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Abstract
When a near-eye display (NED) device reproduces an image at a location close to the eye, the virtual image is implemented at a large angle. The uniformity of the image is unbalanced due to the change in diffraction efficiency by the hologram recording angle and angular selectivity. This study proposes a method for implementing an optimal uniform image by analyzing the diffraction efficiency and the reconstructed image was analyzed using angular selectivity generated while reproducing the source point of the diffused image as an intermediate element by holographic optical element (HOE). This research provides practical results for displaying high diffraction efficiency and immersive holographic images in the NED system with HOE as uniformed intermediate elements.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metaverse technology is becoming increasingly popular and the virtual and augmented reality (VR/AR) market is growing rapidly [1–5]. In particular, the near-eye display (NED), a type of head-mounted display (HMD), is the easiest-to-access device to implement the virtual and augmented reality worlds [6–11]. Besides, NED devices called as “see-through smart glass” utilizing transparent screens are the next-generation portable devices [12–15]. This type of AR device provides a highly immersive display by manipulating viewers into thinking that virtual objects exist in the real world. However, despite these advantages, NED devices are not yet popular in the market. There are various reasons, such as the limitation of the display panel from the image source [16–17], a smaller field of view (FOV) than the viewing angle of human eyes [18], and a narrow eye-box [19]. Therefore, companies, institutions and universities are still working to improve practical and user-friendly NED devices. A solution to the above problems is that light refractive power is input to a screen arranged in front of the human eyes using holography; the optical element created by this technology is called a HOE, which records the optical properties of lens function on thin holographic material with the lens as an object. The lens can be convex, concave, mirror, or aspherical depending on the function that we choose [20–21]. Therefore, the display application implemented using HOE is suitable for improving the form factor and implementing high-depth and large-screen virtual images. Various types of optical systems have been designed to solve the above-mentioned limitations of the NED system using HOE and studies have been conducted to improve image quality [22–26]. However, most of the NED systems with HOE use off-axis direction sources. This prevents the image displayed to have uniform intensity in all locations of HOE screen while illumining display in a direction perpendicular to the eye. If the source image is close to the optical axis, it is reconstructed without aberration and optically imaged from a calculated position. When images are far from the center of the source image, it not only causes aberration but also lowers diffraction efficiency. This is because, considering only the X-Y axis, the focal position in the tangential direction and the sagittal direction is different, and that causes astigmatism [27]. In addition, since the NED system is placed near the eyes, optimizing image input angle is an important factor, and angle must be implemented as the initial condition for high diffraction efficiency and low aberration. Thus, in order to apply HOE to the NED system, it is necessary to analyze how the reconstructed environment will reconstruct the source image completely and display it as a virtual image after off-axis recording. In this study, first, we compare the appropriate amount of light exposure and efficiency of holographic material. Based on this comparison, the source input to the off-axis in the NED system using HOE can represent optimized images at the reconstruction location; further, high-efficiency HOE is created through a spatial division recording method. In the proposed method HOE is segmented into units. This recording method presents an analysis of the result value that varies by recording angle according to the lattice characteristics of the hologram. It is possible to propose a signal processing method of reverse compensation by forcibly inputting aberration into the brightness of the screen or the image for simply restoring the uniform image. However, in a system that utilizes HOE as an intermediate element, it can be developed as a good solution that can replace high N/A and heavy glass-type lenses in the future by implementing almost the same function as commercial lenses before signal processing. This research can be used as a reliable device not only for NED system but also for applications with low-volume optical system with high integration which is can operate high performance. For this analysis, we analyzed the diffraction efficiency of each unit as an image reconstruction at the focal plane. With this data, HOE records the exposure light as a time difference for high uniformity of the entire surface efficiency. The difference in uniformity between the image reconstructed from the general method and the image reconstructed from the proposed method is analyzed in each plane. Second, among the characteristics of HOE, the degree to which angular selectivity affects the efficiency and uniformity of the reconstructed image is also analyzed. We mathematically analyze the change in value of the recording angle between reference light and object light. The thickness of holographic material when recording the hologram in a reflective form can represent the effect of angular selectivity on the display intensity of an HOE screen.
