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Abstract
Head-mounted display (HMD) has been widely used in many fields, and most existing HMDs are complex and typically non-aesthetically pleasing. In this paper, a novel compact, lightweight and wearable off-axis HMD with freeform surface is reported. It is challenging to achieve large field of view (FOV) and maintain compact structure simultaneously for this type system. In this design, the compact off-axis HMD consists of a tilted ellipsoid combiner and a four pieces relay lenses. It offers a diagonal FOV of 30°, and an exit pupil diameter of 7 mm. No diffractive surfaces are used, thus avoiding the effect of stray light and ghost image in previous designs. The x-y polynomial freeform surface is adopted in the relay lens for improving the image quality and minimizing the structure size. Analytical expressions to determine the initial structure of HMD has been given, while structure constrains, optimization strategy and tolerance analysis are also described in details. The optical system is easy to manufacture by ordinary method which is beneficial for mass production. Further, a prototype of this compact HMD is successfully implemented with good imaging performance. The compact structure of HMD makes it well suited for integrating a normal glass, significantly advancing the application of HMD in people’s daily life.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, technological advancements, especially the emergence of various HMDs, have made augmented reality (AR) more feasible in people’s daily life [1–4]. For AR applications, the HMD works in a see-through model which superimposes a virtual image on the real-world scene, and therefore allows the users to see the virtual image of the digital information and real-world scene simultaneously, even 3D display with focus cues [5–7]. The see-through HMD immerses the user by providing digital image information, and has gained wide popularity in many fields (i.e., military, education, medical and tourism, et al). Nowadays, a series of HMDs have been commercially available, such as Google Glasses [8], Microsoft Hololens [9], Epson Moverio [10,11] and Lumus DK50 [12] et al.
As the commercial products, the HMDs are expected to be compact and light but without sacrificing their performance, which is a challenging task for the HMD designers. Different approaches have been developed by both academia and industry to optimize the design of HMDs [13]. For instance, Cheng et al proposed a HMD design using freeform surface prism [14, 15]. Amitai et al used partial reflecting surfaces on a waveguide plate [16, 17]. Microsoft, Sony and BAE have adopted the diffractive or holographic waveguide plate [18–20]. Besides, the off-axis combiner type HMD has stood out with large FOV and pupil size. In 2010, Zheng et al reported an off-axis see-through HMD with 40° × 30° FOV and 70 mm eye relief by using x-y polynomial surface [21]. In 2015, Wang et al developed a lightweight, see through HMD which is composed of a 7-pieces coaxial relay lens group and a freeform surface combiner, achieving a 40° × 30° FOV and 15 mm exit pupil diameter [22]. However, limitations are found with these reported HMDs. First, the freeform surface prisms, typically with five freeform surfaces, are complex and difficult to design and fabricate. Second, waveguide HMD has a limited FOV, largely because of the stray light or chromatic aberrations [23]. Moreover, the triangular or trapezoids microstructures in the waveguide are hard to manufacture [24]. The aforementioned off-axis combiner HMDs are very complex-structured and bulky. More critically, the structures of above HMDs deviate from the “normal glass”, and they are typically non-aesthetically pleasing, making them impractical for everyday use [25].
To design a normal glass alike HMD, Cakmakci et al designed and fabricated a compact off-axis combiner-based HMD which can be packaged inside of the glass frame [26]. It contains a freeform mirror and a diffractive optical element with an 8 mm pupil and a 20° diagonal FOV. McGuire et al proposed a compact off-axis HMD prototype with 20° FOV which use 5 optical elements in the relay lens, and another optical design of 40° diagonal FOV with freeform and diffractive surfaces [27]. However, the FOV of existing compact off-axis HMDs prototype is small (20° diagonal), which is not sufficient for the AR applications. The diffractive surface causes unwanted stray light which decreases the imaging quality. Moreover, few literatures are available for constructing a starting point for such compact off-axis HMDs, which is important for the freeform optical system optimization. Overall, it is challenging to design a compact off-axis combiner HMD with a large FOV, low F-number, and maintain compact structure simultaneously for this type system. In order to solve these problems and design a normal glass HMD, we present a new optical design for the compact off-axis HMD.
