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Abstract
Virtual reality head-mounted displays (VR-HMDs) are crucial to Metaverse which appears to be one of the most popular terms to have been adopted over the internet recently. It provides basic infrastructure and entrance to cater for the next evolution of social interaction, and it has already been widely used in many fields. The VR-HMDs with traditional aspherical or Fresnel optics are not suitable for long-term usage because of the image quality, system size, and weight. In this study, we designed and developed a large exit pupil diameter (EPD), compact, and lightweight VR-HMD with catadioptric optics. The mathematical formula for designing the catadioptric VR optics is derived. The reason why this kind of immersive VR optics could achieve a compact size and large EPD simultaneously is answered. Various catadioptric forms are systematically proposed and compared. The design can achieve a diagonal field of view (FOV) of 96° at -1 diopter, with an EPD of 10 mm at 11 mm eye relief (ERF). The overall length (OAL) of the system was less than 20 mm. A prototype of a compact catadioptric VR-HMD system was successfully developed.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metaverse appears to be one of the most popular terms to have been adopted over the internet recently, and Virtual reality head-mounted displays (VR-HMDs) provide the basic infrastructure and entrance to cater for this evolution of social interaction. VR-HMDs are near-eye display photoelectric devices consisting of an optical magnification system and a medium-sized or micro-sized display [1,2]. Compact size and light weight are the key to augmented reality (AR) and virtual reality (VR) technology. AR technology focuses on the fusion of virtual and real objects by superimposing virtual information on the real world [3–8]. AR-HMDs are currently widely employed in the fields of training [9], manufacturing [10] and medical applications [11–13]. VR technology focusses on deep immersion, bringing users from the real world into virtual private spaces [14–17], and has various applications in entertainment [18,19], education [20,21], and other fields [22,23].
For VR-HMDs, high immersion, good imaging performance, and comfortable wearing experience are the research goals. The realization of ultra-light weight, wide field of view (FOV), large pupil size, and high resolution are vital points for the popularization of VR-HMDs [24–26]. To meet the requirements of users who suffer from myopia, the function of diopter (D) adjustment is becoming an indispensable part. Currently, there are two mainstream traditional optical solutions for commercial VR-HMDs: smooth aspherical optics and Fresnel optics [17,27]. The emerging VR system utilizes catadioptric optics to realize ultra-thin and sunglasses form VR-HMDs. Figure 1 illustrates the comparison of catadioptric optics with traditional VR optical solutions with the similar FOV and ERF, but with different EPD.
Fig. 1. Comparison of optical system for VR-HMDs. (a) Smooth aspherical optics, (b) Smooth aspherical VR product, (c) Fresnel optics, (d) Fresnel VR product, (e) Catadioptric optics, (f) Sunglasses form catadioptric VR product.
Figures 1(a) and 1(b) show the structure of the smooth aspherical optics and commercial products. This type of system offers low stray light, however, a larger-size display and thicker optical elements should be used to realize a wide FOV and good imaging performance. Furthermore, a larger display increases the focal length of the system, leading to a bulky optical system. Similar to Fresnel optics, it is challenging to acquire a large exit pupil diameter (EPD) even when higher-order aspheric coefficients are used. The emission angle of the chief ray on the display is significantly larger than that of the catadioptric optics and Fresnel optics, resulting in low luminance uniformity, and the FOV considerably varied for users with different diopters. As the diopter increases, the display and virtual image become closer to the exit pupil, and the FOV of system ω becomes larger. Meanwhile, when the human eye moves in the eye box, the imaging quality is degraded and the “pupil swim” occurs [28].
The Fresnel optics VR solution and product are shown in Figs. 1(c) and 1(d), respectively. The size and optical performance of Fresnel optics are between those of catadioptric optics and smooth aspherical optics, which is a good compromise solution, and is currently used in most commercial VR-HMDs. The stray light is a common problem for the Fresnel structure and the significant “ring artifacts” can extremely limit the diffraction modulation transfer function (MTF), which finally causes the low contrast and poor resolution [29].
The basic structure of the catadioptric optical system and VR product in the form of sunglasses are shown in Figs. 1(e) and 1(f). Compared with traditional VR optical solutions, the thickness of the entire optical system is significantly reduced. The optical path is folded three times in the optical system. Despite using a smaller-size display, the catadioptric optics can realize a large EPD, small focal length, and high optical performance. Because the chief ray of each FOV is almost perpendicular to the display, the FOV remains constant when conducting the process of diopter adjustment. Nonetheless, it is necessary to introduce polarization optical elements into catadioptric optical systems to reduce stray light [30–33].