2. Near-eye display (NED) method using holographic optical element (HOE)
2.1 Ideal condition for HOE as commercial lens
HOE using holography has no imaging element for reproducing the image of an object. The reason is that the hologram contains imaging effects such as lens. Since the diffraction wave of the object is recorded in the holographic material, it reproduces the image of the object by projecting it backward [28–29]. The HOE recording forms two wavefronts with reference light and object light, like a general analog hologram recording. It is obtained by interfering with light in the holographic material, and it records the pattern of two waves, which is called a holographic interference pattern. In this case, recording is using a spherical wave from light source point or a plane wave from a collimation beam. Here, the function of the optical element can be input by directly refracting power using a lens used as an object. We suppose that a reference light is incident where HOE deviates from the initial condition. If the wavefront is incident at a changed direction and distance, as shown in ${R_2}$, the reconstructed image is shifted from ${O_1}$ to ${O_2}$. This means that the change in input from the initial condition ${R_1}$ to ${O_2}$ shows the result of the change in output, as shown in Fig. 1. As shown in the $({x,\; y,\; z} )$ coordinate system in space, a holographic material is positioned on the $x,\; y$ plane to record object ${O_1}$ as reference light, with a point light source ${R_1}$ having a wavelength of ${\lambda _1}$. Then, by magnifying this m times and reproducing the image of ${O_1}$ to ${O_2}$ with the point light source ${R_1}$ of wavelength ${\lambda _2}$ in ${R_2}$, the modified Eq. (1) can be created based on the lens maker's equation. Here, coordinates of ${R_1}$, ${R_2}$, ${O_1}$, ${O_2}$ represent ${R_1}$ (${\alpha _1}$, ${\beta _1},\; {\gamma _1}$), ${R_2}$ (${\alpha _2}$, ${\beta _2},\; {\gamma _2}$), ${O_1}$ (${x_1},\; {y_1},\; {z_1}$), ${O_2}$ (${x_2},\; {y_2},\; {z_2}$) respectively.
The (+) of the double sign ± represents a direct term, and (-) represents a conjugate term. In addition, the magnification of the phase is represented by Eq. (2) below.
A typical holographic imaging is accompanied by aberration, and in particular, an image without aberration is produced under the conditions of ${\lambda _1}$=${\lambda _2}$, $m = 1$, ${\alpha _1} = \; {\alpha _2}$, ${\beta _1} = \; {\beta _2}$, ${\gamma _1} = \; {\gamma _2}$. Under these conditions, an image is formed with ${M_{lat}} = \; {M_{long}} = 1$ and appears without aberration. Under these conditions, ${M_{lat}} = \; {M_{long}} = m$, theoretically. However, in the case of NED using HOE, it is difficult to implement an optical system without aberration under these conditions because most of the eyes are directed perpendicular to the normal of the screen using a source incident with off-axis. Therefore, research has been conducted to optimize the image in which the input source is reproduced so that the image can enter the eye without aberration as much as possible [30–32].
2.2 Effect factors of lowering NED uniformity
2.2.1. Decrease in efficiency from recording angle on HOE plane
The diffraction efficiency is the measure of how much light contributes to the reconstructed image when reproducing the hologram. High diffraction efficiency means that the reproduced image is bright. Therefore, increasing the efficiency of HOE means increasing the output of the display source image. Since HOE also uses holography, studies involving a coherent laser source with high light output, polarization matching [33] between reference light and object light, and filtering to uniformize the beam intensity profile have been conducted [34–36]. Based on these past studies, it is not difficult to increase the efficiency of holograms. However, in the case of HOE that must be used as an element not only is it recorded as Off-axis but the reconstruction strength of the center and periphery of the reconstructed image varies. This is related to angular selectivity and the angular width, which means this selectivity can be expressed as Eq. (3).
