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Small thickness and light weight are two important requirements for a see-through near-eye display which are achieved in this paper by using two advanced technologies: geometrical waveguide and freeform optics. A major problem associated with the geometrical waveguide is the stray light which can severely degrade the display quality. The causes and solutions to this problem are thoroughly studied. A mathematical model of the waveguide is established and a non-sequential ray tracing algorithm is developed, which enable us to carefully examine the stray light of the planar waveguide and explore a global searching method to find an optimum design with the least amount of stray light. A projection optics using freeform surfaces on a wedge shaped prism is also designed. The near-eye display integrating the projection optics and the waveguide has a field of view of 28°, an exit pupil diameter of 9.6mm and an exit pupil distance of 20mm. In our final design, the proportion of the stray light energy over the image output energy of the waveguide is reduced to 2%, the modulation transfer function values across the entire field of the eyepiece are above 0.5 at 30 line pairs/mm (lps/mm). A proof-of-concept prototype of the proposed geometrical waveguide near-eye display is developed and demonstrated.
© 2014 Optical Society of America
1. Introduction
Nowadays, optical see-through near-eye display (NED) is becoming a very hot topic with numerous potential applications. Sony [1–4], Epson [5, 6], Nokia [7–10], Zeiss [11, 12], Google [13, 14] and some other multinational corporations have already released related products. Small thickness and lightweight are the inexorable tendencies to modern see-through NEDs. In order to achieve eyeglass-type NEDs, researchers have introduced freeform optics [15], scanning technologies [16], diffractive optics [7–10, 17–20], holographic waveguide [1, 21–33] and geometrical waveguide [34, 35] technologies into the development of the see-through NEDs.
Among those technologies, the waveguide technology probably provides the best way that could facilitate ultra-thin and discreet see-through NED. The waveguide is a transparent thin-plate similar to a spectacle lens and it is the core optical element of the NED. The waveguide can be divided into input-coupling and output-coupling sections, and the types of waveguide include the geometrical waveguide [34, 35] and the holographic waveguide [1, 21–33]. The former employs a reflective mirror for the input-coupling optics and an array of partially reflective mirrors (PRMA) for the output-coupling optics, and Lumus, for example, uses this technique in its NED [36]. The latter employs holographic or grating elements for the input-coupling and output-coupling optics, and this method is employed by Sony [1] and Nokia [18, 19].
SEIKO Epson developed the prototype of a waveguide NED (WGNED) with two reflecting mirrors. Its drawback is that the thickness of the waveguide is directly related to the field of view (FOV). The thickness approaches to 23 mm when the FOV is increased to 30° [34]. Lumus released several geometric planar waveguide products. The FOV is from 19° to 40°, and the thickness of the waveguide is less than 3mm [36]. Optinvent issued the Clear-VU prototype based on a surface structure made up of several reflecting structures for the coupling-out optics, and the FOV is about 25° [37]. Since Amitai published the paper on holographic WGNED in 1989 [21], numerous research works have been published on holographic WGNED [1, 21–31]. However, relatively few literatures can be found on geometrical WGNED.
The geometrical waveguide serves as a pupil expander, and there are two different configurations. One configuration expands the exit pupil of the projection optics in one direction [34], while the other configuration expands the exit pupil in two orthogonal directions [35]. The geometrical waveguide transfers the high-definition image from the projection optics directly into the user’s eye. Figure 1(a) shows the schematic diagram of a planar WGNED. The entrance mirror reflects the light exiting from the projection optics in a manner that ensures the light is trapped inside the planar waveguide substrates by the total internal reflection (TIR) condition. After a few reflections on the substrates, the trapped rays reach the PRMA, which couples the light out of the waveguide into the eye of the user.
Although the WGNED has certain supreme advantages over the other see-through state-of-the-art NEDs, there are also some apparent drawbacks. A major problem in a geometrical waveguide is the stay light and ghost image caused by the unexpected reflections on the PRMA. Figure 1(b) shows the situation when there is a bright object in the projection image. The brighter the object in the real scene is, the more serious the ghost image problem will be. The object and its ghost image are symmetric about a line near the center field along the expansion direction. This stray light phenomenon exists in most of the FOVs. As the field angle increases in the expansion direction, the stray light becomes stronger. That is, the ghost image is more obvious in the marginal field than in the center field. Due to the principle of optical path reversibility, a bright object displaced on the miniature display device of the WGNED will cause a similar problem. However, the problem of the stray light in the geometrical waveguide has never been thoroughly investigated. Also in the study of WGNED, the design of the projection optics and the matching between the projection optics and waveguide have seldom been discussed.
