Open Access
Add to BibSonomy
Abstract
Waveguides have become one of the most promising optical combiners for see-through near-eye displays due to the thickness, weight, and transmittance. In this study, we propose a waveguide-type near-eye display using a pin-mirror array and a concaved reflector with a compact outlook, optimized image uniformity and stray light. Issues have been discussed in detail, which include field of view (FOV), eye-box, resolution, depth of field (DOF), display uniformity and stray light artifacts. It can be shown that the DOF can be extended (when compared with traditional waveguide-type near-eye displays) to alleviate the vergence-accommodation conflict (VAC) problem, and the uniformity & stray light can be improved with an optimal structure. Moreover, reflective surfaces have been introduced as the input and output coupling with a compact outlook, an easy-processing structure and the achromatic performance. A prototype based on the proposed method have been successfully developed, and virtual images with an extended DOF can be shown along with the real-world.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Computer-generated virtual information can be seamlessly superimposed onto the real-world view by augmented reality (AR) technique. It may change the way we perceive and interact with digital content, which can be considered as a transformative technology in the information era [1]. Optical see-through near-eye displays [2–6] act as the key devices during the usage of AR applications, and it can provide a mobile computational and visual platform. During the design process, the optical combiner in this kind of displays has been paid more attentions, and it is our dream to obtain a compact display with a light-weight structure, a high-quality performance, and a visual-comfort perception.
Multiple structures have been used as optical combiners in previous works, such as free-space combiners [7], freeform prism combiners [8–12], and waveguide-type combiners [13–18]. Considering the thickness and performance, waveguide-type combiners attracted more extensive attentions in recent years. The light from the display device can be imaged far way using a projection optics system, and the information can be transferred by the input coupling structure into the waveguide. By multiple total internal reflections within the waveguide, the aperture of the light beam can be enlarged and the thickness can be reduced. To be observed by the user, the light with information is then deflected by the output coupling structure into human eye. The waveguides can be divided into two categories based on the structure of output coupling: geometric and diffractive types. Cascaded half-mirrors [19–21], or micro-prism array [22–24] have been introduced as the output coupling components in the type of geometric waveguides. While the diffractive waveguides often employ surface relief grating (SRG) [25–27], holographic optical element (HOE) [28–30], or polarization volume grating (PVG) [31–34] as their output coupling components. Similar to the traditional displays, most state-of-the-art waveguide-type near-eye displays can only produce a single virtual image plane, and the inconsistent between monocular accommodation and binocular convergence depth will exist when providing three-dimensional (3D) contents using parallax cues. This phenomenon, which is called vergence-accommodation conflict (VAC), may cause eye fatigue, visual confusion, and degradation of oculomotor response based on psychological and physiological studies [35].
To get a visual-comfort experience, multi-focal methods [36–38], light-field methods [39,40], holographic methods [41], and Maxwellian-view methods [42,43] have been introduced in designing near-eye displays with waveguides. Multiple virtual depth planes can be generated by a geometric phase holographic lens [44] or multiple holographic waveguides [45]; a micro-lens array [46] or a holographic micromirror array [47] was combined with a geometric waveguide to reconstruct the light field of virtual images; a waveguide-type holographic display has also been reported using a spatial light modulator [48]. Within these methods, part of information from the display device will contribute the depth information, such as the multiple depths, light field and wavefront of virtual images. Thus, the spatial resolution will decrease a lot, and the FOV & eye-box of the systems may be limited. A kind of near-eye displays limit the ray bundles from the virtual image to the paraxial rays, and the DOF of the virtual image can be extended, which is often called as retinal-projection or Maxwellian-view displays. A pin-mirror HOE array has been used in waveguide-type near-eye displays to extend the DOF [49]. Despite of the limited FOV and a required complex projection optics, this work still provides a well reference in designing a compact near-eye display with a visual-comfort perception. A similar structure with a pin-mirror array has also been reported with a relatively large DOF [50]. Currently, the manufacturing difficulty of this type of near-eye display is too high for the commercial market. In additional, some issues for this type of near-eye displays, such as the image uniformity, stray light, and DOF, have not been analyzed in detail, and the performance needs to be improved with the optimal parameters.