With the same parameters of eye relief (ERF) and FOV, the catadioptric optics can achieve a larger EPD (larger than10 mm) and better performance than smooth aspherical optics and Fresnel optics. The thickness of the catadioptric optics is approximately 1/3 that of the smooth aspherical optics and 1/2 that of the Fresnel optics. The catadioptric system was first proposed in 1969 for immersive flight simulators [34]. In the original design, the catadioptric lens group consists of a concave mirror, polarizer, quarter-wave plate, flat beam splitter, and curved beam splitter. Subsequently, the curved beam splitter is changed to a flat holographic mirror to improve the energy efficiency [35]. In 2004, W. Roest designed a catadioptric eyepiece based on a single aspherical plano-concave lens and a Minnesota Mining and Manufacturing (3M) double brightness enhancement film (DBEF) reflective polarizer. The lens group is compact, but the FOV is only 64° [36]. In 2015, R. B. Huxford designed HMDs based on a catadioptric structure with a relay system. The system has an FOV of 120°×67° and an EPD of 20 mm. However, the optical system is bulky, the lens is made of all-glass material, and the total weight exceeds 1 kg [37]. In 2018, B. A. Narasimhan designed a two-piece catadioptric system with a 2.85-inch display, achieving a 100° FOV and a total thickness of 36 mm. The focal length of the lens group decreases in the radial direction, and a higher imaging performance in the central FOV is realized. However, a system with a small pupil size (4 mm) is still in an imaginary state, and the imaging quality is uneven, large distortion and image loss would also occur [38]. In addition, in 2021, Y. Li designed and fabricated a broadband cholesteric liquid crystal (CLC) lens, which replaced the combination of quarter-wave plate (QWP) and a reflective polarizer for chromatic aberration correction of a catadioptric optical system with an FOV of 50°. However, the fabrication cost of the lens is relatively high, and it is still in the experimental stage [39].
Based on the catadioptric structure, in this study, we proposed an ultra-thin VR system with a large FOV of 96° and 10 mm EPD. The system requirements, including compactness, large EPD and FOV, significantly increase the design challenges. We first analyzed the advantages of catadioptric optical system for the VR-HMDs in principle; to our knowledge, this is the first analysis in the literature to explain this advantage. Thereafter, we compared catadioptric optical paths with different structural forms; explored the detailed design procedures; defined and analyzed the pupil swim issue. Finally, we developed a proof-of-concept prototype. The proposed design is compact and lightweight, which can realize VR-HMDs in the form of sunglasses and significantly promote the VR industry.
2. Basic principles
Catadioptric optics can effectively reduce the system length of the VR display by folding the optical path. The schematic diagram is shown in Fig. 2(a), where there are at least two reflective surfaces. This solution folds the optical path, and the light transmits approximately three times the optical path between the two reflective surfaces, however, it only consume one time the physical space, making the overall optical system significantly thin.
Fig. 2. Comparative design. (a) Schematic diagram and spot diagram of catadioptrical design, (b) Schematic diagram and spot diagram of traditional design.
This optical solution can simultaneously achieve three important indicators: large FOV, short focal length, and large EPD. The F-number (F/#) can reach 2.3, which is very difficult to implement in traditional VR optical systems. The main reason for a better optical performance of catadioptric system is the introduction of reflective surfaces.
We set up a singlet catadioptric system and a singlet refractive system as shown in Figs. 2(a) and (b). The first surface S1 is flat, and the curvatures of S2 are c2 and c2’, respectively. The optical power of the two systems can be paraxially defined as:
In the practical system design, as shown in Fig. 2 and Table 1, with the same system parameters, including the FOV, effective focal length (EFL), EPD, and ERF, the radius of curvature (RoC) of the catadioptric system is significantly larger. As listed in Table 1, the RoC of the catadioptric system is 86 mm, roughly 6.6 times of the latter, which is 13.03 mm. Consequently, the spherical aberration is significantly small and is manifested in the root mean square (RMS) spot size, which reduces from 704 µm to 21 µm for the center field and from 848 µm to 72 µm for the marginal field. In the catadioptric system, reflective surfaces assume most of the optical power, which significantly reduces the power of the other optical surfaces. Meanwhile, the reflective surface does not introduce chromatic aberration, and helps achieve a better design.
Table 1. Specifications of the catadioptric design and traditional design
Although catadioptric VR optics has many advantages, there are still some critical points, including the design discussed in the successive sections and ghost image.