In this paper, we concentrate our research on the design of the freeform WGNED system and the stray light suppression method. In section 2, an overview of our WGNED optical system is given, and the major causes of the stray light are analyzed. In section 3, a global searching method with some special constraints are implemented to find a waveguide configuration with the minimal stray light. In section 4, the specifications and the design of the freeform projection optics are presented. Finally, the overall system design and integration are described in section 5.
2. Overview of WGNED system
Since the stray light within a planar waveguide is difficult to eliminate, waveguides that expand the pupil in a single direction have some advantages over those that expand the pupil in two directions, even though the use of the latter can help to reduce the size of the projection optics and result in a wider pupil in two directions. In our design, the former configuration is chosen, because it results in less stray light, and the analysis of stray light is more straightforward and requires much less time to implement. Freeform optics is used in the design of the projection optics to reduce the system size, and which helps to mitigate some of the disadvantages of using a waveguide that expands the pupil in a single direction. The other reason for selecting this design configuration in this study is to facilitate the mounting of the waveguide in a horizontal expansion direction to accommodate users with a wide range of interpupillary distance.
The overall WGNED system consists of projection optics and waveguide optics, as shown in Fig. 2. The waveguide has five critical parameters including (1) the thickness d, (2) the index of the glass material n, (3) the angle θ formed by the entrance mirror and the substrate surface of the waveguide, (4) the distance H1 between the center of the reflecting mirror AB and the first partially reflecting mirror CD, and (5) the distance H2 between two adjacent partially reflecting mirrors. The PRMA are placed in parallel with an equal distance from each other. This distance is determined by d and θ in order to couple the rays out of the waveguide uniformly. The projection optics consists of the microdisplay, the light engine and the eyepiece.
2.1 Causes of stray light
It would be much easier to control the stray light if we know how is it generated in a waveguide, and this subsection focuses on the causes of stray light. After careful investigation, we found that the stray light is primarily generated in three ways. The first condition (Condition 1) is caused by light rays hitting the reflecting mirror (AB) twice, as shown in Fig. 3(a). This problem will be discussed in detail in Section 2.3. The red ray shown in Fig. 3(a) represents the lower boundary. Any light rays positioned below this will not hit the reflecting mirror twice, but rays positioned above it will. The other two causes occur whenever light rays are incident on the PRMA from a direction other than the right side ( + Z-direction). As such, the second source (Condition 2) is caused by rays hitting the PRMA from the left side (-Z-direction) and above ( + Y-direction), as shown in Fig. 3(b), while the third source (Condition 3) is caused by rays incident on the PRMA from its left side (-Z-direction) and bottom (-Y-direction), as shown by the dashed line in Fig. 3(c).
Fig. 3 Three major stray light paths generated by (a) two reflections on the reflecting mirror; (b) and (c) unwanted reflection of the rays reflected by the front substrate and incident on the PRMA.
2.2 Importance of stray light analysis and solution discussion
Since light rays incident on the wrong side of the PRMA are a major cause of stray light, here we evaluate the difference between ray incident angles on the PRMA from both sides. The incident angle on the PRMA of a light ray just reflected by the front substrate surface (S1) is defined by Eq. (1).
where ω' is the refractive angle of the field with an angle of ω along the Y-axis.The incident angle on the PRMA of the ray reflected by the second substrate surface (S2) is defined by Eq. (2).
The reflection angles of unwanted stray light are much larger than the normal reflection angles, as determined by Eqs. (1) and (2), respectively. The difference is typically twice of the wedge angle. Larger incident angle will exhibit stronger reflectivity, which will increase the proportion of stray light. These preliminary results substantiate the necessity and significance of the analyses conducted in this study.
The ray travel direction variance caused by the unwanted reflection is determined by:
It is interesting to note that the incident angle of the stray light on the eye pupil plane is equal to that of normal rays but with an opposite sign when the wedge angle is equal to 30°. Therefore, the intended image and its ghost image are symmetric about the center field along the pupil expansion direction. Otherwise, the intended image and the ghost image are symmetric about a field having an offset of 45-3θ/2 degrees to the center field.
Several possible solutions exist for mitigating the stray light problem in the WGNED system, including stray light suppression methods and optimization methods. We discuss the former solution in this section and will discuss the latter in Section 3.
2.3 Pupil matching of projection and waveguide optics
The size of the entrance mirror is relatively small since the thickness of the waveguide is thin. In order to make full use of the entrance mirror so that the rays from the projection optics can be correctly and fully collected by the reflecting mirror and eliminate stray light caused by Condition 1, the exit pupil size of the projection optics and its position relative to the waveguide entrance must be optimized. Figure 4 shows the relationship between the exit pupil of the projection optics and the entrance of the waveguide. The drawback of this approach is that the rays do not fully fill the exit pupil.