In this paper, a high image uniformity, low stray light and compact waveguide-type near-eye display has been developed with a pin-mirror array. The total reflection can be achieved by the pin-mirror array, and the eyepiece can be processed by injection molding with a low price. The parameters are analyzed in detail, which include the FOV, the eye-box, the extension of DOF, the uniformity and the stray light. The DOF of the virtual image can be effectively extended to alleviate the VAC problem by the proposed waveguide-type near-eye display. A prototype of the proposed near-eye display system has been successfully developed to render optical see-through images with an extended DOF.
2. Waveguide-type near-eye display using a pin-mirror array and a concaved reflector
Figure 1 shows a diagram of the waveguide-type near-eye display using a pin-mirror array and a concaved reflector. From the side view Fig. 1(a) and front view Fig. 1(b) of the waveguide, it can be seen that the light emitted from the micro-display transmits inside the waveguide, reflected by the reflector, and then reaches the pin-mirror array to reflect and couple out. The pin-mirrors are arranged in a discrete manner, so that the light from the real-world can enter the human eye directly through the gap between the pin-mirrors, and the light from each FOV of the virtual image is discretely distributed in the eye-box. The 3D views of the light from central FOV, horizontal FOV and vertical FOV are shown in Fig. 1(c)-(e). When the pin-mirror size is small enough and the spacing is appropriate, the beam size received by the human eye within the eye-box may be smaller than that in the traditional display system. Based on the analysis of the DOF for the virtual image, it can be extended which can slightly alleviate the VAC problem.
Fig. 1. (a) Side view and (b) front view of the waveguide-type near-eye display based on a pin-mirror array and a concaved reflector. 3D view of the light from (c) central FOV, (d) horizontal FOV, and (e) vertical FOV.
Similar to the traditional waveguide-type near-eye display, the exit pupil can be extended by enlarging the size of output coupling structure. In the designed system, the exit pupil expansion can be achieved by increasing the number of rows and columns. Reflective surfaces can be employed as the input and output coupling components in our proposed method, and no additional complex projection optics is required. Thus, a compact outlook and virtual images with a high color uniformity (no chromatic aberration will be introduced) can be provided.
3. Optical performance analysis and optimization of the waveguide-type near-eye display using a pin-mirror array and a concaved reflector
During the design process, some issues of the developed near-eye displays, such as the image uniformity, stray light, and DOF, should be analyzed in detail. The display performance can be improved with optimal parameters.
3.1 FOV and eye-box
Since the pin-mirrors are arranged discretely, the light from each FOV of the virtual image is discretely distributed in the eye-box. When the spacing between adjacent pin-mirrors is too large, the FOV will be discontinuous at some positions in the eye-box. For example, as shown in Fig. 2(a), when the eye moves to the middle of two pin-mirrors, the FOV near the center will disappear if the pin-mirror spacing is too large. To avoid the FOV discontinuity, the spacing p and the eye pupil size D should satisfy the following equation:
As shown in Fig. 2(b), considering both the pin-mirror size s and the pupil size D, the FOV of a single pin-mirror for a viewpoint can be expressed as:
where L is the distance between the waveguide rear surface and the eye pupil plane.Fig. 2. (a) Light is discretely distributed in the eye-box. (b) The FOV generated by multiple pin-mirrors. (c) Limitations on the vertical FOV.
To expand the FOV of the system, it is necessary to increase the number of rows and columns of the pin-mirror array. For a viewpoint in the eye-box, the FOV generated by multiple pin-mirrors can be expressed as
where m is the number of rows of the pin-mirror.However, since the pin-mirror array is located on the rear surface of the waveguide, the vertical FOV cannot be increased infinitely and the expansion limit of the vertical FOV in the + Y and -Y direction is asymmetric. As shown in Fig. 2(c), the upper limit of the FOV in the + Y direction and -Y direction can be expressed as:
where γ1, γ2 are the upper limit of the FOV in the + Y direction and -Y direction, respectively, g is the horizontal distance from the reflector endpoint to the first row of pin-mirrors, and t is the thickness of the waveguide. From Eqs. (4,5), it can be seen that γ1 > γ2 in general, which means the FOV in the -Y direction is smaller than that in the + Y direction.Considering the above analysis, the vertical FOV and horizontal FOV of the waveguide-type near-eye display are expressed by Eqs. (6–8):
As for the eye-box, the concaved reflector has a large horizontal aperture, so the eye-box in the horizontal direction is generally determined by the number of pin-mirrors per row, which can be expressed as:
Due to the small size of the pin-mirror, the vertical aperture of light is limited. It is necessary to stagger each row of pin-mirrors and multiplex the vertical aperture of light to increase the eye-box size in the vertical direction. The vertical eye-box size can be expressed as:
It is worth noting that due to the limited spacing between pin-mirrors, the number of rows should not be excessive to avoid the mutual occlusion of pin-mirrors between each row. Therefore, the eye-box in the vertical direction is smaller than that in the horizontal direction.