In this paper, we present a compact off-axis combiner HMD using freeform surfaces a diagonal FOV of 30°, an exit pupil diameter of 7 mm, and an eye relief of 30 mm. This design does not use the diffractive surfaces, thus avoiding the effect of stray light and ghost image in previous designs. Based on the paraxial optical theory, the coaxial initial optical structure is established to facilitate off-axis freeform system design [28, 29]. We use the rotational symmetric lens group in the relay lens and simple tilt combiner to reduce the volume and manufacture difficulty. Further, the method how to determine surface type of each surface in the optical system is explained in detail. An x-y polynomial surface, which is close to a 0.39 in. OLED (organic light emitting display), is used to lower the F-number, expand the FOV and compensate the off-axis aberrations. The structure constrains, optimization strategy and tolerance analysis are discussed in detail. Based on the tolerance analysis results, the optical system can be fabricated and alignment by ordinary method. We also demonstrate the performance of the prototyped optical system. The compact structure of HMD makes it well suited for integrating a normal glass, significantly advancing the application of HMD in people’s daily life.
2. Design of compact off-axis augmented reality glass
2.1 System specifications
Figure 1 shows the two-dimensional optical layout of the off-axis compact HMD optics in the YOZ plane. There are two ray paths in the system. The first ray path is for the projection system through which the image on the microdisplay is magnified and projected into user’s eye. The second ray path is the see-through system through which a real scene is viewed directly by the eye. The overall optical system consists of a tilted combiner (a half-mirror), a relay lens and an OLED screen. The light emitted from the OLED screen passes through the relay lens and then is reflected by the combiner into the user’s eye. The overall system is set to be symmetric about the YOZ plane, but not the XOZ plane.
In the design, the combiner is a tilted ellipsoid surface which is easy to fabricate. However, the tilt combiner with optical power breaks the symmetry of the optical system, and introduces large aberrations, such as coma, astigmatism and distortion [30, 31]. To balance the serious aberrations, freeform surface is employed in the relay lens. The relay lens consists of 2 plastics lenses and an achromatic doublet lenses. The first plastics lens with aspherical surfaces is applied to correct the field aberrations. Since the color aberration is a shape-independent aberration, the achromatic doublets lenses can be used to reduce the color aberration. The achromatic doublets lenses and the aspherical lens share a common axis which makes the lens mounting easier. The second plastics lens with freeform surface is tilted, decentered, and placed close to OLED screen to balance the residual aberrations between the tilt combiner and the screen. The other surface of the second plastics lens is a simple sphere surface, which benefits the freeform surface manufacture. The interior surface of the combiner is coated with a half reflection film, allowing the ray from the outside real-world scene to transmit through and being incident to the user’s eye, coinciding both the virtual image and the real scene image for the user. Since we aim to design a compact HMD similar to a normal glass, we have strictly designed the geometry shape and constrained the volume of the HMD. Besides, to minimize the volume of the HMD, the parts of the optical lenses where no rays pass through will be removed in the fabrication process.
The OLED (SONY, 1024 × 768 pixels, 7.9 μm pixel size and 500 cd/m2 peak brightness) screen is selected as the image source. OLED uses polymers which emit light in response to an electric current, making a unique display with self-emissive light without added illumination units, significantly decreasing the volume of the HMD. For most applications of a compact see-through HMD, the FOV is typically around 25 to 40 degrees [13, 24, 32]. However, too large FOV will cause eyestrain because the eyes must scan a large angle [33, 34]. In our design, a diagonal full FOV of 30° has been chosen to balance the FOV and potential eye fatigue for the users. The effective focal length (EFL) is calculated as 19 mm based on the OLED size and full FOV. The specifications of the optical system are listed in Table 1.
