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2020,  2 (1):   79 - 85   Published Date:2020-2-20

DOI: 10.1016/j.vrih.2019.12.003
1 Introduction2 Principle of holographic diffraction waveguide grating3 Design of cylindrical lens waveguide grating structure4 Simulation analysis5 Conclusions


Augmented reality (AR) smartglasses are considered as the next generation of smart devices to replace mobile phones, and are widely concerned. But at present, AR smartglasses are usually designed according to the human normal eyes. In order to experience AR smartglasses perfectly, abnormal eye users must first wear diopters.
For people with astigmatism to use AR smartglasses without wearing a diopter lens, a cylindrical lens waveguide grating is designed in this study based on the principle of holographic waveguide grating. First, a cylindrical lens waveguide substrate is constructed for external light deflection to satisfy the users' normal viewing of the real world. Further, a variable period grating structure is established based on the cylindrical lens waveguide substrate to normally emit the light from the virtual world in the optical machine to the human eyes. Finally, the structural parameters of grating are optimized to improve the diffraction efficiency.
The results show that the structure of cylindrical lens waveguide grating allows people with astigmatism to wear AR smartglasses directly. The total light utilization rate reaches 90% with excellent imaging uniformity. The brightness difference is less than 0.92% and the vertical field of view is 10°.
This research serves as a guide for AR product designs for people with long/short sightedness and promotes the development of such products.


1 Introduction
Augmented reality (AR) is a technology that calculates the position and angle of a camera image in real time, and it then adds corresponding images, videos, and three-dimensional models. It can superimpose the virtual world on a screen and interact with the real world[1]. AR smartglasses are the most anticipated products in the field of smart wear. They play an increasingly important role in medical teaching, transportation, industrial design, security patrol, and information pushing[2].
The optical display principles of AR smartglasses include reflection prism[3], freeform optical waveguide[4], birdbath, optical fiber scanning field[5], and holographic waveguide grating technologies. However, the reflecting prism has a larger volume and smaller field of view. The freeform optical waveguide scheme creates distortion of field curvature. The amount of light energy loss from the birdbath technology is quite serious, and the data storage and transmission of the optical fiber scanning field technology are huge. Therefore, AR smartglasses based on the holographic waveguide technology are considered suitable as they not only have a large field of view, wide range of eye movement, and thinner products, but also possess the maturity of semiconductor technology, such that the yield is more considerable compared to that of other schemes.
Based on the holographic waveguide grating technology, a design scheme of concave cylindrical lens waveguide grating structure is proposed to solve the problem where people with astigmatism need to wear diopter lens to perfectly experience AR smartglasses. First, a concave cylindrical lens waveguide substrate that can deflect external light propagation is constructed for normal external scene viewing. Further, a special grating structure is designed on the waveguide substrate surface for projection of light into the human eye in the projector. The structure solves the problem of using AR glasses directly by users with astigmatism on the imaging principle of AR smartglasses, and is of great significance to them.
2 Principle of holographic diffraction waveguide grating
AR smartglasses based on the holographic waveguide grating technology are mainly composed of three diffractive optical elements (DOEs), as shown in Figure 1a. The output light in the micro projector is coupled into DOE1 and deflected by 90°. Next, it is transmitted by total reflection in the planar waveguide. When light travels to DOE2 horizontally, due to the action of waveguide grating, the light beam splits and deflects by 90° at different positions in DOE2 and then propagates vertically downward[6].
The vertically downward parallel light propagates into DOE3, and the light is diffracted in the grating region[3,7]. Due to human visual needs, the light from DOE3 must be diffracted in several areas, so that the image can be projected at all positions of the human eyes. As shown in Figure 1b, while one part of the light is diffracted (blue arrows), the other part of the light continues to show total reflection (red arrows). Diffraction and total reflection also occur when light propagates to the next grating region. To make the brightness of the image uniform, the diffraction efficiency of grating should be increased gradually from left to right with the number of diffractions.