3.2 DOF
Small pin-mirror size and large pin-mirror spacing can achieve a larger DOF, and it can be analyzed by introducing an ideal eye model, as shown in Fig. 3. The influence of the concaved reflector was also considered in the system. It can be found that a larger pin-mirror size corresponds to a better modulation transfer function (MTF) when the eye focuses at infinity, but the MTF decreases rapidly as the eye focuses closer. When s = 0.5 mm, MTF is hardly affected by the eye focusing position, but the resolution becomes poor overall. A better trade-off between the resolution and DOF can be achieved with the s value of 1 mm.
Fig. 3. (a) Optical paths for the developed near-eye display. (b) Performance for different parameters.
In terms of the proposed structure, the situation is more complex than the simple model, as the eye pupil varies from 2 mm to 8 mm according to the surroundings. For a particular FOV and a given pupil size, virtual images from different pin-mirrors come into the human eye. Thus, the surface parallelism between each pin-mirror also affects the resolution due to the ghosting or multiple imaging. Moreover, the analysis of DOF is also different. Based on a simple lens model, the relationship between the DOF and the beam size w can be expressed as [42]:
where f is the focal length of the human eye, d is the focus position of the human eye, and δ is the diameter of the permissible circle of confusion on the retina. As seen in Eq. (11), decreasing w can increase the DOF of the virtual image. It should be noted that in this waveguide structure, the change of DOF becomes complicated because the beam spot size of each FOV at the eye pupil plane may be different. As shown in Fig. 4, for the central FOV of F1 (red line), the beam size is expressed as w = s, however, for the FOV of F2 and F3, the beam sizes are different. Concretely, the beam size of each FOV at the eye pupil plane can be expressed as:It can be seen that the DOF varies for different FOVs. Assuming the pupil size D = 4 mm, the relationship between FOV and the beam size at the eye pupil plane under different pin-mirror spacing is shown in Fig. 5(a). It can be observed that the structure has a narrower beam size than the conventional structure, and the beam size varies a lot with the FOV. Given a focal length of the eye at 22 mm, and a focusing distance at 1 m as an example, the relationship between FOV and DOF under different pin-mirror spacing is presented in Fig. 5(b). As shown in Fig. 5(b), this waveguide structure has a larger DOF than the conventional structure for part of the virtual image. The analysis can also be acted as a reference during the eye-box extension design for retinal projection near-eye displays.
Fig. 5. (a) The relationship between FOV and the beam size under different pin-mirror spacing. (b) The relationship between FOV and DOF under different pin-mirror spacing.
