phase is different in the horizontal direction and the vertical direction of the freeform HOE in order to compensate for image distortion using the freeform HOE. Therefore, the beam does not converge at exactly one point. The image from the projector diffracted by the freeform HOE and is mapped to the camera without distortion, which is called aberration-free warp projection.
Figure 5 shows a k-vector diagram for recording the grating vector ${\vec{G}_H}$ of the freeform HOE. In our experiments, the wavelength of the beam for recording the hologram is different from that of the beam for retrieving. So, the Bragg condition of the volume holography theory, which determines the direction of the diffracted beam, is not satisfied. The diffraction angle is changed even in the case that the retrieving beam has the same direction as that of the recording beam [18–20]. Given the wave vector of the projection beam, ${\vec{k}_p}$ and the wave vector of the diffracted beam, ${\vec{k}_d}$ for aberration-free warp projection, the horizontal component of the grating vector is determined by
As mentioned before, the wavelength of the projection beam, ${\lambda _{proj}}$, is different from the wavelength of the recording beam, ${\lambda _{rec}}$, so the grating vector in the k-vector diagram does not become a chord of the k-sphere of the projection wavelength. When the reference beam for recording hologram is directed in the same direction as the projection beam for retrieving hologram, the k-vector of the recording beam is obtained by
From the parallel component of the grating vector obtained in Eq. (6), the point where the k-sphere of the recording wavelength and the straight line representing the parallel component of the grating vector intersect is obtained as shown in Fig. 5. So, the vertical component of the grating vector is given by
Therefore, k-vector of the object beam for recording is determined by
The deviation between the grating vector caused by the wavelength difference between the recording and retrieving beams is as follow;
This value means the degree of Bragg mismatch, and the larger the $\delta {G_H}$, the lower the diffraction efficiency. In this paper, the recording beam has a longer wavelength and a smaller diameter of the k-sphere compared to the retrieving beam, making it impossible to record some long grating vectors, causing the Bragg mismatch. On the other hand, it's worth considering the opposite case where the recording beam has a shorter wavelength than the retrieving beam. In this case, there are no restrictions on the length of recorded grating vectors.
The phase profile of the freeform HOE is calculated by the line integral of the grating vector:
where ${P_H}$ is a interested point on the freeform HOE and ${P_{H,C}}$ is a center point of the freeform HOE. Table 2 shows RGB wavelengths in projection and recording conditions. In red and blue colors, the differences are more than 20 nm, which are sufficient to cause the Bragg mismatch condition.Table 2. Wavelengths under the projection and recording conditions
Figure 6 shows the phase profiles of the freeform HOE obtained from Eq. (11). The grating vectors in periphery of the freeform HOE are heading to the center as depicted in Fig. 6(a). So, the freeform HOE has a phase curvature similar to a concave mirror and the phase at the center is higher than that of outside. It gives a power to condense the diverging projector beam to the dotted red circle region as shown in Fig. 2.
Fig. 6. (a) Normalized grating vector distribution in the freeform HOE and its phase profiles at (b) 660 nm, (c) 532 nm, and (d) 473 nm.
4. Freeform holographic optical elements for correcting aberration
The freeform HOE is fabricated in units of hogels and the phase profile of the freeform HOE needs to be segmented according to the hogel. Then, the segmented phase profile is decomposed based on the Zernike polynomials as follows:
where m and n are the indices of a hogel in x and y direction, respectively. j is the order of the Zernike polynomial. ${\alpha _{j,m,n}}$ is the coefficient of the j-th order of the Zernike polynomial ${Z_j}$ at (m, n)-th hogel and $({\rho ,\;\theta } )$ is the local polar coordinate of a given hogel. In this paper, the freeform HOE consists of 122 × 72 hogels, and their interval is set 1.2 mm. The first five dominant terms of Zernike polynomial are defined as follows:It is noted that the 1st term and the 2nd term means vertical tilting and horizontal tilting, respectively. The 3rd term and the 5th term means oblique astigmatism and vertical astigmatism, respectively. 4th term determines phase of defocus.
Figure 7 shows the Zernike coefficients of hogels composing the freeform HOE at green wavelength. The coefficients ${\alpha _{1,m,n}}$, ${\alpha _{4,m,n}}$, and ${\alpha _{5,m,n}}$ are even functions of horizontal index, m, but ${\alpha _{2,m,n}}$ and ${\alpha _{3,m,n}}$ are odd functions of horizontal index, m. This results from the geometric symmetry along the x-axis in the projection configuration. The freeform HOE functions as an off-axis aspheric concave mirror and ${\alpha _{4,m,n}}$ represents the amount of the phase curvature. Since the coefficients are obtained by decomposing an individual hogel in local coordinates, the decenter at the hogel apart from the center is represented by tilt terms. Therefore, the coefficients ${\alpha _{1,m,n}}$ and ${\alpha _{2,m,n}}$ changes almost linearly to y-axis and x-axis, respectively.
Fig. 7. Zernike coefficients according to position of the hogel at green wavelength. (a) 1st, (b) 2nd, (c) 3rd, (d) 4th, and (e) 5th coefficients.