3. Initial structure establishment of the catadioptric system
3.1 Comparison of various structural forms
The catadioptric optical system has multiple structure forms owing to the number of lenses and the position of the beam splitter and reflective polarizer. Considering the feasibility of processing, we set the reflective polarizer on a flat surface in the design, as shown in Fig. 3(a). The circularly polarized light emitted from the display passed through a half mirror. A QWP is placed between the half mirror and reflective polarizer for the circularly polarized light to be changed to P-polarized light, and then reflected on the first interaction with the reflective polarizer. Thereafter, the light changes to the orthogonal S-polarized light, and is transmitted on the second interaction with the reflective polarizer. In Fig. 3, we list various structural forms of 22 types of catadioptric optical systems with one to three lenses. In addition, two of the adjacent lenses can be cemented together to make the system more compact, but at the expense of the degrees of freedom and image quality. Therefore, we do not list them in Fig. 3.
Fig. 3. Various structural forms of the catadioptric optical system. (a) Single lens, (b)-(g) Two lenses, (h)-(v) Three lenses.
Through the analysis of catadioptric optical systems with various structural forms, as well as the comparison of their optical specifications and lengths, increasing the lenses can considerably improve the imaging quality of the optical system. The greater the distance between the two reflective surfaces, the shorter is the length of the overall system. Considering the weight, cost, and alignment difficulty, increasing the number of lenses and the distance between the beam splitters does not always work. In addition, product reliability and implementation difficulty are also factors that should be considered. The first surface close to the exit pupil should not be set as a beam splitter to avoid frequent wiping during use, which would damage the reflective polarizer and QWP. By comprehensively weighting the factors above, we selected (p) 3-S2S6 rather than (l) 3-S1S6 as the design structure, which can obtain a design with better imaging quality and compact structure.
3.2 Derivation of starting point for further optimization
The overall system specifications, including the working spectrum, are listed in Table 2. The design uses a 2.1-inch medium-sized display with a resolution of 1600 × 1600 and pixel size of 24 µm, the diagonal FOV is up to 96°, and the corresponding EFL is 22.9 mm. The EPD was set to 10 mm (without any vignetting) to avoid mechanical interpupillary distance (IPD) adjustment structure, however, the diopter adjustment was maintained for people with different eyesight, and the diopter range was from -1 D to -7 D, thus, the ERF was specified as 11 mm.
Table 2. Specifications of the catadioptric optical system
We set the primary diopter at -1 D to improve the user experience. However, in this VR-HMD system, the distortion can be significantly large if it is left without any constraints. Thus, we set a distortion limit of 24% at the marginal field angle and planned to correct the residual distortion using digital correction methods. In terms of other types of aberrations, MTF was selected to evaluate the overall image sharpness, and it was set to be no less than 18% across the entire field at a spatial frequency of 10.4 lp/mm. The overall length (OAL) of the system was less than 20 mm, and the weight of the lenses was less than 20 g.
As shown in Fig. 4(a), a catadioptric system consists of three lenses labeled L1, L2, and L3. A ray emitted from the display is first refracted by L3 next to the display, and then refracted by L2. The ray propagating towards the exit pupil is reflected by the polarization beam splitter on S2 of L1, and then refracted by L2 again. After reflection on S6, the ray is refracted through L2 and L1, and then reaches the exit pupil.
Fig. 4. Optical paths of the catadioptric optics and smooth aspherical optics. (a) Catadioptric system, (b) All refractive system.
A good starting point and design strategies are crucial for optimizing efficiency and results. We assumed that all the lenses are thin lenses, L1 is a plano-convex lens, the RoC of S3 and S4 are opposite numbers, and the RoC of S5 and S6 are equal. Therefore, the power of L3 is zero when it operates in the refractive-refractive mode. The total power of the catadioptric system is defined as [40]:
The optical power of each lens can be written as:
where n is the refraction index of lenses L1, L2, and L3, and c1, c3, c4, and c5 are the curvatures of S1, S3, S4, and S5, respectively.We further assumed that d2 is equal to d3. Equation (2) can be simplified as:
To compare the catadioptric system with the traditional VR system directly, the same focal length was used to calculate the starting point structure of the traditional system as shown in Fig. 4(b). The materials of the lenses were also set as HK9L and the optical power of the system can be described as:
The RoC of all the surfaces is 77.51 mm, which is significant stronger than that of the catadioptric system and the start point spot diagram of all refractive system is much larger than that of catadioptric optics.3.3 Establishment of the starting point
After a systematic comparison of various structural forms, we selected the most reasonable solution and further implemented the optimization process. In the design of the catadioptric system, the parameters of the three lenses were modeled using the optical design software CODEV [41], Thereafter, the surface shapes and distances of the successive lenses were picked up from the first three lenses using the same physical lens.