Figure 2(a) shows that the angle to be displayed also changes according to the shifting of the angle when recording and generating HOE. The reconstructed image shows the discrepancy caused by this angle selectivity, as shown in Fig. 2(b). In order to obtain a high-depth enlarged image using diffuser, the diffuser is positioned on the focal plane of the HOE. At this time, the diffused light rays at the central source point show high efficiency because they match with the angle used to record HOE. However, in the case of areas outside the center, the efficiency is extremely low. This is because it is different from the initially recorded θr value. In addition, the efficiency decreases because only a part of the beam emitted toward the end of the diffuser is incident on the effective area recorded in the hologram. In addition, in the case of NED, it is important for users to expand small source images to large virtual images. Because it is a small portable application. For this reason, HOE using a high refractive index has to be designed to have a large FOV near the eye. Therefore, the difference in efficiency between the center and the edge of the HOE is larger than that of large applications. This causes that is important to improve the uniformity of the output in NED. Thus, the various perspectives considered to improve uniformity in HOE recording are not sufficient to solve various problems that occur when the device operates with this application. For this reason, in this study, it is necessary to present and analyze the HOE recording conditions optimized for NED operating as off-axis.
Fig. 2. Angle selectivity of HOE (a) HOE from reconstructed image with different incidence angle (b) Intensity distribution according to angle of reconstructed image observed from human eyes.
2.2.2. Imaging problems from optical systems close to the human eye
Identifying which images are played and where they are played is the most crucial analysis for application using HOE. If the conditions used for recording are used as they are, perfect image playback is performed, as confirmed in Chap 2.1.
However, regular glass lenses are also used in many layers for the reproduction of images without aberration. For this reason, in the case of a lens using a thin holographic material within 1 mm of thickness, the reproduction of an image outside the initial condition causes more aberration than that by a conventional commercial glass lens. Therefore, it is important to devise an optical design of the optimal environment within the minimum tolerances acceptable to the user, which is a more important factor in the case of near-eye NED. Equation (3) shows the reproduction position of the image using the basic lens equation.
Figure 3 shows HOE using the reflective hologram recording method generally used for NED. As shown in Fig. 3(a), an object is used as a lens to input the function of the lens as a hologram, and a reference beam entering a plane wave from an infinity distance is incident at an angle $\theta $ to finally produce HOE with a focal length of f value in the off-axis direction. Figure 3(b) shows that the light emitted from the center of the device displayed in the same direction as the reference beam is modulated with HOE and reproduced as a point. In this case, the regenerated light from Eq. (3) is shifted by Δf. This can make the image blurry by accurately focusing the image, but there may not be much difference in the visual experience of the user. Therefore, it is important to analyze the degree of resolution of the angle changed in the recording conditions on the reconstructed image and to set the best value for the NED optical system designed with a small form factor under conditions that can improve uniformity.
Fig. 3. Recording and generation for HOE (a) Recording for HOE from infinity distance (b) Reconstruction of HOE from finite distance
3. Experimental setup
3.1 Spatial division recording method for display uniformity compensation
A source display used in a general HOE recording method is formed using the most uniform collimation beam in the center by setting up a uniform diffusion beam. Besides uniformity, efficiency is also important. In the case of an optical hologram that records and reproduces the amplitude and phase of a conventional object as it is, even if the efficiency is a little low, there is no inconvenience to the observer's eyes if the hologram image is accurately recorded without distortion. On the other hand, when a HOE is used as a device for phase regeneration in the middle of an optical system, it is natural to create it with the aim of 100% modulation and imaging without aberration, such as commercial lenses.
However, as mentioned in Section 2.2, diffraction efficiency and angle selectivity should be optimized for the final application system. For fabrication of HOE, a photopolymer named Bayfol HX200 by Covestro is used as a holographic material; the specifications are shown in Table 1. For exposing light into HX200 with 491 nm (blue color), 532 nm (green color) 660 nm (red color) coherent laser in the experiment with 15$\textrm{mJ}/\textrm{c}{\textrm{m}^2},$ 20$\textrm{mJ}/\textrm{c}{\textrm{m}^2},$ 25$\textrm{mJ}/\textrm{c}{\textrm{m}^2}$ energy is needed respectively. In this experiment, since it was a full-collar record using white beam combined with red, green, and blue, the appropriate exposure was considered as an intermediate value, 20$\textrm{mJ}/\textrm{c}{\textrm{m}^2}$ and light exposure was performed.