Table 1. Specifications of the ultra-compact off-axis HMD
2.2 Structure constrains
In order to make the compact off-axis HMD wearing comfortable, the frame and size constrains should be carefully considered. Structure constrains are required to ensure that the HMD can be worn by most people like a normal glass, and that all the rays across the fields can be traced without obstruction. Figure 2 illustrates the structure constrains to be considered in binocular configuration. As shown in Fig. 2, the P and P’ denote the center of the left and right pupil, respectively. A and B denote the maximum field of the OLED in positive and negative Y direction, respectively. C is the intersection points of the marginal ray of max field in positive Y direction with the extension line of PP’. D denotes the intersection points of the chief ray of center field with the combiner surface. Since the relay lens are placed at the left and right sides of the user head, and near the users’ ears, the rays between relay and tilt combiner should not be blocked by the head. The distance between C and P is controlled to adapt the size of human head.
Based on the physical structure mentioned above, the structure constrains are defined as:
where all the Y, Z coordinates in the equations are referenced to the global coordinate system, for which the origin is located at the center of the exit pupil.
2.3 Design of the initial structure
A compact off-axis HMD system may be tentatively optimized from an existed patent by putting constraint conditions in an optical software package. However, after numerous tries, we found, the existing off-axis HMD patents with large volume are far from the compact design optimum point, which would result in a drastic change of the structure and the surfaces, and consequently, lead to low design efficiency and even failure. Thus, a reasonable initial is rather important in the design process. We begin the design from a coaxial system with spherical surfaces, as shown in Fig. 3. The system contains the stop, combiner, relay lens and image plane. There is an intermediate image between the combiner and relay lens.
Based on the paraxial optical theory and the reflecting imaging formula:
For , the relationship among focal length, surface curvature and magnification can be established as:
where r is the radius of the combiner mirror, is the magnification of relay, and are the focal length of combiner and whole system, respectively.According to the effective focal length specifications (EFL = 19 mm), and to balance the size of optical structure and the aberrations, the magnification of relay is. The radius of the combiner can be obtained r = 38 mm from Eq. (4). Based on the geometry aberration theory, when a stop is set at the center of the spherical mirror, the Seidel coefficients of the coma, astigmatism, distortion and color aberration are all zeroes which are beneficial for constructing an initial coaxial structure. Based on this advantage, the distance between the stop and the mirror is 38 mm. The relay lens is to imaging the intermediate image onto the image plane, and correcting the aberrations introduced by the combiner. A 4 pieces patented design with 1x magnification in CODE V database (Japan patent 60_4963 850207) has been selected as the relay lens to match the spherical combiner. After scaling the relay lens, we combine the spherical mirror and the relay lens to construct the coaxial initial structure of the HMD and shown in Fig. 4. The pupil diameter is 4 mm, and the EFL is 19 mm. The initial detailed parameters of the optical system are shown in Table 2.
Table 2. Initial configuration parameters
2.4 Optimization
The optical system is optimized in optical design software package CODE V. During the optimization process, four wavelengths of 486.1, 546, 587.6, and 656.3nm are used to optimize and evaluate the image quality [14]. Due to the YOZ plane symmetry of the system, the system has to be optimized over half of the full FOV sampled in rectangular grid. The merit function is built by evaluating the transverse ray aberration. The structure constrains mentioned above are defined to avoid unwanted obscuration in the ray path. The effective focal lengths in both the tangential and sagittal planes are constrained to be 19 mm. The coordinates of rays striking the image plane are constrained to control the distortion. The following parameters are set as variables in the optimization:(1) the radius, (2) the thickness and air gap, (3) the coefficients of the aspherical and freeform surfaces, (4) decenter in Y and Z directions, and (5) tilt about X axis.
It is challenging to optimize an initial coaxial system to obtain an off-axis freeform system. The tilt combiner with optical power breaks the symmetry of the optical system, and introduces large aberrations, such as coma, astigmatism and distortion. The surface type of the optical system should be complex to compensate these aberrations. Thus, how to determine the surface type of each optical element in the optical system is a significant issue.