We set the three-piece catadioptric starting point, as shown in Fig. 5(a), according to the calculation in Section 3.2. Four representative wavelengths, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm, were set with weights of 1, 1, 2, and 1, respectively. Figure 5(b) presents the spot diagram of the starting point when the focal length was 25 mm, and the RMS spot diameter was approximately 1 mm.
We further adopted the convention of tracing the system backward, namely rays traced from the exit pupil to the display. The calculated EFL is 27 mm, that is, slightly larger than 25 mm, which is the system requirement due to the thin lens assumption. To rectify this deviation, we calculated a group of surface radii according to Eq. (6) for different system EFL to investigate the relationship between the RoC of S5 and the required EFL. Subsequently, we set the EFL of the system to 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, 45 mm, and 50 mm, and the corresponding RoC for each case was calculated and input into CODEV.
The calculated EFL by ray tracing was obtained. The relationship between the calculated and required EFLs is shown in Fig. 6(a). When the required EFL is small, the calculated EFL is larger, but when the required EFL reaches 50 mm, the calculated EFL is almost the same.
Fig. 6. (a) Relationship between the required EFL and calculated EFL, (b) Relationship between the calculated radius and corrected radius.
To minimize the EFL deviation, we can revise the RoC of S5, which is calculated by Eq. (6). Figure 6(b) plots the RoC before and after the revision, and the relationship is described by Eq. (8) using the linear fitting method. Therefore, we can obtain the system with the required EFL accurately.
where ccorrected is the corrected curvature, and ccalculated is the curvature calculated from Eq. (6).4. Catadioptric system design optimization process
4.1 Optimization process
For the optimization procedure, we need constrain the EFL to 25 mm and further improve the imaging quality. The curvatures of S3, S4, S5, and S6 were set as independent variables to increase the optimization degree of freedom. As shown in Fig. 7(a), each lens of the one-loop optimized system has a positive edge thickness. Figure 7(b) presents the spot diagram. Compared with the starting point, the spots size of all sampled fields were significantly reduced. The image quality of the center field was significantly improved, and the spot size was less than one pixel.
The glass expert macro in CODEV is useful for exploring the choice of glass material for each lens. We limited the materials to the optical polymer to reduce the weight. Furthermore, considering the requirements for low stress birefringence in polarized optical path, we set a user-defined glass catalog (UDGC), including APEL, EP-XR10, EP7000, and OPTIMAS7500, as replacement materials. The glass of the lens was replaced with the material within the UDGC, and after optimization, the system with the smallest error function was saved. Thereafter, we replaced it with the other materials one by one in the UDGC for optimization until all the materials in the UDGC were tested. The system with the smallest error function was chosen as the starting point for the next design stage. Figure 8 shows the variation of error function in the process of glass replacement optimization. The error function decreased significantly from 250 to 165 during the first few optimization loops.
Figures 9(a) and (b) show the optical layout and spot diagram evaluated after the glass exploration process. The polychromatic RMS spot sizes were significantly reduced. Thereafter, we upgraded the surfaces of L1 and L2 from sphere to asphere and gradually increased the aspherical polynomial order. To improve the fabricability of the lens, the first derivative and the second derivative of the surface were constrained to avoid curvature inflection of the surface shape and form a seagull surface. We also controlled the clearance of the system to create sufficient space for the later optimization for other positions with different diopters, to ensure that the final lens would not physically interfere and collide with the display during the diopter adjustment process.
Fig. 9. (a) Optical path of the structure after glass replacement, (b) Spot diagram, (c) The optical path of the structure after optimization, (d) Spot diagram after optimization.
To further improve the image quality, the L3 material was replaced with glass material. The optimized system optical layout and spot diagram are shown in Figs. 9(c) and (d), respectively. The spot size at the marginal field, reduces from 373 µm to 143 µm. The RMS spot gradually increases from the center field to the marginal field, which meets the human observation habit.
The system discussed above was only designed with one virtual image distance of -1 D. Further, we set the optical system with multiple object distances to analyze the optical performance for users with different eyesight. Figure 10(a) shows the RMS spot size at different diopters, as the diopter value decreases, the RMS spot size of the marginal field increases to 450 µm at -7 D.
Fig. 10. Spot size of each diopter at different FOV (a) Before optimization, (b) After optimization.
For the last optimization stage, the distance between the display and L3 was varied and zoomed for different virtual image distances for different diopters. In addition, the exit pupil position was shifted, and a 4 mm exit pupil was used to simulate the movement of the human eye in the entire 10 mm exit pupil. The decenter of the exit pupil zoom positions was set to +1, +2, and +3 mm in the radial direction. Finally, the multi-configuration system with different diopters and exit pupil positions was further optimized.