At present, the DOE3 used for AR smartglasses is mostly planar periodic grating structures[8,9], which only meet the virtual-real fusion experience of the normal visual acuity group. Structural changes to DOE3 match the imaging effect with various visual requirements (such as astigmatismus and short-sightedness).
3 Design of cylindrical lens waveguide grating structure
In this study, DOE3 is designed as a variable spacing grating structure on the surface of the concave cylindrical lens waveguide substrate. It not only deflects the light from the outside world, but also makes the light from a micro projector in the guided wave transmit via total reflection, and diffracts the image into the human eye at a specific area, thereby meeting the AR needs of people with astigmatism.
D = 1 / f
W = 100 × D
f = n - 1 r
The radius of curvature of the cylindrical lens is 175mm. The size of the substrate used in this study is 34mm long, 17mm wide, and 1mm thick at the center. The substrate model of curved waveguide and the total reflection of light in the waveguide are shown in Figure 2.
The incident angle condition for determining the total reflection of light in the cylindrical lens waveguide using ray tracing should be
  θ > 48 °
. The light incident on DOE3 with an incident angle of
55 ° - 65 °
is emitted to the human eyes at an angle of view of
- 5 ° - 5 °
, and the incident light at 60° is the central beam, which is normally incident vertically to the human eyes after being diffracted by the grating. In Figure 2b, the incident light at 60° diffracts five times at five different areas of the cylindrical lens waveguide substrate surface, which are referred to as the first, second, third, fourth, and fifth diffractions of light on the substrate surface.
The grating period of diffraction region 1 is calculated by considering the first diffraction of light with an incident angle of 60°. The diffraction phenomena of curved grating are shown in Figure 3.
In Figure 3, the gray area represents the substrate structure of the cylindrical lens waveguide and the red arrows represent the light in the waveguide. AB is the incident light, BF is the diffraction light, OB is the normal line of the diffraction area,
is the incident angle, and
is the diffraction angle. On calculating the Z-axis coordinates when the total reflection of light reaches the concave surface, the distance between A and E can be obtained, and the diffraction angle can subsequently be calculated using the following geometric formula:
α = a r c s i n A D 2 - A E O B
The angle of incidence can be obtained by viewing the light properties using LightTools, and
=57.86°. Finally, the grating period in the diffraction region is calculated as follows[10,11]:
Λ n s u b s i n θ ± n s u p s i n α = m λ
is the grating period, m is the diffraction order,
is the wavelength of incident light set to 620 nm,
n s u b
is the refractive index of the base of the cylindrical lens waveguide whose value is 1.7, and
n s u p
is the refractive index of the medium air around the waveguide, which is 1. If the incident and diffracted lights are on the same side of normal, the +sign is used, otherwise, the
sign is used. Finally, it is concluded that the grating period of the first diffraction region of the incident light at 60° should be 419.8nm.
Based on the above-mentioned method, calculations can be performed to obtain the position coordinates and the grating period of the corresponding diffraction region when the light incident at 55°-65° changes at intervals of 1′ (the sensitivity unit of the human eyes to this angle is 1′). The results show that the grating period and the diffraction position of parallel light in curved waveguide alters slightly with a small change in the incident angle. However, the grating structure with the same period is maintained at a length of approximately 0.02mm, i.e., about 45 grating periods with the same period, allowing the concave cylindrical lens waveguide grating structure to still have a normal diffraction function.
4 Simulation analysis
After the previous calculation is completed, the periodic arrangement of grating with variable period on the cylindrical lens waveguide substrate is obtained. To meet the visual requirements of the human eyes, the diffraction efficiency of the grating needs to be sequentially increased. Through theoretical analysis, the ordinary two-dimensional rectangular grating and blazed grating have lower diffraction efficiency in the
1st order, compared to slant grating, which has higher diffraction efficiency. Therefore, slant grating is the optimal choice for the curved waveguide substrate grating structure.
The structure of slant grating is shown in Figure 4.
is the grating period, h is the grating etching depth, d is the grating linewidth, and
is the grating slant angle. The effects of grating duty cycle and slant angle variation on the
1 order diffraction efficiency were investigated using COMSOL software simulation to determine the optimum duty cycle slant angle.