3.3 Image uniformity
Since the waveguide uses discrete microstructures as the output coupling component, the light from each FOV is distributed discretely, so the image illumination uniformity in the eye-box needs to be analyzed and optimized comprehensively. The illumination uniformity at different FOVs and different positions in the eye-box are considered simultaneously. The illumination uniformity of different FOVs can be expressed as:
Further, the effect of pin-mirror size and pin-mirror spacing on the illumination uniformity is investigated to find the waveguide structure with the optimal illumination uniformity. To ensure an increase of DOF, the pin-mirror size cannot be too large, so the variation range of s is set at 0.5 mm-2 mm. To ensure the continuity of the FOV, the pin-mirror spacing should not be larger than the eye pupil diameter; in addition, to avoid the pin-mirror of each row to obscure each other and ensure a high real-world light efficiency, the pin-mirror spacing generally cannot be less than 2 mm. Therefore, the variation range of pin-mirror spacing p is set at 2 mm-4 mm. According to this parameter setting, the illumination uniformity S1 of the waveguide is optimized and analyzed with an eye-box area of 14 mm (H) $\times$ 6 mm (V) and a FOV range of 40° (H) $\times$ 8° (V). The effects of the pin-mirror size s and spacing p on the illumination uniformity of different FOVs are shown in Fig. 6. It can be observed that both the pin-mirror size and spacing have a large impact on the illumination uniformity S1. The larger the pin-mirror size, the smaller the S1 which corresponds to a higher illumination uniformity of different FOVs. The pin-mirror spacing has a relatively irregular effect on S1, with an optimal field illumination uniformity when p = 4 mm and 2.5 mm if s is in the range of 1.25 mm to 1.75 mm. When s is set from 0.5 mm to 1.25 mm, it can obtain a well illumination uniformity when p = 3 mm and 2.5 mm. The three structures with the optimal illumination uniformity for different FOVs include: (1). s = 2 mm, p = 4 mm (S1 = 0.096); (2). s = 1.5 mm, $p$= 2 mm (S1 = 0.107); (3). s = 1 mm, $p$= 2.5 mm (S1 = 0.138).
To calculate the illumination uniformity at different positions, the eye-box is divided into M × N grids, and then can be expressed as:
Similar to the analysis and optimization method of S1, the effects of pin-mirror size s and spacing p on the illumination uniformity at different positions in the eye-box are shown in Fig. 7. The difference is that the eye-box is divided into 7 (H) $\times$ 3 (V) grids. As can be seen in Fig. 7, the pin-mirror spacing has a large effect on S2, while the pin-mirror size has a relatively small effect on S2. The smaller the pin-mirror spacing, the smaller the S2 which corresponds to a higher illumination uniformity at different positions in the eye-box. The three structures with the optimal illumination uniformity at different positions are: (1). s = 1.5 mm, p = 2 mm (S2 = 0.918); (2). s = 0.5 mm, p = 2 mm (S2 = 0.931); (3). s = 1 mm, p = 2 mm (S2 = 0.977).
Fig. 7. The effects of pin-mirror size and spacing on the illumination uniformity S2 at different positions in the eye-box.
Based on the above analysis, when s = 1.5 mm and p = 2 mm, it has a high field illumination uniformity and a high position illumination uniformity at the same time, which is the optimal image uniformity structure. The illumination maps for different FOVs with a pin-mirror size of 1.5 mm and a spacing of 2 mm are shown in Fig. 8. It can be observed that the illumination values are close to each other except for the FOV of (0°, −2°) and (0°, −4°). The illumination value of the FOV in the -Y direction is significantly smaller than that of the FOV in other directions, which means that the FOV in the -Y direction is the main factor leading to the decrease of field illumination uniformity. This result coincides with the conclusion drawn from the previous FOV analysis (the FOV in the -Y direction is smaller than that in the + Y direction).
Fig. 8. The illumination map of different FOVs with a pin-mirror size of 1.5 mm and a spacing of 2 mm.