Figure 8 shows the population distributions of Zernike coefficients at the green wavelength. Most of the 1st coefficient are positive as shown in Fig. 8(a) since the freeform HOE diffracts the oblique incident beam to normal direction of the screen. The reflected light from the substrate of the freeform HOE is separated from the diffracted light. In addition, the freeform HOE makes the diffracted beam converge at virtual projection reference point. So, this physical separation is helpful to filter an annoying DC term out. The population distributions of ${\alpha _{2,m,n}}$ and ${\alpha _{3,m,n}}$ are symmetric because of the projection geometry. All values of ${\alpha _{4,m,n}}$ is negative since the freeform HOE functions as a concave mirror. It is noted that the values of ${\alpha _{3,m,n}}$ and ${\alpha _{5,m,n}}$ are negligibly small compared to the others coefficients. Therefore, the only three terms Z1, Z2, and Z4 which represent local tilts and defocus in the HOE are concerned.
Fig. 8. Population distributions of (a) 1st, (b) 2nd, (c) 3rd, (d) 4th, and (e) 5th Zernike coefficients at the green wavelength.
5. Experimental results
5.1 Fabrication of freeform holographic optical elements
In order to record the freeform HOE, we modified the hologram printer suggested in our previous study [17]. The optical intensity of the projector is so high that a large freeform HOE is required for correcting the wavefront. Practically, it is not easy to form the recording beam which covers the large HOE. In this paper, we use a hologram printer to record the large freeform HOE where the HOE is recorded sequentially hogel by hogel with the diameter of 1.2 mm. The hologram printer is specialized for recording a hogel diffracting the light composed of three Zernike polynomials Z1, Z2, and Z4. These three terms are related with the tilting angles and diverging angle of the light. The tilting mechanism is realized by using goniometers to record phase profiles of vertical and horizontal tilt. The adjusting diverging angle of beams is realized by using tunable lenses. In this paper, the incident wave on a freeform HOE is not a plane wave, so we need to implement the hologram printer to rotate not only an object head but also a reference head. Also, the divergence of the light from both heads are controllable. This structure is helpful to increase the coupling efficiency in the hologram medium.
Figure 9 shows a hologram printer for freeform HOEs. The demanded phase curvature on a hogel is realized by goniormeters and tunable lenses depicted in Fig. 9(a). Figures 9(b) and 9(c) show the photos of the whole hologram print system and its heads. For each head, two goniometers, BGS80CC and BGS50CC produced by Newport are combined with rotation ranges of ±30° and ±45° along x- and y-axis, respectively. The goniometers moved on two x-y stages, LTS-300/M of Thorlabs with traveling distance of 300 mm to define the hogel for recording. It can be observed in Fig. 9(c) that reflective collimators and tunable lenses are assembled and attached on each goniometer. RGB laser sources are combined and delivered via optical fibers, and the light are collimated by reflective collimators. Then, its diverging angle is manipulated using tunable lenses. The hologram medium is placed between the two tunable lenses and it is recorded by interference of two illumination beams. The wavelengths of RGB lasers are 660 nm, 532 nm, and 473 nm. As the hologram medium, photopolymer film made by Liti hologram is used, which has $16\,\mathrm{\mu}\mathrm{m}$ thick and 6 × 8 inch size. Table 3 shows the specifications of our hologram printer.
Fig. 9. Hologram printer for freeform HOEs. (a) The method for recording demanded phase curvature, (b) a photo of the system, and (c) its printer heads.
Table 3. Specifications of the proposed hologram printer
5.2 Warp projection with freeform holographic optical elements
Figure 10 shows the experimental setup of the holographic aberration-free warp projection. The points obtained on the horopter screen using Eq. (5) are converted into STL files, and it is printed as eight pieces using a 3D printer as shown in Fig. 10(a). Figure 10(b) shows the freeform HOEs fabricated by the proposed hologram printer. The phase profile of the HOE is segmented to 122 × 72 hogels, and the hogel pitch is set to 1.2 mm. Total recorded area of a HOE is 134.4 mm × 86.4 mm. The total recording time of one hogel is 0.4 milliseconds, and stage moving interval takes about 4 seconds. The total recording time is about 10.74 hours. In general, the shrinkage during the curing process is very important for the photopolymer. But, the shrinkage effect was not severe in our experiments. We guess that it may result from the condition that the HOEs were cured naturally for a long time by soft room light with broad bandwidth of wavelength. The warp projection system configuration is depicted in Fig. 10(c). The system dimension is 727 × 1213 × 1000 mm3 ($W \times L \times H$). The projector uses laser sources with wavelengths of 640, 524, and 447 nm, and it had a liquid crystal on silicon device with WXGA resolution. A DC filter is installed at the VP to block the reflected beam from the substrate of the HOE which disturbs the observation of the image. A camera is set at the origin to observe the aberration-free image on the horopter screen. Figure 10(d) shows the photo of the system. The beam from the projector propagates to the freeform HOE and is diffracted on the HOE. The diffracted beam converges at the VP. Then, the projected beam at the VP is illuminated on the horopter screen. The projected image is observed by the camera positioned at the center of the system.