Table 1. Specification of Bayfol HX200 by Covestro
Figure 4 shows appropriate energy of exposure of light reconstructed according to the hologram recording time. The photopolymer reaction may be divided into two reaction parts. In the initial reaction, the initial photosensitive agent absorbs a specific wavelength and interacts with the photo initiator and in the later reaction part, the monomer is polymerized as a result of a photochemical reaction. The monomer serves to store practical information and generates an interference pattern inside the recording medium through a photopolymerization reaction. Therefore, if the polymerization reaction is partially spatial divided at the halfway when it is initiated and the reaction is saturated, the uniform environment can be reproduced when using as an element in the display. This can solve the issue at the boundary between sub-HOEs when the hologram is divided and recorded. In the divided HOE, the lines overlapping at each boundary are the parts that are saturated after the recording is completely completed. Therefore, if the fill-factor is used more than 100% of the light distribution when recording spatially separately, it does not affect the reconstructed image. This recording method is called the spatial division recording method in our study. Figure 5 shows the optical system for spatial division recording.
The reference beam is collimated and illuminated as a plane wave and the object beam is designed to allow HOE to function with a focal length of 100 mm such as a convex lens. The HOE plane was divided into nine planes from ${H_{00}}$ to ${H_{22}}$ and was recorded to obtain an initial value for the diffraction efficiency value. In the reflective HOE record, the diffraction efficiency restored varies depending on the angle between the reference beam and the object beam. The diffraction efficiency of the reflective phase hologram of the slanted grating from Kogelnik's coupled wave theory is indicated by ${\eta _R} = \textrm{tan}{\textrm{h}^2}[{\pi \mathrm{\Delta }nd/\lambda {{({\cos {\theta_R}\cos {\theta_O}} )}^2}} ]$ [37]. Here, $\Delta n$, d, $\lambda $, ${\theta _R}$ and ${\theta _O}$ refer to the refractive index modulation value of the holographic material, the thickness of the holographic material, the wavelength of the recording beam, the reference beam, and the object beam, respectively. It was set up with the same conditions at $\cos {\theta _R} = 50^\circ $. Smaller the angle of the reproduced ${\theta _O}$, lower the efficiency. The color-map shows the partial diffraction efficiency value of the recorded HOE before using the proposed spatial division recording method, as shown in Fig. 5. It is seen that the efficiency of each HOE is different from the off-axis record even though we used a uniform beam using spatial filters. Hence, in order to reproduce a uniform image of the final display used as an element, it is necessary to compensate the reconstruction ratio on each side.
3.2 Comparison of effective diffraction areas according to angle selectivity
In general, the biggest advantage of HOE compared to DOE devices is the narrow characteristic of angle selectivity [38]. This means that noise restored for all light sources coming from the outside can be selectively filtered to show high resolution input image to the observer. However, in the case of NED using HOE, the image in the center of the screen and the edge parts do not enter at the same angle. Figure 6 shows the effective area of the HOE that causes diffraction according to the width of angle selectivity.
Fig. 6. Effective diffraction area at the edge of the display source. (a) Case with wide angle selectivity (b) Case with narrow angle selectivity
In this way, the narrow angle selectivity mentioned above as an advantage shows low restoration ability in terms of efficiency. Therefore, widening the angle selectivity within the minimum resolution degradation range acceptable to the observer means that the image in the imaging diffuser is the source can be efficiently. The diffusion angle can be calculated by Eq. (11) defined in Chap 2.2. In this study, we used a diffusing glass with 40° diffusion angle. Bayfol HX200 is used as the holographic material with refractive index 1.5 and thickness 16 µm, and recording angle of incidence 50°. It is recommended to produce a reflective hologram using a small angle, but due to the NED characteristics, a large incident angle was used as the source display should be placed close to the eye. When calculated in this way, $\varDelta \theta $ is 4.55°. Considering one point light source emitted from the diffuser, the image incident on the HOE screen at a divergence angle 40° from the diffuser displayed in consideration to the specifications of the photopolymer and laser is selectively restored. In this study, the selective restoration area of the reproduced image was analyzed in consideration to the values of the above variables, and the parameters of the optimized system were derived.