4. Stray light analysis and optimization of the waveguide-type near-eye display using a pin-mirror array and a concaved reflector
Since light may have a total internal reflection on the front and rear surfaces of the waveguide, stray light artifacts can be generated, leading to image ghosting or flipping problems. Therefore, it is necessary to analyze and optimize the stray light for each FOV. The light path of the central FOV is shown in Fig. 9(a). The normal light (purple) is emitted from the micro-display, reflected by the reflector, and finally reaches the pin-mirror array which reflects the light and couples it out. In addition, there are two types of stray light artifacts: 1. the light emitted by the micro-display has a total internal reflection on the front and rear surfaces of the waveguide and deviates from the normal light path (orange); 2. the light emitted by the micro-display has a total internal reflection on the front surface of the waveguide, which also deviates from the normal light path (blue). The stray light path of the FOV in the -Y direction is the same as the central FOV, and the same two types of stray light artifacts exist, as shown in Fig. 9(c). In addition to the above two types of stray light artifacts, there is stray light path 3 (purple) of the FOV in the + Y direction, as shown in Fig. 9(b). The light emitted from the micro-display is reflected by the reflector and undergoes total internal reflection on the rear surface of the waveguide, and finally reaches the pin-mirror array to be coupled out. As can be seen from Fig. 9(b), the stray light paths 1 and 3 cause image flip, and the stray light path 2 causes image ghosting in the + Y direction. A way to eliminate stray light needs to be figured out. The ratio of normal light can be expressed as follows:
where Pn is the normal light power, and Ps is the stray light power. It can be seen from Fig. 9(a)-(c), that the stray light paths 1 and 2 deviate greatly from the normal light path. Therefore, most of the stray light in the eye-box can be eliminated by appropriately increasing the exit pupil distance. The relationship between the distance from the eye-box to the waveguide rear surface L and the proportion of normal light R is investigated, as shown in Fig. 10. It can be observed that when the distance between the eye-box and the waveguide rear surface increases from 13.5 mm to 21.5 mm, the proportion of normal light rapidly increases from 46.4% to 87.85% (s = 1 mm and p = 2 mm). When the distance is further increased, the proportion of the stray light is almost unchanged, but the total normal light power decreases. Therefore, the eye-box is set at 21.5 mm away from the waveguide rear surface.Fig. 9. (a) The normal light path (purple), stray light path 1 (orange), and stray light path 2 (blue) of the central FOV. (b) The normal light path (red), stray light path 1 (yellow), stray light path 2 (blue), and stray light path 3 (purple) of the FOV in + Y direction. (c) The normal light path (blue), stray light path 1 (purple), and stray light path 2 (yellow) of the FOV in -Y direction.
Fig. 10. The relationship between the distance from the eye-box to the waveguide rear surface and the proportion of normal light.
Further, the effect of pin-mirror size and pin-mirror spacing on the stray light ratio is investigated to optimize the optical structure with a minimized amount of stray light. Similar to the illumination uniformity analysis, considering the DOF and the continuity of the FOV, the pin-mirror size variation range is set to 0.5 mm−2 mm and the spacing variation range is set to 2 mm−4 mm. According to this parameter setting, the proportion of normal light is optimized and analyzed with an eye-box area of 14 mm (H) $\times$ 6 mm (V) and a FOV range of 40° (H) $\times$ 8° (V). Figure 11 shows the effects of pin-mirror size s and spacing p on the normal light ratio and the results indicate that the pin-mirror size has a great impact on the normal light ratio. When the pin-mirror size takes the middle value around 1 mm or 1.5 mm, the normal light ratio can get a well performance. The three structures with the optimal normal light ratio are s = 1. 5 mm, p = 2 mm (R = 89.2%), s = 1 mm, p = 2.5 mm (R = 88.9%) and s = 1.5 mm, p = 2.5 mm (R = 88.3%). It is worth noting that when s = 1.5 mm and p = 2 mm, it also has a high field illumination uniformity and a high position illumination uniformity. Therefore, this structure has both the optimal stray light and optimal image uniformity.
5. Prototype and experimental results
To verify the design method, a prototype of the waveguide-type near-eye display based on a pin-mirror array and a concaved reflector was successfully developed, as shown in Fig. 12. The injection gate and the die core can be seen in Fig. 12(c-d). Note that the refractive index of the used optical plastic is 1.636. As shown in Fig. 12, as there are no additional projection optics required in the system and the micro-display is affixed to the upper surface of the waveguide, the whole system has a compact wearable outlook. A 0.71-inch Micro-OLED with a resolution of 1920 ×1080 was used as the display source, and the pin-mirror size is set as 1 mm × 1 mm in the prototype. To imitate the human eye, an objective lens with an aperture of 4 mm and a Charge-coupled Device (CCD) sensor (SHL-500 W) was used to capture the images at the eye-box position of the system. When the camera focused at 0.3 m, the real objects such as the 3D tag and the banana are clear in the near distance, while the real objects such as the 0.2D (Reciprocal of meter) tag and box are blurred in the far distance. In contrast, when the camera focused at 5 m, the real objects such as the 3D tag and banana in the near distance are blurred, while real objects such as the 0.2D tag and box in the far distance are clear, as shown in Fig. 13(b), (d) and (f). Whether the camera focused at 0.3 m or 5 m, the sharpness of virtual images such as the dog, parrot, lion, and bear hardly changes. It can be seen that the DOF of the virtual image generated by the developed system can be extended to a certain extent, which can alleviate the VAC problem. Due to the use of reflective surfaces for both input and output coupling components, no chromatic aberration exists based on the principle. The virtual images have shown a high color uniformity, which can be seen in Fig. 13(a-b). The stray light artifact can be observed in the results, especially when the light intensity of the micro-display is increased (for example, in Fig. 13(c)). This issue can be improved in the future based on the discussion in Section 4.