4.2 Design results and performance analysis
After balancing the imaging quality and fabrication requirements, we completed the optical design and obtained an ultra-thin, large FOV, high-resolution VR-HMD system that has good optical performance, and can achieve low cost and mass production. The final optical powers of the three lenses are calculated by averaging the power of the three lens positions, the center, half, and marginal aperture, as described in Eq. (9) and compared with the system power. There is some difference between the optical powers calculated in Eq. (5) and Eq. (9). Because the calculation model in Eq. (5) used spherical thin lenses and does not consider the influence of lens thickness, material and asphericity.
Figure 10(b) plots the RMS spot sizes at different diopters: -1 D, -2 D, -4 D, and -7 D. It can be observed that after integrated optimization, the spot sizes of each diopter are well balanced, and the imaging quality of other diopters have been greatly improved. In particular, at the position of -7 D, the maximum RMS spot size considerably decreased from 470 µm to 160 µm.Figure 11 demonstrates the design result and optical performance at position of -1 D, including the distortion grid, lateral color aberration, and polychromatic and central-wavelength MTF curves. The distortion curve of the optical system shown in Fig. 11(b) is less than 24% and regular, which is difficult to constrain in the design process, however, it can be easily corrected using the digital method. The lateral color aberration is less than 80 µm, as shown in Fig. 11(c), similarly, it can also be corrected using the digital method. The center MTF of the system is close to the diffraction limit at a spatial frequency of 10.4 cycles/mm, as shown in Figs. 11(d) and (e), and the worst MTF close to 0.2 is at the marginal field, which represents a good resolution. In the process of exit pupil position shift, the MTF of the optical system decreases slightly, as shown in Fig. 12, and it does not change significantly, indicating that the system has a good display quality and compatibility.
Fig. 11. Image quality of -1 D simulation in CODEV. (a) Final optical system. (b) Distortion curve. (c) Lateral color aberration curve. (d) MTF curve within the range of visible wavelength. (e) MTF curve at the central wavelength of 532 nm.
Fig. 12. MTF@10.4 cycles/mm with the 4 mm exit pupil offset of 1 mm, 2 mm, and 3 mm at -1 D. (a) +1 mm, (b) +2 mm, (c) +3 mm.
4.3 Definition and analysis of pupil swim
Because the chief ray aberration of each position is different, the incident angle of the ray emitted from the same pixel on the display varies when the human eye moves in the eye box, which makes the rays focus on different positions of the retina, resulting in a “swimming” sensation of the image, thus it is called “pupil swim” [28]. Figure 13 shows how the image changes as the eye moves, and Fig. 13(a) shows an ideal viewing situation. Compared with Fig. 13(a), when looking at the other directions, as shown in Fig. 13(b), or as shown in Fig. 13(c), for people whose IPD is larger or smaller than that of the system, the eyes will deviate from the center of the exit pupil. Thereafter, owing to the pupil swim, the image moves, and the imaging depth is inconsistent with the initial VID. Furthermore, the binocular alignment difference of each image point is disorderly and will result in an uncomfortable experience. Figure 13(d) shows how the image moves when the pupil moves within the eye box. Pupil swim exists in almost all near-eye display systems, and this phenomenon directly affects user experience.
Fig. 13. Brief sketch of how the image changes. (a) When viewed in an ideal position, (b) When looking to the left, (c) When a person with a large interpupillary distance looks at it and (d) When pupil moving within the eye box.
Because the system is rotationally symmetric, adding an offset to the central exit pupil in the radial direction can simulate the linear translation of the human eye in the eye box.
The first and most important impact of the pupil swim is the change in imaging distortion. To quantitatively evaluate the effect of pupil swim, the method of reverse tracing rays is used to obtain the chief ray angle (CRA), so that the changes in CRA of each field at different positions in the eye box can be obtained, and the pupil swim can be observed more intuitively, as shown in Fig. 14. The Z-axis represents the variation of CRA, which is the difference of the CRA between the offset position and the center of the eye box.
The CRA of each field at different pupil positions exhibits a certain change, and the change is non-linear. The CRA at 0.3 to 0.5 relative field changes relatively obvious. This is because, to improve the imaging quality of the marginal field, the marginal field was provided a higher weight during optimization, and the central field was ignored to a certain extent. Different diopters exhibited varying degrees of variation. The CRA changes of -1 D, -2D, and -4 D are slight and less than 0.3°, respectively. For -7 D, the CRA has a relatively large variation when the offset distance exceeds 2 mm, thus the user will perceive a slight pupil swim when the eyes move to the edge of the eye box.
