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We propose a see-through near-eye display, which is dedicated to the visually impaired users who suffer from refractive anomalies. Our solution is characterized by a pair of corrective lenses coated with multiplexed volume holograms. Its key performance including diffraction efficiency, field of view, modulation transfer function, and distortion has been studied.
© 2017 Optical Society of America
1. Introduction
Augmented reality (AR) [1] is a technology that merges the digital information with the real world in real time. See-through near-eye display (NED) [2–4] is a key component of AR, through which the computer-generated images or videos are displayed on top of the existing environment. Unlike flat panel displays, such as liquid crystal display [5], NED is wearable and very close to the eyes. Therefore, not just the optical performance of the displays but also the vision acuity of the users needs to be considered. According to a recent study on the global prevalence of myopia―also known as nearsightness―half of the world’s population will be nearsighted by 2050 [6]. Unfortunately, with current NED solutions [7–16], users, who are more or less visually impaired, are required to wear extra eyeglasses. If doing so, both the user experience and device performance will be deteriorated, as the device becomes bulky and the eyes are further from the exit pupil [17]. Microsoft’s Hololens [18], among others, is such an example for being not quite friendly to visually impaired users. They have to squeeze their eyeglasses into the headset and worry about the deformation and scratch. The worse thing is that the image they see is sometimes not as big as the one seen by eyeglasses-less users. This is because part of the field of view (FOV) would be blocked by the frames of both Hololens and eyeglasses. As an alternative, users can choose to wear contact lens or even contact-lens-like NED [19]. But for aged people, it might not be a wise option for their eyes are dry and the removal of the contact lens is inconvenient.
Motivated by the above issue, we propose a compact design of see-through NED, which features a pair of corrective lenses coated with multiplexed volume holograms. With this design, for those who have refractive anomalies―e.g. myopia and hyperopia―extra eyeglasses or contact lens are no more needed. Based on numerical simulations, its FOV, modulation transfer function (MTF), and distortion have been evaluated.
2. Operational principle
2.1 Proposed structure
Figure 1 outlines the structure of the proposed monocular see-through NED, where θ is an angle intersected by the central or optical axis of the corrective lens and that of the projection lens, s2 is the distance between the projection lens and corrective lens, and s3 is the distance between the corrective lens and eye. The pico projector consists of a micro-display and a 4-element projection lens [20], as depicted in Fig. 2. The corrective lens is used for compensating the refractive anomalies of the eyes. They can come in a variety of shapes and designs, depending on the visual acuity and preference of the user. By way of example, a divergent lens with negative power for correcting the myopia is adopted. The volume hologram is coated on the inner surface of the corrective lens in order to reflect the light toward the eye. Alternatively, it can be also coated on the outer surface of the corrective lens.
Fig. 1 Schematic drawing of the proposed monocular see-through NED. θ is an angle intersected by the central or optical axis of volume hologram and that of the projection lens, s2 is the distance between the projection lens and corrective lens, and s3 is the distance between the corrective lens and eye.
Fig. 2 Schematic drawing of the pico projector. The pico projector consists of a micro-display and a 4-element projection lens.
2.2 Design rules
Since the potential users of NEDs are most likely nearsighted, the design rules for the case of myopia are to be explained. By unfolding the optical paths from Figs. 1 & 2, the equivalent, coaxial optical path diagrams for the real and virtual images are illustrated by Figs. 3(a) and 3(b), respectively, where the 4-element projection lens is briefly described as a single lens for the sake of clarity. For the real image, light rays emitting from the real object should be diverged by a corrective lens before arriving the eyes. The diopter or optical power Pc of the corrective lens is related to the visual acuity and it can be obtained directly from the eyeglass prescription. The design of the corrective lens shall follow from the lensmaker’s equation [21], as given by Eq. (1)
where fc is the focal length of corrective lens, nc and nair, in turn, denote the refractive indices of corrective lens and air, and R1 and R2 are the radii of curvature of first and second surfaces of the corrective lens, respectively. In order to be consistent with Eq. (1), spherical surfaces are adopted for the corrective lens. For the virtual image, light rays emitting from the microdisplay will be first converged by the projection lens, forming an intermediate magnified virtual image S′, and then be reflected by the volume grating, which is regarded as a spherical mirror, forming the final magnified virtual image S″ received by the eyes. The distance s′, defined as the distance between the image S′ and projection lens, can be determined from the thin-lens equation [21] aswhere s1 is the distance between the microdisplay and projection lens, and Pp is the diopter of projection lens. Similarly, the distance s″, defined as the distance between the image S″ and eye, can be derived asThe lateral magnification m―defined as the ratio of lateral size of S″ to lateral size of microdisplay―can be written asFig. 3 Unfolded optical path diagrams for the (a) real and (b) virtual images. The 4-element projection lens is briefly described as a single lens for the sake of clarity.