Fig. 4 Relationship of the exit pupil of the projection optics and the entrance pupil of the waveguide.
The entrance pupil location of the waveguide with respect to the first substrate surface is defined by the following equation:
The entrance pupil size in YOZ plane along the expansion direction is defined as follows:
In order to avoid stray light caused by Condition 1, we choose a critical ray R1 that separates rays hitting the mirror once from those hitting it two times, as shown in Fig. 4. The pupil size is then modified by the following equation in accordance to the critical ray.
where θi is the incident angle of a ray on the substrate surface, which equals 2 × θ + ω'.3. Optimization of waveguide optics
The geometrical structure of the waveguide is determined by parameters θ, H1, and the thickness d. Besides these geometrical parameters, the index n would also affect the proportion of regular rays and those attributed to stray light. A mathematical model of the waveguide using the above four parameters and a non-sequential ray-tracing algorithm are developed, and an automatic global search algorithm is implemented to find a planar waveguide having the least amount of stray light. This automatic search algorithm is employed to avoid the necessity of modeling the waveguide, performing the ray tracing, and manually obtaining the simulation results using commercial ray-tracing software for every different configuration. During the non-sequential ray-tracing process, all rays are divided into three groups: regular rays, stray light rays, and missed rays, and peak to valley (P-V) and root mean square (RMS) energy values of the stray light relative to the intended image light in the exit pupil plane are used to construct the merit function for each waveguide configuration.
During the stray light suppression process, satisfaction of system requirements must be the first priority. For example, the thickness of the waveguide has a strong influence on the diameter and location of the exit pupil. Therefore, constraints are set up for each parameter according to the system requirements so as to narrow down the search space.
3.1 Exit pupil constraints on thickness
The exit pupil diameter (EPD) of the waveguide at a fixed eye position is defined by:
where m1 is the number of times of the ray incident on the substrates, the selected ray is from the maximum field in + Y direction, and it has the largest Y value when it exits the waveguide. m2 in Eq. (13) represents the number of times of the ray incident on the substrate surfaces, where the ray is from the maximum field in -Y direction and it has the smallest Y value when it exits the waveguide. m1 and m2 are even number, and they satisfy the condition m1>m2. The symbol ERFs in Eq. (7) represents the eye relief of the WGNED system and it is usually greater than 20mm. From Eq. (7), the EPD at fixed ERFs increases with the thickness of the waveguide. Figure 5 shows the relationship between the EPD and the thickness.3.2 Wedge angle constraints
The angle of incidence of a ray incident on the substrate surface (S2) is defined by Eq. (2). To keep the rays trapped inside the waveguide, the incident angle must be larger than the critical angle. The critical angles for several refractive indexes n are plotted in Fig. 6. The incident angles linearly vary as the wedge angle increase, and the FOV of the system along the Y-axis is ± 12°, which indicates, for example, that the wedge angle must be greater than 20° when the index n is equal to 1.5.
3.3 H1 constraints
The value of H1 is determined by the exit pupil location, and the distance from the pupil center to the edge of the in-coupling section is approximately 20-25mm. The exit pupil location along the expansion direction is a function of H1 and can be simply defined as,
Light rays might be reflected many more times in the waveguide as the value of H1 increases and this would increase the design difficulty of the eyepiece. This factor will be discussed in Section 4.2. Furthermore, we have to consider the coating design. Although the transmission ratio would not be considered as a variable, a higher value for the refraction index would complicate the coating design and limit the reflectivity; therefore, the index needs to be constrained within a small range. On the other hand, the refractive index of glass is typically in the range from 1.5 to 1.8. Additionally, a higher index allows for a smaller critical angle such that the waveguide can accept a bundle of rays having a much wider FOV.
3.4 Global searching method
By constructing the constraints above, each parameter can be limited into a relatively smaller range so that the overall search space is dramatically decreased, and the time of search can be diminished greatly. The value of θ is limited within 28° and 32° by a step size of 0.4°; the value of index n varies from 1.5 to 1.78 by an increment of 0.04; H1 varies from 13 mm to 18 mm with a step size of 1mm. The thickness of the waveguide varies from 1.6 mm to 3.2 mm with a step size of 0.2mm. The reflectivity of the PRMA is set to 15%. Total 4752 configurations were included in the global search. Figure 7 shows the global searching results. The search was carried out in the order of angle θ, index n, thickness d, and then H1.