Generally, the freeform combiner half-mirror is good at correcting the high-order aberrations since it is located near the aperture stop [22, 35]. However, if the freeform combiner is used, both the interior and exterior surfaces are needed to be freeform profiles to ensure the undistorted view through the combiner which make the freeform lens difficult to fabricate and increase the cost. The ellipsoid surface is preferred to represent the combiner surface, since when the pupil is located at one conic focus of the ellipsoid surface, the ellipsoid surface does not introduce the astigmatism. If one conic focus is at the pupil, and another conic focus is at the pupil of relay lens, the spherical aberration can be eliminated [36, 37]. Moreover, the ellipsoid combiner is easy to fabricate comparing with the freeform combiner.
The achromatic doublets lenses are used to correct the color aberrations, so that the surface type of the achromatic doublets lenses are spherical surfaces in our design for easy fabrication. To making the lens mounting easier, the achromatic doublets lenses and the lens 2 share a common axis in our design. A rotationally symmetric surface type is preferred to represent the surface type of lens 2. Considering the fabrication and cost of lens 2, even aspherical surface type is selected which has been widely used in optical system.
However, the large off-axis aberrations introduced by the tilt combiner are difficult to control with traditional components such as an aspheric lens. Freeform surface is non-symmetric surface, and it is suitable for correcting these aberrations. The common freeform surface are x-y polynomial surface and Zernike polynomial surface. Compared to the Zernike polynomial, x-y polynomial surfaces are easier to process due to the consistence with the numerical control (NC) optical expression form [38]. The x-y polynomial surface has been applied successfully in many optical system [39–43]. Thus, the x-y polynomial surface type is selected in our paper. The other surface of the single lens 1 is a simple sphere surface, which benefits the freeform surface manufacture.
A progressive strategy is adopted in the design. The whole design procedure is divided into two steps, as illustrated in Fig. 5. At the beginning of the optimization procedure, the design goal is to remove the obscuration and obtain a reasonable off-axis structure from the initial coaxial system. Only the biased fields along the tangential direction are sampled. The combiner and relay lens are tilted and decentered gradually to avoid obscuration in the optical path and meet the structure constrains with small pupil size. Meanwhile, the off-axis aberrations are increased. The surface type of the right surface of lens 1 and lens 2 are converted to even aspherical surface, and the materials of lens 1 and 2 are replaced with plastics material. The spherical combiner has been converted to the ellipsoid surface.
At the second step, the pupil size and FOV are enlarged, which introduces larger high-order aberrations that can be corrected with freeform surface, which offering more degrees of freedom. The aspherical surface of lens 1 is converted to a low order x-y polynomial surface with the least square algorithm [44]. As the optimization progresses, the pupil size and FOV are expanded to the specification values, and the higher order terms of x-y polynomial surface are gradually added to improve the imaging quality. Moreover, to ensure the manufacturability of the freeform surface, the local curvature constraints of the freeform surface during the optimization process are used to control the local curvature variation of freeform surface to avoid rapid surface shape changes. The x-y polynomial surface is expressed as:
where c is the curvature, r is the radial coordinate in lens units, k is the conic constant, N is the number of polynomial coefficients in the series and Ai is the coefficient on the polynomial term.Due to the symmetry about the YOZ plane, the coefficients of the odd terms of x in x-y polynomial expression are zeroes. Considering the convergence rate in the optimization process and the manufacture difficulty, the highest order of the freeform surface is limited at 6-order polynomials in our design, which is sufficient based on an acceptable optical system performance [15], thus the expression is:
2.5 Design results and performance analysis
After the optimization with x-y polynomial surfaces, a compact off-axis HMD is obtained. The system is illustrated in Fig. 6, which consists of an ellipsoid combiner and a 4-pieces relay lens group. The pupil stop is located 30 mm in front of the ellipsoid combiner. The ellipsoid combiner is tilted about the x-axis by 22.5°. The distance between the ellipsoid combiner mirror and the OLED screen is 67 mm in Z direction and 56 mm in Y direction. The 3D model of compact off-axis HMD and a human head is shown in Fig. 7. The overall structure of the HMD is very compact and simple, which is suitable for integrating a normal glass.