To sum up, our design rules involve the following steps. First, determine the diopter of corrective lens. Second, specify the surface shapes and refractive index of corrective lens using Eq. (1). Third, determine the target value of image distance and predefine the positions of each component. Fourth, calculate the diopter of projection lens using Eq. (3). Fifth, set up the target value of one or more constraints―e.g. effective focal length, distortion etc.―and perform the optimization for all variables. Sixth, evaluate the performance. Apart from myopia, the above design rules can be applied to hyperopia as well. In this case, without changing correction lens’ second surface, we only need to re-design its first surface to produce positive power. As for astigmatism, correction lens needs to be cylindrical [21].
2.3 Corrective lens
Consider a case that the user has only 3 diopters of myopia, disregarding the astigmatism and other types of refractive anomalies. The material of lens is chosen as the polycarbonate, which is predominantly used for eyeglasses. The shape of lens is meniscus, which has a steeper concave surface and a thinner thickness at the center than at the periphery. Compared to plano-concave and biconcave, meniscus is more acceptable for the consumer market for both aesthetic and weight reasons [22]. Our design wavelength is set as 532 nm. Following the above design rules, a corrective lens can be designed using the parameters as given in Table 1.
Table 1. Parameters used for the corrective lens
2.4 Projection lens
Referring to Fig. 2, a 4-element projection lens design, consisting of four different lenses, is adopted. Once the distances s1 and s2 are predefined―say 3.8 mm and 20 mm, respectively―by using Eqs. (3) and (4), the image distance S″ and lateral magnification m can be calculated as a function of the diopter of projection lens Pp, as shown in Figs. 4 and 5, respectively. It can be seen that when Pp approaches 278.92 m−1, at which the focal length of projection lens is close to s1, the image distance will be the infinity. In order for the image to be a magnified virtual image, Pp has to be less than 278.92 m−1―or in other words, the microdisplay should be placed within or nearby the focal length of projection lens. If the target value of image distance S″ is set as 3 m, this will roughly correspond to Pp = 278.35 m−1 and m = 604.32.
Fig. 4 Image distance versus the diopter of projection lens. It can be seen that when Pp approaches 278.92 m−1, at which the focal length of projection lens is close to s1, the image distance will be the infinity.
Fig. 5 Lateral magnification versus the diopter of projection lens. If the target value of image distance S″ is set as 3 m, this will roughly correspond to Pp = 278.35 m−1 and m = 604.32.
2.5 Volume hologram
Volume hologram plays a critical role in our solution, as it would significantly affect FOV and overall light utilization. Whereas it is considered as a spherical mirror for tracing light rays as above, its diffractive properties have to be analyzed using the physical optics―e.g. Fourier modal method [22–24]―rather than the geometrical optics. The design of volume hologram shall follow from the Bragg’s law, which is expressed as
where θB denotes the Bragg angle, n is a positive integer, λ is the incident wavelength in the free space, Λ is the period of hologram, λc is the construction wavelength, θr and θo are the incident angles of reference and object waves, respectively. For achieving full-color volume hologram, wavelengths of red (R), green (G), and blue (B) colors are supposed to match with the same Bragg angle. To satisfy this condition when n = 1, it requires that λ∙sin((θr-θo)/2)/λc be a constant. For achieving wide-angle volume hologram, different Bragg angles are supposed to match with the same incident and construction wavelengths. To satisfy this condition when n = 1, it requires that sin(θB)/sin((θr-θo)/2) be a constant. Since a single hologram could only satisfy one Bragg’s condition [25], to achieve either full-color or wide-angle, multiplexing or stacking of multiple holograms is inevitable.3. Results and discussion
3.1 Simulation settings
Our simulation is implemented with the softwares Code V (Synopsys) and VirtualLab (Wyrowski Photonics). The former deals with the ray tracing for analyzing the imaging properties, including MTF, distortion, and imaging simulation. Although Code V could handle several types of gratings by using Kogelnik’s coupled-wave theory [26], for a more exact analysis, VirtualLab is used separately for calculating the diffraction efficiency (DE) of volume holograms.
Figure 6 plots a two-dimensional (2D) view of our NED, with the numbering of all surfaces being labelled. A 0.47″ microdisplay with an aspect ratio of 16:9 is employed. According to the design rules said before, we could create an initial structure by presetting the parameters for each object. Then, an optimization, whose error function type is set as transverse ray aberration [27], is carried out by constraining the effective focal length fe of the whole system as the desired value―i.e. 17.56 mm―and distortion less than 1%. The parameters after the optimization are listed in Table 2. Besides, more detailed parameters for defining aspherical surfaces are listed in Table 3.