Fig. 12. The 3D layout of (a) the developed near-eye display system, and (b) the display system along with a head model. Pictures of (c-f) mechanical dies of the eye piece, the developed eye piece and the near-eye display system.
Fig. 13. Captured virtual images alongside the real-world (a)(c)(e) when the camera is focused at 3D, and (b)(d)(f) when the camera is focused at 0.2D.
6. Conclusions
In this paper, a compact waveguide-type near-eye display has been described, analyzed and optimized with a pin-mirror array. Issues have been discussed in detail, which include uniformity, stray light, FOV, and the extension of DOF. Based on the proposed structure, the results show that when the pin-mirror size is 1.5 mm and the spacing is 2 mm, this waveguide structure has the optimal illumination uniformity and stray light overall; the DOF can be effectively extended for part of FOV, which can alleviate the VAC problem to a certain extent. The eyepiece can be processed by injection molding due to the total reflection of the pin-mirror array, and the price can be friendly to the commercial market. A prototype of the proposed near-eye display system has been successfully developed, providing virtual images with an extended DOF alongside the real-world. The performance can be improved using the detailed analysis in the future works.
Funding
National Natural Science Foundation of China (62002018, 61727808, 61960206007).
Acknowledgments
We would like to thank Synopsys for providing the educational license of CodeV and LightTools.
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.
References
1. Y. Itoh, T. Langlotz, J. Sutton, and A. Plopski, “Towards Indistinguishable Augmented Reality: A Survey on Optical See-through Head-mounted Displays,” ACM Comput. Surv. 54(6), 1–36 (2021). [CrossRef]
2. C. Jang, C. K. Lee, J. Jeong, G. Li, S. Lee, J. Yeom, K. Hong, and B. Lee, “Recent progress in see-through three-dimensional displays using holographic optical elements,” Appl. Opt. 55(3), A71–A85 (2016). [CrossRef]
3. J. Y. Hong, C. K. Lee, S. Lee, B. Lee, D. Yoo, C. Jang, J. Kim, J. Jeong, and B. Lee, “See-through optical combiner for augmented reality head-mounted display: index-matched anisotropic crystal lens,” Sci Rep 7(1), 2753 (2017). [CrossRef]
4. Q. Zhang, W. Song, Y. Liu, and Y. Wang, “Design and implementation of an optical see-through near-eye display combining Maxwellian-view and light-field methods,” Opt. Commun. 510, 127833 (2022). [CrossRef]
5. W. Song, Y. Wang, D. Cheng, and Y. Liu, “Light field head-mounted display with correct focus cue using micro structure array,” Chin. Opt. Lett. 12(6), 060010 (2014). [CrossRef]
6. H. Hua, X. Hu, and C. Gao, “A high-resolution optical see-through head-mounted display with eyetracking capability,” Opt. Express 21(25), 30993–30998 (2013). [CrossRef]
7. Dream Glass, https://www.dreamworldvision.com/.
8. D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009). [CrossRef]
9. H. Huang and H. Hua, “High-performance integral-imaging-based light field augmented reality display using freeform optics,” Opt. Express 26(13), 17578–17590 (2018). [CrossRef]
10. D. Cheng, J. Duan, H. Chen, H. Wang, D. Li, Q. Wang, Q. Hou, T. Yang, W. Hou, D. Wang, X. Chi, B. Jiang, and Y. Wang, “Freeform OST-HMD system with large exit pupil diameter and vision correction capability,” Photonics Res. 10(1), 21–32 (2022). [CrossRef]
11. A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018). [CrossRef]
12. L. Wei, Y. Li, J. Jing, L. Feng, and J. Zhou, “Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface,” Opt. Express 26(7), 8550–8565 (2018). [CrossRef]
13. M. Xu and H. Hua, “Finite-depth and vari-focal head-mounted displays based on geometrical lightguides,” Opt. Express 28(8), 12121–12137 (2020). [CrossRef]
14. G. Quaranta, G. Basset, O. J. Martin, and B. Gallinet, “Recent advances in resonant waveguide gratings,” Laser Photonics Rev. 12(9), 1800017 (2018). [CrossRef]
15. J. D. Waldern, R. Morad, and M. M. Popovich, “Waveguide Manufacturing for AR Displays, Past, Present and Future,” Frontiers in Optics, FW5A-1 (2018).
