Patent Publication Number: US-2022229396-A1

Title: Refractive index modulation modification in a holographic grating

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This patent application is a divisional of U.S. Non-Provisional patent application Ser. No. 16/550,046, filed Aug. 23, 2019, entitled “REFRACTIVE INDEX MODULATION MODIFICATION IN A HOLOGRAPHIC GRATING,” which is herein incorporated by reference in its entirety for all purposes. 
    
    
     BACKGROUND 
     An artificial reality system, such as a head-mounted display (HMD) or heads-up display (HUD) system, generally includes a near-eye display system in the form of a headset or a pair of glasses and configured to present content to a user via an electronic or optic display within, for example, about 10-20 mm in front of the user&#39;s eyes. The near-eye display system may display virtual objects or combine images of real objects with virtual objects, as in virtual reality (VR), augmented reality (AR), or mixed reality (MR) applications. For example, in an AR system, a user may view both images of virtual objects (e.g., computer-generated images (CGIs)) and the surrounding environment by, for example, seeing through transparent display glasses or lenses (often referred to as optical see-through). 
     One example of an optical see-through AR system may use a waveguide-based optical display, where light of projected images may be coupled into a waveguide (e.g., a transparent substrate), propagate within the waveguide, and be coupled out of the waveguide at different locations. In some implementations, the light of the projected images may be coupled into or out of the waveguide using a diffractive optical element, such as a holographic grating. In some implementations, the artificial reality systems may employ eye-tracking subsystems that can track the user&#39;s eye (e.g., gaze direction) to modify or generate content based on the direction in which the user is looking, thereby providing a more immersive experience for the user. The eye-tracking subsystems may be implemented using various optical components, such as holographic optical elements. 
     SUMMARY 
     This disclosure relates generally to holographic optical elements. According to certain embodiments, a holographic grating may include a polymer layer. The polymer layer includes a first region characterized by a first refractive index, a second region characterized by a second refractive index, the second refractive index being higher than the first refractive index, and a plurality of nanoparticles dispersed in the polymer layer, the nanoparticles having a higher concentration in either the first region or the second region. 
     According to some embodiments, in the holographic grating, the nanoparticles are monomers. In some embodiments, the nanoparticles have the higher concentration in the second region and the nanoparticles have a third refractive index that is higher than the second refractive index. In some embodiments, the nanoparticles have the higher concentration in the first region and the nanoparticles have a third refractive index that is lower than the first refractive index. In some embodiments, the nanoparticles in the first region or the second region have a substantially constant concentration with respect to a thickness of the polymer layer. In some embodiments, the polymer layer comprises a multiplexed volume Bragg grating. 
     According to certain embodiments, a grating includes a polymer layer. The polymer layer includes a first region characterized by a first refractive index, a second region characterized by a second refractive index, the second refractive index being higher than the first refractive index, and a plurality of nanoparticles dispersed in the polymer layer, the nanoparticles having a higher concentration in proximity to a surface of the polymer layer in one or more of the first region or the second region, such that a refractive index modulation of the grating is apodized. 
     According to certain embodiments, in the grating, the nanoparticles are monomers. In some embodiments, the nanoparticles have the higher concentration in the first region and the nanoparticles have a third refractive index that is higher than the first refractive index In some embodiments, the nanoparticles have the higher concentration in the second region and the nanoparticles have a third refractive index that is lower than the second refractive index. In some embodiments, the polymer layer comprises a multiplexed volume Bragg grating. 
     According to certain embodiments, a holographic grating may include a polymer matrix. The polymer matrix includes a first region characterized by a first refractive index and a second region characterized by a second refractive index, the second refractive index being higher than the first refractive index. The holographic grating further includes a resin layer disposed on the polymer matrix, the resin layer comprising a support layer and a first plurality of nanoparticles dispersed in the support layer of the resin layer. 