3.3 Near-eye display setup using HOE
Figure 7(a). is an HOE-based NED system used in this study. The system's display source is a laser projector. Collimation lenses were used to make plane waves have a focal length at a certain distance. In order to illuminate light as a point source for imaging and having each pixel on the focal plane, a glass diffused to 40° was used. Figure 7(b) shows the equivalent model to analyze the enlarged size and display distance of the virtual image according to the focal length of HOE. ${L_v}$, ${L_d}$, ${d_{dh}}$, ${d_{oh}}$ and ${d_{vh}}$ each represent the size of the reconstructed virtual image, the size of the image imaged in the diffuser, the distance from diffuser to HOE, the distance from the converse plane to HOE, and the distance from the virtual image to HOE, respectively. Two prerequisites are required to interpret this model. The first is that HOE is approached with thin lenses and that there is no spherical aberration. Under these two conditions, the eye-box is located near the focal length of the HOE. We used the Lens maker's formula so that 1/ ${d_o}$+1/ ${d_{di}}$=1/ f is applied, ${d_o}$ represents the distance of the object and ${d_{dh}}$ in an equivalent model.
Fig. 7. Near-eye display based on HOE (a) Optical NED system setup (b) Equivalent model for design NED parameters
Since the lens is located in direction opposite to the traveling direction, it may be expressed as ${f_{HOE}}$=(${d_{vh}}\Delta {d_{dh}}$)/(${d_{vh}}$- ${d_{dh}}$) by using $- {d_{dh}}$. Under the above approximation condition called thin len, ${d_{oh}}$ can be written as HOE. Therefore, HOE with a refractive power of convex lens at a ratio of ${d_{oh}}\Delta {L_d}$ = ${d_{vh}}$ :${L_v}$ can produce the size of the virtual image and the depth of ${d_{vh}}$ [39–40].
4. Results and discussion
4.1 Optimization of HOE plane for diffraction uniformity
As shown in Fig. 5, when HOE with a focal length of 100 cm was recorded using incidence angle of 50 degrees, the nine surfaces showed different diffraction efficiencies.
Based on the x-axis, the ${H_{00}}$, ${H_{10}}$, ${H_{20}}$ planes have smaller angles with the z-axis than the ${H_{02}}$, ${H_{12}}$, ${H_{22}}$, which are the surfaces on which the reference beam closes first on the recording surface. In addition, based on the y-axis, the angles of reference beam and object beam are smaller in ${H_{00}}$, ${H_{10}}$, ${H_{20}}$ and ${H_{02}}$, ${H_{12}}$, ${H_{22}}$ than in ${H_{01}}$, ${H_{11}}$, ${H_{21}}$ on the y-axis. Therefore, as we go toward the negative direction of the x-axis. Therefore, as the negative direction of the x-axis increases, the efficiency decreases as it moves away from the center of the y-axis. Figure 8 shows the results of reconstructed images for each region of segmented HOE. Figure 8(a) to (i) indicate each divided area and the upper left indicates its position. 200$\mathrm{\mu} \mathrm{mW}$ filtered uniform light was used as the reference beam for recording and 130 $\mathrm{\mu}\mathrm{mW}$ (65%), 122$\,\mathrm{\mu} \mathrm{mW}$ (61%), 112$\,\mathrm{\mu} \mathrm{mW}$ (56%), 124$\,\mathrm{\mu} \mathrm{mW}$ (62%), 120$\,\mathrm{\mu} \mathrm{mW}$ (60%), 106$\,\mathrm{\mu} \mathrm{mW}$ (53%), 128$\,\mathrm{\mu} \mathrm{mW}$ (64%), 122$\,\mathrm{\mu} \mathrm{mW}$ (61%) and 108$\,\mathrm{\mu} \mathrm{mW}$ (54%) were shown from ${H_{00}}$ to ${H_{22}}$, respectively. The efficiency of ${H_{22}}$ having the largest ${\theta _o}$ was 65% and the efficiency of ${H_{10}}$ having the lowest ${\theta _o}$ was 53%. In the most basic form of HOE of convex lenses of general off-axis, the results of having different efficiency of 10% or more locally were shown. The hologram was re-recorded by varying the recording time according to the ratio of the response of the hologram exposing energy to the segmented HOE plane. Referring to line R+ G+ B of the graph in Fig. 4, a method of adjusting the integrity of the reconstructed image by inputting insufficient energy at an appropriate time was used to reduce the efficiency by 10%. As a result, the HOE screen was created uniformly by downgrading so that it could have a consistent restoration strength with an efficiency level of 53%. Figure 9 shows the comparison of the results of HOE produced in comparison. As each side is recorded separately, a fine boundary line is visible. As shown in Fig. 9(b), each side shows a uniform intensity at a constant focal length regardless of the angle of incidence. The ${H_{00}}$, ${H_{10}}$, and ${H_{20}}$ parts (Fig. 9(a)), which were particularly unevenly higher than other parts, showed uniform efficiency overall, even if the efficiency was reduced by 10% or more at 50% (Fig. 9(b)).