Fig. 7 Searching results of possible configurations with (a) the average and RMS value of the stray light over the regular light when Texd = 0; (b) the average and RMS value of the stray light over the regular light when Texd = d; (c) the average and RMS value of the stray light over the regular light when Texd is matched; (d) the P-V value of the stray light over the regular light when Texd = 0; (e) the P-V value of the stray light over the regular light when Texd = d; (f) the P-V value of the stray light over the regular light when Texd is matched.
Table 1 lists the top five results representing the highest merit functions resulting in the smallest amount of straylight. AVE means the average value of the stray light energy over the useful ray, EPDY means the EPD along the expansion direction with an eye relief of 20mm.
Table 1. Top 5 optimal waveguide configurations
4 Overall system designs
4.1 Determination and analysis of waveguide optics
By considering the coating design, it is best if the index of the waveguide is smaller than 1.7 because this helps to increase the reflectivity of the PRMA. A configuration having smaller index value corresponds to the glass of F4. From Table 1, we note that the PV value of this configuration is little worse than the best solution (0.01). Table 2 lists the parameters of the chosen configuration and the distribution of the light.
Table 2. The solution with a smaller index
The waveguide was modeled using LightTools with the parameter listed in Table 2. Figure 8 shows the ray-tracing results of the regular and stray light paths for the chosen configuration. The traced field is −12°, the energy of the stray light relative to the display image is about 4%, and the average is about 2%, much smaller than the worst case (16%).
Fig. 8 The ray path layout and illuminance chart, (a) regular ray path; (b) illuminance chart of the regular ray path;(c) stray light path caused by same ray bundle as (a); (d) illuminance chart of the stray light path.
Figure 9(a) shows graph of the output energy of the normal rays and stray light rays versus the input power across the field in pupil expansion direction. The blue curves show the results traced by our algorithm, while the red curves show the results traced by LightTools. The curves nearly overlap, especially for the stray light values. The accuracy of the non-sequential ray-tracing algorithm is verified. The energy plots across the entire fields are shown in Fig. 9(b).
Fig. 9 Proportion of the useful and stray light over the total power for the (a) FOV along the expansion direction; (b) entire FOVs of the WGNED system.
A critical feature of the waveguide for the design of the projection optics attracts careful attention, as shown in Fig. 10. The three-dimensional layout of the waveguide with three ray bundles from the fields ( ± HFOV, 0) and (0, 0) was plotted. The plot shows that the ray bundle from different fields diverge when the projection optics has its exit pupil located on the entrance of the waveguide, as shown in Fig. 10(a). The user would be unable to view the entire image under this situation, the correct relationship is shown in Fig. 10(b).
Fig. 10 3-D layout of the waveguide with three bundles of rays from the center and marginal fields along the X-axis, (a) the exit pupil of the projection optics locates on the entrance of the waveguide; (b) the exit pupil of the projection optics locates on the exit pupil of the WGNED system.
Figure 11(a) shows that, if the projection optics has its exit pupil planes located at the entrance of the waveguide, the system cannot form a common exit pupil at the eye position in the XOZ plane. The rays from different fields in the XOZ plane diverge and separate with each other, as shown in Figs. 10(a) and 11(b). In order to form a common exit pupil at the eye position, as shown in Figs. 10(b) and 12(b), the projection optics design should separately place its pupil planes such that the exit pupil plane in the YOZ (tangential) plane should be located at the entrance of the waveguide, as shown in Fig. 12(a), while the exit pupil in the XOZ plane should be directly located at the eye position.
4.2 Design of freeform projection optics
The projection optics must match the waveguide, project highlight, and good-quality image to the waveguide, and this necessity increases the design difficulty. The requirements of the eyepiece design include (a) long working distance and (b) a separate exit pupil plane in the two orthogonal directions. The long working distance is necessary to provide sufficient space for the light engine. A small incident angle is also preferred.
As discussed in the above section, the exit pupil planes of the projection optics in the sagittal and tangential planes should be located at different positions so as to correctly relay the exit pupil to the system’s exit pupil correctly. The exit pupil of the projection optics in YOZ plane should be located at the entrance of the waveguide. The exit pupil in the XOZ plane should be at the system’s exit pupil plane.