The optical performance of the optimized system is assessed at the following representative field angles for the four design wavelengths: (0°, 0°), (0°, ± 6°), (4.5°, 0°), (4.5°, ± 6°), (4.5°, ± 12°), (9°, ± 6°), (0°, ± 12°), (9°, ± 12°), (9°, 0°). In practical application, the pupil diameter of the human eye is 3 mm, and a 3 mm eye pupil is therefore selected for both centered and decentered pupils [14]. The modulation transfer function (MTF) values over the defined 15 fields for a centered 3 mm pupil at the spatial frequency of 64 cycles/mm, which correspond to the Nyquist frequency of the OLED, are shown in Fig. 8. The MTF performance is better than 0.2@64 cycles/mm over full field of view. The spot diagrams of the designed optical system are also shown in Fig. 9(a). The maximum RMS spot diameter over the field is 18μm, which can satisfy the resolution of the user. Figure 9(b) indicates the distortion of the designed compact HMD. The maximum distortion is 6.88% which is caused by the tilt combiner and difficult to correct in optical design process. However, the residual distortion can be corrected with digital method [14].
Fig. 9 (a) RMS spot diameter across the full fields; and (b) the distortion grid of the optical system.
For the optical see-through path, the exterior surface of the tilt combiner should be designed to maintain the good image quality without distorting the real-world scene. We trace the rays from the real world to the pupil stop, and insert a perfect lens at the stop with an EFL equivalent to the human eye to focus the collimated rays. The exterior surface of the combiner is set to conic surface, and the radius and coefficient of the exterior surface are variables. The optimized combiner is shown in Fig. 10(a). The MTF plots and distortion grid are shown in Fig. 10(b) and 10(c), which demonstrate the optical performance of the optical see-through path.
To evaluate the manufacturability of the freeform surface, the local curvatures of the freeform surface along with x and y axis have been calculated and shown in Fig. 11. The local curvatures vary from 0.0158 to −0.0433. Comparing the fabricated freeform surfaces, our designed freeform surface has proper local curvature [15, 45, 46]. Thus, we can conclude that the freeform surface in this design is reasonable.
The optical system parameters and the coefficients of even aspherical and x-y polynomial surfaces are detailed in Table 3 and Table 4, respectively.
Table 3. Optical system parameters
Table 4. Coefficients of even aspherical and freeform surfaces
3. Tolerance analysis
The tolerances determine the difficulty and cost of the fabrication and alignment for the optical system. The tolerances of the compact HMD are analyzed in CODE V using wavefront differential tolerancing (TOR) method. In our analysis, the radius, index, thickness, decenters in y and z directions, the element tilts and displacements in x and y directions, surface irregularity and surface sag are considered. The location of the OLED is used as the compensator to obtain the maximize performance at final assembly process. The MTF @ 64 cycles/mm is utilized as the nominal criterion.
By the TOR calculation in CODE V, the sensitivity of each tolerance over the fields with default tolerance values is obtained firstly. All tolerances are chosen based on nearly the same amount of degradation of the MTF in inverse sensitivity model after 5000 trials. We found five most sensitivity tolerance items among all the items, and they are listed in Table 5.