     According to certain embodiments, in the holographic grating, the nanoparticles are monomers. In some embodiments, the polymer matrix further comprises a second plurality of nanoparticles, the second plurality of nanoparticles have a higher concentration in the second region than in the first region, and the second plurality of nanoparticles have a third refractive index that is higher than the second refractive index. In some embodiments, the polymer matrix further comprises a second plurality of nanoparticles, the second plurality of nanoparticles have a higher concentration in the first region than in the second region, and the second plurality of nanoparticles have a third refractive index that is lower than the first refractive index. In some embodiments, the nanoparticles in a given region have a substantially constant concentration with respect to a thickness of the polymer matrix. In some embodiments, the polymer matrix comprises a multiplexed volume Bragg grating. 
     According to certain embodiments, a holographic grating may be fabricated by the following process. A holographic recording material layer is obtained. The holographic recording material layer is exposed to a recording light pattern, the recording light pattern creating, in the holographic recording material layer, a first region having a first refractive index and a second region having second refractive index that is higher than the first refractive index. After exposing the holographic recording material layer to the recording light pattern, a first resin layer comprising a first plurality of nanoparticles is applied to the holographic recording material layer, thereby causing diffusion of at least a portion of the first plurality of nanoparticles into the holographic recording material layer. 
     According to certain embodiments, in the fabricated holographic grating, the first plurality of nanoparticles has a third refractive index that is higher than the second refractive index and the first plurality of nanoparticles preferentially diffuses into the second region. In some embodiments, the first plurality of nanoparticles has a third refractive index that is lower than the second refractive index and the first plurality of nanoparticles preferentially diffuses so as to be more highly concentrated in proximity to one or more of a top side or a bottom side of the second region. In some embodiments, the first plurality of nanoparticles has a third refractive index lower than the first refractive index and the first plurality of nanoparticles preferentially diffuses into the first region. In some embodiments, the first plurality of nanoparticles has a third refractive index that is higher than the first refractive index; and the first plurality of nanoparticles further diffuses so as to be more highly concentrated in proximity to one or more of a top side or a bottom side of the first region. In some embodiments, the steps further comprise removing the first resin layer and disposing a substrate on the holographic recording material layer. In some embodiments, the steps further include applying a second resin layer comprising a second plurality of nanoparticles to the holographic recording material layer, thereby causing diffusion of at least a portion of the second plurality of nanoparticles into the holographic recording material layer. In some embodiments, the nanoparticles in a given region have a substantially constant concentration with respect to a thickness of the holographic recording material layer. 
     According to certain embodiments, a holographic grating may be fabricated by the following process. A holographic recording material layer is obtained. A first resin layer comprising a first plurality of nanoparticles is applied to the holographic recording material layer. After applying the first resin layer, the holographic recording material layer is exposed to a recording light pattern, the recording light pattern creating, in the holographic recording material layer, a first region having a first refractive index and a second region having second refractive index that is higher than the first refractive index, wherein at least a portion of the first plurality of nanoparticles diffuses from the first resin layer into the holographic recording material layer. 
     According to certain embodiments, in the fabricated holographic grating, the first plurality of nanoparticles has a third refractive index that is higher than the second refractive index and the first plurality of nanoparticles preferentially diffuses into the second region. In some embodiments, the first plurality of nanoparticles has a third refractive index that is lower than the second refractive index and the first plurality of nanoparticles diffuse so as to be more highly concentrated in proximity to a top side or a bottom side of the second region. In some embodiments, the first plurality of nanoparticles has a third refractive index lower than the first refractive index and the first plurality of nanoparticles preferentially diffuses into the first region. In some embodiments, the first plurality of nanoparticles has a third refractive index that is higher than the first refractive index and the first plurality of nanoparticles diffuse so as to be more highly concentrated in proximity to a top side or a bottom side of the first region. In some embodiments, the steps further include applying a second resin layer comprising a second plurality of nanoparticles to the holographic recording material layer, thereby causing diffusion of at least a portion of the second plurality of nanoparticles into the holographic recording material layer. In some embodiments, the nanoparticles in a given region have a substantially constant concentration with respect to a thickness of the holographic recording material layer. 
     This summary is neither intended to identify key or essential features of the claimed subject matter, nor is it intended to be used in isolation to determine the scope of the claimed subject matter. The subject matter should be understood by reference to appropriate portions of the entire specification of this disclosure, any or all drawings, and each claim. The foregoing, together with other features and examples, will be described in more detail below in the following specification, claims, and accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Illustrative embodiments are described in detail below with reference to the following figures. 