Fig. 8. Reconstruction result from segmented HOE plane (a) ${H_{20}}$ (b) ${H_{21}}$ (c) ${H_{22}}$ (d) ${H_{10}}$ (e) ${H_{11}}$ (f) ${H_{12}}$ (g) ${H_{00}}$ (h) ${H_{01}}$ (i) ${H_{02}}$.
Fig. 9. Comparison of diffraction efficiency in segmented HOE (a) General recording method (b) Spatial division recording method
As shown in Fig. 10, an NED display is implemented using HOE formed in this way. As shown in Fig. 10(a), the left side is visually higher than the right side. Figure 10(b) shows that the brightness of the overall area is relatively dark but has a uniform value.
Fig. 10. Result for comparative uniformity of reconstructed image (a) Recording result with general recording method (b) Recording result with Spatial division recording method (c) Comparison of standard deviation between two recording methods.
Using this uniformed HOE, virtual image was displayed and analyzed with an NED system placed close to the eye at a 100 mm position. The distance between HOE and eyes was set to 100 mm in NED with HOE setup for projection diffusing images. HOE screen used in the experiment has a size of 75 mm(width) ${\times} $ 50 mm(height) and the image is also produced in the same size. The optical diffuser used a 100 mm ${\times} $ 100 mm product from EDMUND OPTICS and it has a 120-grit glass material with 40 degrees of divergence angle. the intensity of the projected image and the HOE screen are very close in such a system with a small form factor. The beam detector measured the difference in intensity between the center and the edge portion of the image within 3% and we conducted the experiment assuming that the projection image uniformly illuminates the entire area of the HOE screen and displays the image uniformly from the diffuser to the HOE screen. The size of the observer's eye-box can be calculated from Fig. 7(b). When using a diffusing glass with a diffusing angle of 10 degrees from 200 mm which is the distance obtained by adding ${\textrm{d}_{\textrm{dh}}}$ and ${\textrm{d}_{\textrm{oh}}}$, From this, eye-box size can be 70 mm. For the size of the image, the HOE has a focal length of 100 mm and the image also matches the screen size of the HOE, so it has a virtual image of 150 mm wide and 100 mm long at a depth of 200 mm from the observer's eye-box. From those values, FOV can be calculated. After we considered proportional to the size of the image, FOV of vertical is 22.5 degrees and FOV of horizontal is 41.2 degrees. Figure 10(c) shows the average deviation after selecting a specific area of the restored image and measuring the brightness from the two types of HOEs. The HOE using the general recording method has an average of 96.38 $\textrm{mW},$ which is 5.38 $\textrm{mW}$ higher than the image restored using the HOE produced using the spatial division recording method. The value has a ratio of approximately 5%. However, when looking at the standard deviation of the two recording methods, the general method reported 6.98 while the proposed method showed 2.12. The overall surface reconstruction uniformity is higher when using HOE from the spatial division recording method recorded by segmentation.