The relationship between the -1st order diffraction efficiency of the slant grating and the duty cycle/slant angle of the grating is shown in Figure 5, where
  λ = 620 n m
Λ = 419.8 n m
h = 106 n m
, and
θ = 57.9 °
. When the -1st order diffraction efficiency is maximum, the duty ratio of the slant grating is 0.5 and the slant angle is 50°, thereby determining the specific structural parameters of tilt grating. The calculated grating period for each region is sequentially simulated by the selected grating structure. The grating structure parameters are as follows: incident light wavelength
  λ = 620 n m
, grating duty cycle
η = d / Λ = 0.5
, slant angle
  β = 50 °
, and grating etching depth h set to a variable between 50-400nm. The simulated field strength distribution of the grating structure during the first diffraction when the light is incident on the waveguide at an angle of 60° is as described below.
The grating structure in Figure 6 is transmission grating, where the upper part is of waveguide material and the lower part is air. The blue arrows indicate the direction of the incident light in the waveguide, and the red arrows indicate the propagation direction of the -1st order diffracted ray. The simulated diffraction angle is consistent with the calculated result. Further, the diffraction simulation of the light incident at 60° is conducted sequentially, and the diffraction efficiency curve of the -1st order is shown in Figure 7.
The simulation results show that under ideal conditions, the total light energy utilization rate can reach 90%. In other words, the -1st order diffraction efficiencies in five different regions are 18.00%, 21.95%, 28.13%, 39.13%, and 64.29%. The etching depths of the gratings in these five regions are 149nm, 151nm, 169nm, 217nm, and 405nm. The results show that the slant grating structure not only meets the requirements of diffraction imaging, but also has a high light efficiency.
In addition, as the light propagating in the waveguide does not have a single wavelength value, it is necessary to consider a variable wavelength range. To equalize the luminance of the beam, it is necessary to ensure that the -1st order diffraction efficiency is constant when the grating incident light has a certain range of wavelength. For the red light in our study, 620nm has been considered as the central wavelength, and the range of variation is assumed to be +10nm. The etching depth in the grating region of the five diffractions is set to 138nm, 139nm, 152nm, 183nm, and 269nm, as shown in Figure 8.
From the above information, it is noted that in each diffraction process, the -1st order diffraction efficiency decreases with an increase in the wavelength, but the variation is quite less compared to the central wavelength diffraction efficiency, where the maximum is not beyond 0.92%.
The obtained simulation results are representative, and the diffraction phenomena and results of incident light at different angles between 55°-65° are similar to the ones mentioned above. It can be concluded that the diffraction efficiency of the grating model is constant for a certain range of wavelength changes, and the brightness of the light entering the human eyes is uniform, resulting in a perfect imaging effect.
The results show that the cylindrical lens waveguide grating structure not only satisfies the deflection requirement of people with astigmatism in the real world, but can also make the diffraction image of the light transmitted by total reflection of the guided wave enter the human eye. Further, the structure perfectly meets the requirement of the users enabling them to directly use AR smartglasses without having to wear a diopter lens.
5 Conclusions
To address the problem associated with people with astigmatism having to wear a diopter lens to use AR smartglasses, a design scheme for the cylindrical lens waveguide grating is proposed and the working principle of holographic waveguide grating is introduced. In this paper, an astigmatic eye with a horizontal axis of -400° is considered as an example. First, a cylindrical lens waveguide model is established to deal with the astigmatism effect when a user views the external world. Further, to make the light from a mini projector diffract normally toward the human eyes, a variable period grating structure is established on the cylindrical lens waveguide substrate. Finally, the structural parameters of grating are optimized so that the total light energy utilization under ideal conditions can reach 90%. The final result shows excellent light lens uniformity of the cylindrical lens waveguide grating structure, with the light brightness difference being less than 0.92%, and the field of view being 10°, which allow the users with astigmatism to directly experience the virtual-real fusion of AR smartglasses without wearing a diopter lens. Further, it provides guidance for the diversity of AR smartglasses design.



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