         FIG. 1  is a simplified block diagram of an example of an artificial reality system environment including a near-eye display system according to certain embodiments. 
         FIG. 2  is a perspective view of an example of a near-eye display system in the form of a head-mounted display (HMD) device for implementing some of the examples disclosed herein. 
         FIG. 3  is a perspective view of an example of a near-eye display system in the form of a pair of glasses for implementing some of the examples disclosed herein. 
         FIG. 4  illustrates an example of an optical see-through augmented reality system using a waveguide display that includes an optical combiner according to certain embodiments. 
         FIG. 5A  illustrates an example of a volume Bragg grating (VBG).  FIG. 5B  illustrates the Bragg condition for the volume Bragg grating shown in  FIG. 5A . 
         FIG. 6  illustrates an example of a holographic recording material including two-stage photopolymers. 
         FIG. 7A  illustrates the recording light beams for recording a volume Bragg grating and the light beam reconstructed from the volume Bragg grating. 
         FIG. 7B  is an example of a holography momentum diagram illustrating the wave vectors of recording beams and reconstruction beams and the grating vector of the recorded volume Bragg grating. 
         FIG. 8  illustrates an example of a holographic recording system for recording holographic optical elements. 
         FIG. 9  illustrates an example of a grating including regions of different refractive index. 
         FIGS. 10A-10B  illustrate an example of modifying refractive index modulation in a holographic grating. 
         FIGS. 11A-11C  illustrate an example technique for modifying the refractive index modulation in a holographic grating. 
         FIGS. 12A-12D  illustrate examples of refractive index modulation modification, according to some embodiments. 
         FIGS. 13A-13B  illustrate variations in refractive index modulation modification in a grating, according to some embodiments. 
         FIG. 14  illustrates a grating with tapered refractive index modification. 
         FIGS. 15A-15B  illustrate an example of a refractive index modulation profile in an apodized grating. 
         FIGS. 16A-16B  illustrate sidelobe reduction using an apodized grating in accordance with some embodiments. 
         FIG. 17  is a simplified flow chart illustrating an example of a method of fabricating a holographic optical element according to certain embodiments. 
         FIG. 18  is a schematic diagram showing another holographic optical element fabrication method according to some embodiments. 
         FIG. 19  is a simplified block diagram of an example of an electronic system of a near-eye display system (e.g., HMD device) for implementing some of the examples disclosed herein according to certain embodiments. 
     
    
    
     The figures depict embodiments of the present disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods illustrated may be employed without departing from the principles, or benefits touted, of this disclosure. 
     In the appended figures, similar components and/or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label by a dash and a second label that distinguishes among the similar components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label. 
     DETAILED DESCRIPTION 
     Techniques disclosed herein relate generally to holographic optical elements. More specifically, and without limitation, this disclosure relates to modifying the refractive index of recorded holographic optical elements (HOEs) to enhance the refractive index modulation or apodize the recorded holographic optical elements, in order to improve the diffraction efficiency and/or the contrast of the displayed images by, for example, increasing the number of gratings in the multiplexed grating and reducing the sidelobes of a grating (and thus crosstalk between gratings in a multiplexed grating). Various inventive embodiments are described herein, including materials, systems, modules, devices, components, methods, compositions, and the like. 
     In various optical systems, such as artificial reality systems including virtual reality, augmented reality (AR), and mixed reality (MR) systems, to improve the performance of the optical systems, such as improving the brightness of the displayed images, expanding the eyebox, reducing artifacts, increasing the field of view, and improving user interaction with presented content, various holographic optical elements may be used for light beam coupling and shaping, such as coupling light into or out of a waveguide display or tracking the motion of the user&#39;s eyes. These holographic optical elements may need to have a high refractive index modulation, a small pitch or feature size, high clarity, high diffraction efficiency, and the like. 