4.2. Analysis of angular selectivity for uniformity
The variable values in the factors that determine angle selectivity are: the angle formed between the object light, the reference light during hologram recording, and the thickness of the holographic material. Figure 11(a) shows the Δθ value that changes according to the angle formed by the object light and the reference light during recording, and Fig. 11(b) shows the angle selectivity according to the thickness of the holographic material. Good angle selectivity ($\Delta \theta $ is narrow) means that light deviated from the angle of the initial beam used is not diffracted, and only narrow light rays are accepted from the source point diffused on the display. Bad angle selectivity ($\Delta \theta $ is wide) is said to blur the image by accepting unwanted sources other than the target source point, but it is the same as saying that the target source point can be diffracted by accepting even a large area. Since the $\Delta \theta $ value has a value proportional to the wavelength, the larger the wavelength value, higher is the $\theta $ value. For this reason, the angle difference between $\Delta {\theta _{RED}}$ and $\Delta {\theta _{GREEN}}$ is greater than the angle difference between $\Delta {\theta _{GREEN}}$ and $\Delta {\theta _{BLUE}}$. As seen from the graph in Fig. 11(a), the recording angle of 50 degrees has the smallest angular width in all wavelength bands R, G, and B. Figure 11(b) shows the change of $\Delta \theta $ according to thickness, and the values of $T1$, $T2$, and $T3$ were compared using 523 nm which is the center wavelength. In the case of the Bayfol HX200, as seen from the datasheet specification, the change shown in a graph in Fig. 11(b) depends on the thickness of $T1,\; T2$ with twice the thickness of $T1$, and $T3$ with three times the thickness. Since Δθ is proportional to the $1/T$ value, if it is thinner or thicker than a predetermined thickness, saturation is performed to a specific value. Figure 12 shows the result of the image reproduced from HOE according to $\Delta \theta $.
Fig. 11. Reconstructed image from shifting of $\Delta \theta $ according to the angle of the reference beam $(\textrm{a} )\; \Delta \theta $=4.92° (b) $\Delta \theta $=2.28°
The HOE as shown in Fig. 12 has a focal length of 100 mm and is implemented to be reproduced at a depth of 200 mm through the calculation of Section 3.2, and the image has an enlargement ratio exactly twice. Figure 12(a) is a display image reproduced using a recording angle of 60 degrees on a medium with a thickness of 16 µm, and $\Delta \theta $ = 4.92 degrees. Figure 12(b) shows that the thickness of 32$\mathrm{\mu} \mathrm{m}$ was used by overlapping two films, and the recorded image was also recorded using 50 degrees, resulting in $\Delta \theta $ showing 2.28 degrees. The degree of 4.92 brightness can be checked visually with eye, but the clarity of the top of the image was not seen by the human eye. In order to analyze quantitative sharpness differences, the evaluation of image quality loss information was analyzed with peak signal-to-noise ratio (PSNR) compared to the original image. The PSNR is calculated by Eq. (6) as below.
where $MA{X_I}$ is the maximum value of the corresponding image $MSE$ is the mean square error and can be calculated as Eq. (7).5. Conclusions
The greatest advantage of applying HOE to optical applications is that the target specification can be implemented with a single thin film screen. However, systems such as NED have a very short distance between the source and the eyes from the HOE screen. Further, the source image input is small because the effective area of the HOE is small. In order to implement the magnification and high depth, light refractive power is applied to the HOE screen, resulting in a factor that degrades the quality of the restored image. In this study, we analyzed the diffraction difference between the effective HOE, which may occur in NED systems that reconstruct the visual images for image input off-axis. Reflective holographic recording was used and HOE recorded using a lens of 100 mm at an angle of 50 degrees on a holographic material of 50 mm × 75 mm. HOE exhibited difference in efficiency between the upper part with a large angle and the lower part with a small angle by approximately 10%. In addition, the surface of HOE, which is diffracted even in the actual reconstructed image, has higher efficiency as the hologram recording angle is smaller. This is a spatial division recording method that separately records each unit and displays the finally reconstructed image uniformly. In addition, the efficiency is increased by varying the recording angle and thickness so that the efficiency reduced due to angular selectivity can be increased at the level of minimum resolution degradation acceptable to the user. This study presented an analysis to increase uniformity of reconstructed image generated in small applications such as NED using HOE, as well as to improve display reproduction and diffraction efficiency that can be applied in the future using holography.
Acknowledgement
This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2020-0-00922, Development of holographic stereogram printing technology based on multi-view imaging). This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2020-0-01846, Research and development of realistic content device technology). This research is supported by Ministry of Culture, Sports and Tourism and the Korea Creative Content Agency (Project Number: R2021040083). The present research has been conducted by the Excellent researcher support project of Kwangwoon University in 2021.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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