To further observe the influence of pupil swim on imaging quality, we utilized the spot diagrams under different offset positions for evaluation, as shown in Fig. 15.
The spot size of 0.4 relative field changes by a factor of approximately two, thus the user might perceive a slight “swimming” sensation of the image. When the human eye moves to the edge of the exit pupil, the imaging quality deteriorates, especially at the marginal fields. With the variation of the pupil position, the spot size of the other fields changes slightly and is negligible.
In summary, it can be observed from the results of the CRA and imaging quality changes at various offset positions under different diopters that the pupil swim of this system is relatively slight and can meet the requirements of use.
4.4 Tolerance analysis
Tolerance analysis is used to systematically evaluate the influence of different perturbations or defects on the performance of optical system and determine the reasonable limits for fabrication and alignment errors. It plays an important role in system design because it is directly related to the difficulty of design, optical fabrication, alignment, and processing cost.
Unlike the general optical system, parts of the optical surfaces are reused in the catadioptric optical system. The tolerances added to the reused surfaces should be consistent by the setting of “pickup” and grouped tolerances. The position and tilt of the display were defined as the compensators.
The tolerance of the catadioptric system was analyzed in two stages: first, the default tolerance and specified tolerance items based on the characteristics of the catadioptric system were added, the numeric ranges can be obtained through reverse sensitivity analysis and interactive tolerance analysis, and then perturbations were added to the sensitive items to re-optimize the system. Second, appropriately tightened the tolerances of higher-sensitivity items based on the fabrication capabilities. The two-stage analysis can clearly show the influence of various tolerances, directly obtain the guidance of re-optimization, and adjust the tolerance items carefully to achieve the maximum coordination between optical performance and fabrication costs.
The sensitive items for each tolerance type are shown in Table 3. Among the different tolerances, surface sag error (DLS), surface tilt (DLA, DLB), and barrel tilt (BTX, BTY) tolerance are more sensitive than others. 2000 Monte Carlo simulation trials were carried out, and Fig. 16 shows the cumulative probability for different MTF values under the conditions in Table 3. The MTF for all fields has a 94% chance of being above 0.15, and the probability of center MTF larger 0.9 is more than 93% at the center of the eye box, as shown in Fig. 16(a). When the pupil was at the edge of the eye box, the MTF curve was still relatively steep, indicating that the MTF consistency was good, except for the reasonable changes in the marginal field, as shown in Fig. 16(b). Because of the higher weights added to the marginal field during optimization, the image quality of the marginal field remained good after the pupil moved to the edge of the eye box, while the image quality of the middle field slightly worsen. However, the MTF value with tolerance disturbance is consistent, which indicates that the tolerance range is reasonable. Although the tolerances are relatively stringent, the tolerance curve is steep with the using of the compensators, thus the requirements can be met by using active alignment equipment during mass processing.
Fig. 16. Changes of MTF value for tolerance analysis at different field. (a) pupil was at the center of the eye box, (b) pupil was at the edge of the eye box
Table 3. Sensitive items of each type of tolerance
5. Prototype and experimental results
A lens system was fabricated and developed in this study. The system finally adopts a glass-plastic hybrid form to balance the optical performance and weight requirements. Figures 17(a) and (b) show the prototype and optomechanical design of the compact catadioptric VR-HMD module. Compared with traditional VR optics, the system is thinner and lighter, and its thickness is only approximately 1/3 that of traditional VR optics, as shown in Fig. 17(c).
Fig. 17. (a) Optomechanical design of catadioptric VR-HMDs, (b) Prototype of catadioptric VR-HMDs, (c) Catadioptric VR optics VS traditional VR optics.
A camera with a 4 mm pupil in front of the lens was used to measure the image sharpness under different diopter conditions. The camera was located at the exit pupil of the catadioptric system. Figure 18(a) shows the image on the display, and Fig. 18(b) shows a photo taken at the exit pupil position, which shows an ultra-high performance. Furthermore, we chose a high-contrast picture with white characters on a black background, as shown in Fig. 18(c), for stray light testing. Figure 18(d) shows that the stray light of the system is minimized.
Fig. 18. Experimental demonstration. (a) Test original image on the display, (b) Virtual image captured by camera, (c) A high-contrast picture on the display, (d) High performance of the stray light elimination.