16. E. Dehoog, J. Holmstedt, and T. Aye, “Field of View Limitations in see-through HMDs using geometric waveguides,” Appl. Opt. 55(22), 5924–5930 (2016). [CrossRef]
17. J. Yang, P. Twardowski, P. Gérard, and J. Fontaine, “Design of a large field-of-view see-through near to eye display with two geometrical waveguides,” Opt. Lett. 41(23), 5426–5429 (2016). [CrossRef]
18. M. L. Piao and N. Kim, “Achieving high levels of color uniformity and optical efficiency for a wedge-shaped waveguide head-mounted display using a photopolymer,” Appl. Opt. 53(10), 2180–2186 (2014). [CrossRef]
19. D. Cheng, Y. Wang, C. Xu, W. Song, and G. Jin, “Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics,” Opt. Express 22(17), 20705–20719 (2014). [CrossRef]
20. Q. Wang, D. Cheng, Q. Hou, L. Gu, and Y. Wang, “Design of an ultra-thin, wide-angle, stray-light-free near-eye display with a dual-layer geometrical waveguide,” Opt. Express 28(23), 35376–35394 (2020). [CrossRef]
21. L. Gu, D. Cheng, Q. Wang, Q. Hou, and Y. Wang, “Design of a two-dimensional stray-light-free geometrical waveguide head-up display,” Appl. Opt. 57(31), 9246–9256 (2018). [CrossRef]
22. https://www.kickstarter.com/projects/optinvent-ora1/ora-1-smart-glasses-developer-version.
23. J. W. Pan and H. C. Hung, “Optical design of a compact see-through head-mounted display with light guide plate,” J. Disp. Technol. 11(3), 223–228 (2015). [CrossRef]
24. K. Zhao and J. Pan, “Optical design for a see-through head-mounted display with high visibility,” Opt. Express 24(5), 4749–4760 (2016). [CrossRef]
25. Z. Liu, C. Pan, Y. Pang, and Z. Huang, “A full-color near-eye augmented reality display using a tilted waveguide and diffraction gratings,” Opt. Commun. 431, 45–50 (2019). [CrossRef]
26. Z. Liu, Y. Pang, C. Pan, and Z. Huang, “Design of a uniform-illumination binocular waveguide display with diffraction gratings and freeform optics,” Opt. Express 25(24), 30720–30731 (2017). [CrossRef]
27. J. Xiao, J. Liu, J. Han, and Y. Wang, “Design of achromatic surface microstructure for near-eye display with diffractive waveguide,” Opt. Commun. 452, 411–416 (2019). [CrossRef]
28. J. Han, J. Liu, X. Yao, and Y. Wang, “Portable waveguide display system with a large field of view by integrating freeform elements and volume holograms,” Opt. Express 23(3), 3534–3549 (2015). [CrossRef]
29. Z. Lv, J. Liu, J. Xiao, and Y. Kuang, “Integrated holographic waveguide display system with a common optical path for visible and infrared light,” Opt. Express 26(25), 32802–32811 (2018). [CrossRef]
30. T. Oku, K. Akutsu, M. Kuwahara, T. Yoshida, E. Kato, K. Aiki, I. Matsumura, S. Nakano, A. Machida, and H. Mukawa, “High-luminance see-through eyewear display with novel volume hologram waveguide technology,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp.46(1), 192–195 (2015).