Fig. 6 2D view of the proposed NED. The numbering of all surfaces is labelled either as their original names or as numbers.
Table 2. Optimized parameters for the proposed NED
Table 3. Parameters for aspherical surfaces
3.2 Diffraction efficiency
In order to realize a full-color display, the wavelength multiplexing is employed. From Eq. (7), three volume holograms can be constructed to reflect R/G/B colors, as defined in Table 4, where d is the thickness, Δn denotes the refractive index modulation―the difference between the maximum and minimum refractive indices, θr is 0°―coincident with the normal of the hologram center―and θo = θ = 50°―approximated by assuming s2 = 20.16 mm and s3 = 12.96 mm and that s2 and s3 would form a right triangle, as shown in Fig. 1. It should be noticed that s3 is a variable, as the headset where NED is mounted must be adjustable. In order to broaden the angular bandwidth, the angular multiplexing is employed. Similarly, three volume holograms can be constructed to exhibit different Bragg angles, as defined in Table 5. Following the Fourier modal method, individual DEs ηR/G/B for each hologram are calculated with respect to the wavelengths and incident angles, respectively, as shown in Fig. 7 and Fig. 8. When three holograms are multiplexed, the overall DE η shall be written as
Table 4. Parameters of volume holograms used for wavelength multiplexing
Table 5. Parameters of volume holograms used for angular multiplexing
Fig. 7 Calculated DE with respect to wavelengths. For wavelength multiplexing, the wavelength bandwidths of R/G/B colors for individual DE>10% are 13 nm (637~649 nm), 12 nm (536~547 nm), and 14 nm (462~475 nm), respectively.
Fig. 8 Calculated DE with respect to incident angles. For angular multiplexing of green color, the angular bandwidth for overall DE>10% is 33° (36~68°).
For wavelength multiplexing, the wavelength bandwidths of R/G/B colors for individual DE>10% are 13 nm (637~649 nm), 12 nm (536~547 nm), and 14 nm (462~475 nm), respectively. For angular multiplexing of green color, the angular bandwidth for overall DE>10% is 33° (36~68°).
3.3 Field of view
FOV of our NED is defined as the angular extent of the image of microdisplay that is observed by the fixed eyes. It may be measured horizontally, vertically, or diagonally, and it could also be directly calculated as follows [27]
where dm represents the size of microdisplay measured in a given direction. For our case, the diagonal FOV is approximately 38°―or equivalently 33° measured horizontally―which well matches with the above angular bandwidth of the multiplexed volume holograms.3.4 Modulation transfer function
By computing Fourier transform of the line spread function, the diffraction MTFs of real and virtual images at the central and marginal angles are plotted in Fig. 9(a) and Fig. 9(b), respectively, where MTFs of real images for all angles are above 0.4 at 150 cycles/mm, and MTFs of virtual images for all angles are above 0.4 at 6 cycles/mm.
Fig. 9 Calculated MTFs of (a) real and (b) virtual images. For real images, MTFs for all angles are above 0.4 at 150 cycles/mm. For virtual images, MTFs for all angles are above 0.4 at 6 cycles/mm.
3.5 Distortion
Distortion grids of real and virtual images, defined as the displacement of image height or ray location, are plotted in Fig. 10(a) and Fig. 10(b), respectively, where distortion of real images is less than 0.15%, and distortion of virtual images is less than 0.63%.
Fig. 10 Calculated distortion grids of (a) real and (b) virtual images. For real images, distortion is less than 0.15%. For virtual images, distortion is less than 0.63%.
3.6 Simulated imaging
For a qualitative analysis of imaging quality, both real and virtual images are visualized from the imaging simulation that takes into account the effects of distortion, aberration blurring, diffraction blurring, and relative illumination, as shown in Fig. 11(b) and Fig. 11(c). By comparing the original and simulated images, it can be seen that the distortion is almost unnoticeable, while the brightness is reduced and blurring is more apparent for the virtual image, which agrees with the foregoing results.
Fig. 11 (a) Original, (b) real, and (c) virtual images. By comparing the original and simulated images, it can be seen that the distortion is almost unnoticeable, while the brightness is reduced and blurring is more apparent for the virtual image, which agrees with the foregoing results.
4. Conclusion
A compact design of see-through NED, featuring a pair of corrective lenses coated with multiplexed volume holograms, has been proposed. Based on the simulation, its optical performance including DE, FOV, MTF, and distortion has been studied. By eliminating the need for extra glasses or contact lens, this type of see-through NED could be particularly appealing to the users who are more or less visually impaired. In addition to myopia, our future work will extend to hyperopia, presbyopia, astigmatism, and combinations of different refractive anomalies.
Funding
National Natural Science Foundation of China (NSFC) (61307028).
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