6. Conclusion
In this study, we designed a compact catadioptric VR-HMD system with a wide FOV, large EPD, and good image quality. The diagonal FOV was 96°, with a 10 mm EPD. The lens system is compact and lightweight, with an overall thickness of less than 20 mm and a weight of 20 g per eye. The novel optical structure construction and the design methods were thoroughly discussed in four stages: 1) the starting point from the theoretical paraxial calculation, 2) glass material replacements, 3) surface upgradation from sphere to asphere, 4) integrated design with multiple virtual image distance. The design results were comprehensively analyzed and experimentally tested, and the results demonstrated good performance and compact sunglass form. The methods of birefringence and stray light elimination will be discussed in a future study. We believe that this catadioptric design will replace traditional VR lenses, and greatly promote the VR industry in recent years.
Funding
National Key Research and Development Program of China (2021YFB2802101); National Natural Science Foundation of China (61822502); Beijing Municipal Science and Technology Commission (Z201100004020011); Young Elite Scientist Sponsorship Program by CAST (2019QNRC001).
Acknowledgments
We would like to thank Synopsys for providing the education license of CODE V.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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. B. C. Kress, “Optical architectures for augmented-, virtual-, and mixed-reality headsets,” (SPIE Press Book, 2020).
2. O. Cakmakci and J. Rolland, “Head-worn displays: a review,” J. Disp. Technol. 2(3), 199–216 (2006). [CrossRef]
3. H. Hua, L. D. Brown, and C. Gao, “Scape: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graph. Appl. 24(1), 66–75 (2004). [CrossRef]
4. D. Cheng, Q. Wang, Y. Liu, H. Chen, D. Ni, X. Wang, C. Yao, Q. Hou, W. Hou, G. Luo, and Y. Wang, “Design and manufacture AR head-mounted displays: A review and outlook,” Light: Adv. Manuf. 2, 24 (2021). [CrossRef]
5. T. Zhan, Y. Kun, J. Xiong, Z. He, and S. Wu, “Augmented reality and virtual reality displays: perspectives and challenges,” iScience 23(8), 101397 (2020). [CrossRef]
6. 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, “A freeform OST-HMD system with large exit pupil diameter and vision correction capability,” Photon. Res. 10(1), 21–32 (2022). [CrossRef]
7. H. Hua and B. Javidi, “Augmented reality: easy on the eyes,” Opt. Photon. News 26(2), 26–33 (2015). [CrossRef]
8. 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]
9. A. Sisodia, A. Riser, M. Bayer, and J. P. McGuire, “Advanced helmet mounted display (AHMD) for simulator applications,” Proc. SPIE 6224, 62240O (2006). [CrossRef]
10. V. Elia, M. G. Gnoni, and A. Lanzilotto, “Evaluating the application of augmented reality devices in manufacturing from a process point of view: an AHP based model,” Expert Syst. Appl. 63(187), 187–197 (2016). [CrossRef]
11. M. Bajura, H. Fuchs, and R. Ohbuchi, “Merging virtual objects with the real world: Seeing ultrasound imagery within the patient,” Comput. Graphics 26(2), 203–210 (1992). [CrossRef]
12. A. J. Lungu, W. Swinkels, L. Claesen, P. Tu, J. Egger, and X. Chen, “A review on the applications of virtual reality, augmented reality and mixed reality in surgical simulation: an extension to different kinds of surgery,” Expert Rev. Med. Devices 18(47), 47–62 (2021). [CrossRef]
13. T. Sielhorst, M. Feuerstein, and N. Navab, “Advanced medical displays: a literature review of augmented reality,” J. Display Technol. 4(4), 451–467 (2008). [CrossRef]
14. J. Xiong, E. Hsiang, Z. He, T. Zhan, and S. Wu, “Augmented reality and virtual reality displays: emerging technologies and future perspectives,” Light: Sci. Appl. 10(1), 216 (2021). [CrossRef]
15. Y. Wang, “Design of a viewing lens for virtual reality,” Proc. SPIE 2778, 277810 (1996). [CrossRef]
16. J. Hecht, “Optical dreams, virtual reality,” Opt. Photon. News 27(6), 24–31 (2016). [CrossRef]
17. Y. Wang, W. Liu, X. Meng, H. Fu, D. Zhang, Y. Kang, R. Feng, Z. Wei, X. Zhu, and G. Jiang, “Development of an immersive virtual reality head-mounted display with high performance,” Appl. Opt. 55(25), 6969–6977 (2016). [CrossRef]