Fig. 10. Experimental setup for proposed holographic aberration-free warp projection. (a) Horopter screen fabricated by a 3D printer and (b) printed freeform HOEs. (c) Dimensions and (d) photo of holographic warp projection.
Figure 11 shows the experimental results with and without the compensation of distortion. One in Fig. 11(a) is a result by directly projecting a grid pattern on the horopter screen and severe distortion is obviously observed. The reference point of the projector is positioned at the virtual projection point of the system. On the other hand, in Fig. 11(b), the distortion is corrected when the projector projected the source image via the HOE. The holographic warp projection demonstrates that the vertical and horizontal lines are parallel to each other, which indicates that the HOE functions appropriately warped the projection by correcting the distortion. It is noted that the image is projected on the horopter screen by correcting the distortion at the green wavelength. The optical efficiency of diffraction is calculated by measuring the optical power at the projection and virtual projection points. The optical powers at the projection and virtual projection points are 13 mW and 0.87 mW in the green laser, respectively. The diffraction efficiency is 6.69%. The diffraction efficiency is low for several reasons. The main reasons are a loss due to reflection on the substrate and a loss due to Bragg mismatch from a difference of the wavelengths used for recording and reproducing [21].
Fig. 11. Holographic aberration-free warp projection with the green laser. Projected image (a) without and (b) with the freeform HOE.
In Fig. 11(b), the brightness in the outer region is relatively low. This comes from that the Bragg mismatch is significant in the outer region. The relative diffraction efficiency is calculated from the Bragg mismatch vector:
where T is the thickness of the HOE, and $\hat{n}$ is normal vector of the HOE plane. Figure 12 shows the normalized diffraction efficiency of RGB HOEs from Eq. (12). The diffraction efficiency of the red and green lasers decreases toward the outside, and the ratio of decrease is higher in the green laser than in the red laser as shown in Figs. 12(a) and (b). The efficiency of the blue laser represents the shape of a ring. The center and outer parts had a relatively low efficiency as shown in Fig. 12(c). Figure 12(d) shows the diffraction efficiency along the lines A-A’. The deviations of diffraction efficiency are 10%, 55%, and 20% in the red, green, and blue lasers, respectively.Fig. 12. Normalized diffraction efficiency of HOEs depending on the wavelengths of (a) red, (b) green, and (c) blue laser. (d) Normalized diffraction efficiency along line A-A’.
Figure 13 shows the proposed holographic warp projection with full-color images. Figure 13(a) is a source image of the projector, showing the scenery of Anapji pond, a famous historical site in South Korea. The results of off-axis projection and aberration-free warp projection are shown in Figs. 13(b) and (c), respectively. The red dotted line represents the physical edge of the horopter screen. In Fig. 13(c), it is obvious that the vertical and horizontal straight lines of the building are observed without distortion. Figure 13(d) is a source image, fruits as source image of the projector. The results of its off-axis projection and aberration-free warp projection are shown in Figs. 13(e) and (f), respectively. In Figs. 13(c) and (f), it is distinguishable that the color of the projected image becomes purplish and the color balance changes around the edge. As mentioned above, the diffraction efficiency of the green wavelength is drastically reduced due to the Bragg mismatch. The mismatch may be simply solved making the wavelengths of recording light equal to that of retrieving light. Even in the case that the difference of the wavelength exists, the uniformity of diffraction efficiency can be improved by optimizing the optical power and scheduling the exposure [22,23]. We consider the fine control of the exposure time for each hogel as a next work.
Fig. 13. Experimental results of the proposed holographic warp projection with full-color images. (a) Photo of Anapji pond in South Korea. The image through (b) off-axis projection and (c) warp projection. (d) Photo of fruits. The image through (e) off-axis projection and (f) warp projection.
6. Conclusion
The projection on a curved surface such as a horopter screen causes some practical problems that the image is hard to be focused on the entire screen and its magnification is partially different. The aberration-free warp projection is a powerful solution since it changes the optical path from an object plane to an image plane. Since a horopter screen has a complex surface shape, the freeform optical elements for the aberration-free warp projection need high surface gradient and high NA. The freeform HOE for the aberration-free warp projection is fabricated following three steps. First step is calculation of grating vectors through geometric ray analysis. Next step is extraction of the phase profile from grating vectors with inverse gradient algorithm. The phase profile is computed under consideration of Bragg mismatch resulting from the difference between the wavelengths for recording and retrieving. In the final step, the phase profile is recorded on the photopolymer by the tailor-made hologram printer which has ability to record freeform holograms with a maximum NA of 0.5 over a 6”×8” area where three HOEs for RGB colors are fabricated respectively. The feasibility of our proposed method is verified that the freeform HOEs effectively remove the distortion and defocus aberration on the horopter screen. In near future, we plan to modify the hologram printer to record the trichroic HOE that diffracts the light in the desired directions according to the RGB colors.
Funding
Ministry of Science and ICT, South Korea (2020-0-00914).
Acknowledgments
This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (2020-0-00914, Development of hologram printing downsizing technology based on holographic optical element (HOE)).
Disclosures
The authors declare no conflicts of interest
Data availability
No data were generated or analyzed in the presented research.
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