31. K. S. Shin, M. H. Choi, J. Jang, and J. H. Park, “Waveguide-type see-through dual focus near-eye display with a polarization grating,” Opt. Express 29(24), 40294–40309 (2021). [CrossRef]
32. Y. H. Lee, K. Yin, and S. T. Wu, “Reflective polarization volume gratings for high efficiency waveguide-coupling augmented reality displays,” Opt. Express 25(22), 27008–27014 (2017). [CrossRef]
33. Y. Weng, D. Xu, Y. Zhang, X. Li, and S. T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016). [CrossRef]
34. K. Yin, H. Y. Lin, and S. T. Wu, “Chirped polarization volume grating with ultra-wide angular bandwidth and high efficiency for see-through near-eye displays,” Opt. Express 27(24), 35895–35902 (2019). [CrossRef]
35. J. W. Bang, H. Heo, J. Choi, and K. R. Park, “Assessment of Eye Fatigue Caused by 3D Displays Based on Multimodal Measurements,” Sensors 14(9), 16467–16485 (2014). [CrossRef]
36. J. Rolland, M. Krueger, and A. Goon, “Multifocal planes head-mounted displays,” Appl. Opt. 39(19), 3209–3215 (2000). [CrossRef]
37. S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, “Tomographic near-eye displays,” Nat. Commun. 10(1), 2497 (2019). [CrossRef]
38. Q. Chen, Z. Peng, Y. Li, S. Liu, P. Zhou, J. Gu, J. Lu, L. Yao, M. Wang, and Y. Su, “Multi-plane augmented reality display based on cholesteric liquid crystal reflective films,” Opt. Express 27(9), 12039–12047 (2019). [CrossRef]
39. C. Yao, D. Cheng, T. Yang, and Y. Wang, “Design of an optical see-through light-field near-eye display using a discrete lenslet array,” Opt. Express 26(14), 18292–18301 (2018). [CrossRef]
40. D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 1–10 (2013). [CrossRef]
41. Y. Peng, S. Choi, J. Kim, and G. Wetzstein, “Speckle-free holography with partially coherent light sources and camera-in-the-loop calibration,” Science Advances 7 (46), eabg5040
42. W. Song, X. Li, Y. Zheng, Y. Liu, and Y. Wang, “Full-color retinal-projection near-eye display using a multiplexing-encoding holographic method,” Opt. Express 29(6), 8098–8107 (2021). [CrossRef]
43. L. Wang, Y. Li, S. Liu, Y. Su, and D. Teng, “Large Depth of Range Maxwellian-Viewing SMV Near-Eye Display Based on a Pancharatnam-Berry Optical Element,” IEEE Photonics J. 14(1), 1–7 (2022). [CrossRef]
44. C. Yoo, K. Bang, C. Jang, D. Kim, C.-K. Lee, G. Sung, H.-S. Lee, and B. Lee, “Dual-focus waveguide see-through near-eye display with polarization dependent lenses,” Opt. Lett. 44(8), 1920–1923 (2019). [CrossRef]
45. https://www.magicleap.com/magic-leap-1.
46. M. Xu and H. Hua, “Geometrical-lightguide-based head-mounted lightfield displays using polymer-dispersed liquid-crystal films,” Opt. Express 28(14), 21165–21181 (2020). [CrossRef]
47. N. Darkhanbaatar, M. Erdenebat, C. Shin, K. Kwon, K. Lee, G. Baasantseren, and N. Kim, “Three-dimensional see-through augmented-reality display system using a holographic micromirror array,” Appl. Opt. 60(25), 7545–7551 (2021). [CrossRef]
48. H. J. Yeom, H. J. Kim, S. B. Kim, H. Zhang, B. Li, Y. M. Ji, S. H. Kim, and J. H. Park, “3D holographic head mounted display using holographic optical elements with astigmatism aberration compensation,” Opt. Express 23(25), 32025–32034 (2015). [CrossRef]
49. M. H. Choi, K. S. Shin, J. Jang, W. Han, and J. H. Park, “Waveguide-type Maxwellian near-eye display using a pin-mirror holographic optical element array,” Opt. Lett. 47(2), 405–408 (2022). [CrossRef]
50. S. Park, “Augmented and Mixed Reality Optical See-Through Combiners Based on Plastic Optics,” Inf. Disp. 37(4), 6–11 (2021). [CrossRef]