18. M. Karpman and B. Wells, “Virtual displays for entertainment applications: hitting cost/performance with LED arrays,” Proc. SPIE 3000, 161–168 (1997). [CrossRef]
19. A. Rendon, E. Lohman, D. Thorpe, E. Johnson, E. Medina, and B. Bradley, “The effect of virtual reality gaming on dynamic balance in older adults,” Age Ageing 41(4), 549–552 (2012). [CrossRef]
20. P. Wang, W. Peng, J. Wang, H. Chi, and X. Wang, “A critical review of the use of virtual reality in construction engineering education and training,” Int. J. Environ. Res. Public Health 15(6), 1204 (2018). [CrossRef]
21. L. Jensen and F. Konradsen, “A review of the use of virtual reality head-mounted displays in education and training,” Educ. Inf. Technol. 23(4), 1515–1529 (2018). [CrossRef]
22. X. Li, W. Yi, H. Chi, X. Wang, and P. Chan, “A critical review of virtual and augmented reality (VR/AR) applications in construction safety,” Autom. Constr. 86, 150–162 (2018). [CrossRef]
23. S. Choi, K. Jung, and S. Noh, “Virtual reality applications in manufacturing industries: past research, present findings, and future directions,” Concurrent Eng. 23(1), 40–63 (2015). [CrossRef]
24. C. Yao, D. Cheng, and Y. Wang, “Matrix optics representation and imaging analysis of a light-field near-eye display,” Opt. Express 28(26), 39976–39997 (2020). [CrossRef]
25. A. Maimone and J. Wang, “Holographic optics for thin and lightweight virtual reality,” ACM Trans. Graph. 39(4), 1–14 (2020). [CrossRef]
26. J. Zou, T. Zhan, E. Hsiang, X. Du, X. Yu, K. Li, and S. Wu, “Doubling the optical efficiency of VR systems with a directional backlight and a diffractive deflection film,” Opt. Express 29(13), 20673–20686 (2021). [CrossRef]
27. K. Bang, Y. Jo, M. Chae, and B. Lee, “Lenslet VR: thin, flat and wide-FOV virtual reality display using Fresnel lens and lenslet array,” IEEE Trans. Visual. Comput. Graphics 27(5), 2545–2554 (2021). [CrossRef]
28. Y. Geng, J. Gollier, S. Mcnally, B. Bryars, and S. Mceldowney, “Field curvature corrected display,” U.S. Patent 0,255,015A1 (7 September 2017).
29. O. Cakmakci, Y. Qin, P. Bosel, and G. Wetzstein, “Holographic pancake optics for thin and lightweight optical see-through augmented reality,” Opt. Express 29(22), 35206–35215 (2021). [CrossRef]
30. J. Xiong and S. Wu, “Planar liquid crystal polarization optics for augmented reality and virtual reality: From fundamentals to applications,” eLight 1(1), 3–20 (2021). [CrossRef]
31. Q. Li, W. He, H. Deng, F. Zhong, and Y. Chen, “High-performance reflection-type augmented reality 3D display using reflective polarizer,” Opt. Express 29(6), 9446–9453 (2021). [CrossRef]
32. T. Wong, Z. Yun, G. Ambur, and J. Etter, “Folded optics with birefringent reflective polarizers,” Proc. SPIE 10335, 103350E (2017). [CrossRef]
33. Y. Geng, J. Gollier, B. Wheelwright, F. Peng, Y. Sulai, B. Lewis, N. Chan, W. S. T. Lam, A. Fix, D. Lanman, Y. Fu, A. Sohn, B. Bryars, N. Cardenas, Y. Yoon, and S. McEldowney, “Viewing optics for immersive near-eye displays: pupil swim/size and weight/stray light,” Proc. SPIE 10676, 5 (2018). [CrossRef]
34. J. LaRussa, “Infinite optical image-forming apparatus,” U.S. Patent 3,443,858 (13 May 1969).
35. J. LaRussa and A. Gill, “The holographic catadioptric window TM,” Proc. SPIE 0162, 120–129 (1978). [CrossRef]
36. W. Roest, “Head-mounted display with a polarization-dependent mirror,” U.S. Patent 6,710,928 (23 March 2001).
37. R. Huxford, “Wide-FOV head-mounted display using hybrid optics,” Proc. SPIE 5249(1), 230–237 (2004). [CrossRef] .
38. B. Narasimhan, “Ultra-compact pancake optics based on ThinEyes super-resolution technology for virtual reality headsets,” Proc. SPIE 10676, 134 (2018). [CrossRef]
39. Y. Li, T. Zhan, Z. Yang, C. Xu, P. LiKamWa, K. Li, and S. Wu, “Broadband cholesteric liquid crystal lens for chromatic aberration correction in catadioptric virtual reality optics,” Opt. Express 29(4), 6011–6020 (2021). [CrossRef]
40. H. Gross, Handbook of optical systems: fundamentals of technical optics (Wiley-VCH Verlag GmbH & Co, KGaA, 2015), Vol. 1.
41. Synopsys, Inc., CODE V, Reference manual (Synopsys, 2021).