Table 5. Five most sensitive tolerance items influencing the optical system
The five most sensitivity tolerance items are about the element alignment and freeform or aspherical surface profile. Therefore, the fabrication and alignment precision should be guaranteed. After adjusting all the tolerance items carefully, the overall tolerance items are conducted until the fabrication cost and the system performance reach a good tradeoff. The preliminary fabrication tolerances are listed in Table 6. Based on the tolerances listed in Table 6, we run a Monte Carlo simulation 1000 times, and use the normal distribution to analyze the MTF value @ 64 cycles/mm. The Monte Carlo analysis is a statistical model that is suitable to predict system performance. Figure 12 is the cumulative probability for different MTF values under the conditions in Table 6. There is an 80% probability that the MTF is higher than 0.15 @ 64 cycles/mm for all tolerances concerned and the image quality should be acceptable, which is verified by the experimental results in Section 4. According to the tolerances in Table 6, the optical elements fabrication and system alignment can be achieved by ordinary method which is beneficial for mass production and reducing the cost.
Table 6. Tolerances of the compact off-axis of HMD
4. Experimental test
The optical system is fabricated and implemented. Figure 13(a) shows the developed prototype of the compact off-axis HMD in binocular configuration. Comparing with a normal glass, the developed prototype has equivalent size, and better industry design will be completed in our future work to update the appearance of the prototype. Single point diamond technology (SPDT) is used for fabrication of the aspherical and freeform elements in the prototype. According to the tolerances listed in Table 6, the aspherical lenses and freeform lens can also be fabricated with injection molding technology to reduce the cost. The fabricated freeform lens is shown in Fig. 13(b), and the size of the freeform lens is 16 mm × 13 mm × 5 mm. The total weight of the five lenses is only 15.6 grams. The mechanical structure of the prototype is fabricated by 3D print technology.
To verify the image quality of the prototype of the compact off-axis HMD, a camera is located at the exit pupil of the optical system to capture the image. Figure 14(a) shows the image from the real world. The prewrapped virtual image is displayed on the OLED and a photo is taken at the exit pupil which is shown in Fig. 14(b). As shown in the figure, the minimum lines and graphics can be seen clearly in both see-through path and virtual image path. The distortion of the virtual image path has been well corrected by digital method. We also measure the MTF curves of the optical system to evaluate its optical performance for both the real world path and the virtual image path. The MTF values are calculated based on the images (Fig. 14(a) and 14(b)). The approach that we utilize to calculate the MTF values is explained in reference [47]. As shown in Fig. 14(c) and 14(d), the MTF amplitude values fall to 0.4 @ 50 cycles/mm for the real world path, and 0.15@ 64 cycles/mm for the virtual image path. The measure results prove our design and analysis.
Fig. 14 The experiment demonstration: (a) the real scene through the combiner captured by camera; (b) the virtual image reflected by the combiner from the OLED captured by camera; (c) MTF curve of the real world path; and (d) MTF curve of the real world path.
Moreover, an augmented reality image (a hawk on the table) captured by the camera is shown in Fig. 15, and the experiment test results demonstrate that the developed compact off-axis HMD have good image performance and compact structure.
5. Conclusions
In this paper, a novel compact, lightweight, and wearable off-axis HMD with 30° FOV, 7 mm exit pupil and 30 mm eye relief is designed and implemented. The HMD has very compact structure which is assembled as a normal glass. The initial structure design, structure constrains and optimization strategy are discussed in detail. The designed HMD consists of a tilt combiner and a four pieces relay lenses. The image quality of the virtual image path reveals an MTF lager than 20% @ 64 cycles/mm and the maximum distortion is 6.68% which has been corrected by digital prewrapped. The tolerance analysis, including sensitive analysis and Monte Carlo simulation, is comprehensively performed, and the results indicate that the compact HMD can be manufactured easily. Furthermore, the manufacturability of the freeform surface is also fully evaluated. Finally, a binocular compact off-axis HMD prototype is fabricated. The performance of the optical system has been experimentally tested and the results demonstrate the good performance of the compact off-axis HMD.
Funding
Beijing Municipal Science& Technology Commission (Y75X02A21N); Innovation Project of Chinese Academy of Sciences (CXJJ-16S043); Innovation Project of Academy of Opto-Electronics, Chinese Academy of Sciences (Y70B01A11Y).
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