Figure 13 shows a side view of the waveguide. Rays emitted from the eyepiece in the XOZ plane propagate to the eye position. The parallel mirrors don’t alter the ray travel direction along the X-axis; therefore, the exit pupil distance of the projection optics in the XOZ plane should be sufficient long to reach the system exit pupil. The exit pupil distance of the eyepiece in the X-direction is determined by the following equation.
where ωx is the maximum horizontal FOV (HFOV), ω′x is the refraction angle, and m3 is the total number of chief rays (HFOV°, 0°) incident on the substrates and twice on the mirrors.ERFe must be limited within a range that ensures an eyepiece design having an acceptable size and weight. This factor is greatly influenced by the number m1 of incident rays which itself depends on the waveguide parameter H1.
ERFt is the exit pupil distance of the eyepiece in the YOZ plane. This distance is set to 10mm to leave sufficient space for placing a folding mirror between the eyepiece and the waveguide. Since the ERFs, and ERFt have already been determined, m1 is given as 8; ERFe is approximately 38 mm. The EPD is approximately 4.07 mm, calculated from Eq. (6). A wedge shaped prism with three freeform surfaces (FFS) was used for the eyepiece design.
Figures 14(a) and 14(b) show the 2-D layouts of the eyepiece design in tangential and sagittal planes, with the two exit pupil planes located at different positions. Figure 15 shows the polychromatic module transfer function (MTF) of the eyepiece. The MTF values are all above 0.5 at 30lps/mm for all the fields.
Fig. 14 Optical layout of the freeform eyepiece in (a) sagittal plane, (b) three-dimensional view, (c) tangential plane.
4.3 Integration of projection and waveguide optics
On the basis of the designs of the waveguide and the projection optics, a geometrical WGNED system is further integrated. Figure 16 shows the layout of overall system. Taking into account ergonomic and aesthetic factors, the whole system is horizontally mounted to cover most of the population with different interpupillary distance.
5. Prototype and experimental validation
It is necessary to implement proof-of-concept experiments to validate the design and evaluate its pros and cons. However, it takes a very long time to have the free-form surface (FFS) prism fabricated. Instead we used an FFS prism that was developed for an optical see-through head-mounted display in our previous study [38]. Figure 17(a) shows the optical layout of FFS prism, the FOV is 36°, the EPD is 7 mm and the eye relief (ERF) is 23mm, which is larger than the FFS prism designed in this study. In order to match with the waveguide, the ERF and EPD of the prism are modified appropriately. The red rays shown in Fig. 17(a) are the useful light for our previous application, while the blue rays illustrate the extent of useful light in this prototype. In principle, such a modified prism yields the same function as the FFS prism in this study. Figure 17(b) shows the 3D virtual prototype. A 0.61 inch eMagin OLED microdisplay is used as the image source in this prototype.
Figure 18 shows the MTF field map plot across the fields of the modified design for the frequency of 16 lps/mm. The minimum value is 0.367.
Fig. 18 The MTF field plot of FFS system (16lps/mm) in (a) tangential direction; (b) sagittal direction.
Figure 19 shows waveguide plate and the proof-of-concept prototype. Figure 20(a) shows the image of the USAF resolution test chart and Fig. 20(b) shows the image captured in front of the waveguide, the same photo is displayed on the microdisplay and transmitted through the FFS prism and the waveguide. The image would be blurred if the parallelism error of the PRMA exceeds 0.125 arcmin, and the problem can be solved when the fabrication and assembly accuracy is guaranteed. The final image quality of the NED with the FFS prism designed in this paper will be greatly improved, because the MTF value of the designed FFS prism is much higher than the FFS prism used in this prototype, as shown in Figs. 15 and 18.
6. Conclusions
In this study, geometrical waveguide and freeform optics are used to develop an ultra-thin and light weight NED. The two technologies have advantages that complement each other. The waveguide greatly reduces the thickness of the optical element in front of the eye, while the FFS prism significantly reduces the size and weight of the projection optics. The causes of the stray light in geometrical WGNED systems are investigated in detail. A global searching algorithm is implemented to find an optimal and feasible waveguide design with minimal stray light. The results are ranked according to the merit function constructed using the PV, average, and RMS values of the stray light energy relative to the display image energy. The projection optics matching the designed waveguide is studied and designed. The performance of the complete system design is analyzed. The EPD of the system is 9.6 mm, the eye relief is 20 mm and the FOV is 28°. A WGNED prototype using the designed planar waveguide and a fabricated prism is presented and demonstrated.
Acknowledgments
This research is partially supported by the National Basic Research Program of China (973, No. 2011CB706701), the National Science Foundation of China (NSFC, No. 61205024, 61178038), the National High Technology Research and Development Program of China (863, No. 2013AA013901), and the New Century Excellent Talents in University 2012 (NCET-12-0043). We thank you Synopsys for education license of CODEV and LightTools.
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