     The diffraction efficiency of a holographic optical element is related to the difference in refractive index in different regions of a grating. Given the relatively small range of refractive index modulation available in materials suitable for recording a holographic grating, there is a limit on the diffraction efficiency achievable using traditional methods. Another limitation in these gratings is sidelobes in the diffraction pattern, which may affect image quality. In the case of multiplexed gratings, the sidelobes of a grating may overlap with the main lobes of other gratings, resulting in crosstalk. To reduce crosstalk, one option is to reduce the number of gratings multiplexed, which can be undesirable in many applications. Techniques described herein can be applied to increase the refractive index modulation in an HOE to improve diffraction efficiency, and/or to apodize a grating to eliminate or reduce sidelobes/crosstalk without limiting the number of gratings that may be multiplexed in a holographic material layer. 
     According to certain embodiments, a layer of resin material including a support matrix and monomers (or other nanoparticles) dispersed in the support matrix, such as a monomer reservoir buffer layer, may be formed on a photopolymer layer, either before or after the holographic recording in the photopolymer layer. Depending on, for example, the sizes of the monomers and the affinity between the monomers and the polymers in the recorded holographic optical elements, the monomers in the layer of resin material may more preferentially diffuse to the high refractive index regions of the HOE than to the low refractive index regions of the HOE, or more preferentially diffuse to the low refractive index regions than to the high refractive index regions. As such, the refractive index in the high refractive index regions (or the low refractive regions) may be changed more than the low refractive index regions (or the high refractive index regions). The changes may include increasing the refractive index in the diffused regions if the monomers in the layer of resin material have a higher refractive index than the refractive index in the diffused regions, or decreasing the refractive index in the diffused regions if the monomers in the layer of resin material have a lower refractive index than the refractive index in the diffused regions. Thus, the refractive index may be selectively increased or decreased in different regions to increase or decrease the refractive index modulation. 
     In some embodiments, the refractive index in the low refractive index regions of the HOE may be decreased by preferentially diffusing lower refractive index monomers to the low refractive index regions. In some embodiments, the refractive index in the high refractive index regions of the HOE may be increased by preferentially diffusing higher refractive index monomers to the high refractive index regions. In some embodiments, the refractive index in both the high and low refractive index regions of the HOE may be increased, but the refractive index in the high refractive index regions of the HOE may be increased more due to the preferential diffusion of higher index monomers. In some embodiments, the refractive index in both the high and low refractive index regions of the HOE may be decreased, but the refractive index in the low refractive index regions of the HOE may be decreased more due to the preferential diffusion of lower index monomers. Thus, the refractive index modulation of the HOE can be increased to increase the diffraction efficiency and/or to multiplex more gratings in a photopolymer material layer. 
     In some embodiments, the layer of resin material may include a lower concentration of monomers or the diffusion may be controlled to occur in limited time, and thus the monomers may not diffuse through the full depth of the HOE. As a result, the HOE may have different refractive index modulations at different depths. For example, the monomers in the layer of resin material may have a lower refractive index and may more preferentially diffuse into the high refractive index regions through a certain thickness of the HOE such that the refractive index modulation may taper from the center of the HOE in the thickness direction. In some embodiments, the layer of resin material including the support matrix and monomers may be formed on opposite sides of the photopolymer layer, such that the refractive index modulation may taper from the center of the HOE in the thickness direction to the opposite sides, forming a bell-shaped refractive index modulation profile. Thus, the HOE may be apodized to reduce sidelobes in the diffraction efficiency curves and thus crosstalk between gratings in a multiplexed grating. 
     In some embodiments, the layer of resin material including the support matrix and monomers (or other nanoparticles) dispersed in the support matrix may be formed after the HOE is recorded and a cover layer is removed, and may or may not remain in the final device after the diffusion of the monomers in the layer of resin material. In some embodiments, the layer of resin material (e.g., the monomer reservoir buffer layer) may be formed on the photopolymer layer before the holographic recording and may or may not remain in the final device. For example, the support matrix of the monomer reservoir buffer layer may be similar to a substrate and may remain in the final device after the monomers diffuse into the HOE. 
     As used herein, visible light may refer to light with a wavelength between about 380 nm and about 750 nm, between about 400 nm and about 700 nm, or between about 440 nm and about 650 nm. Near infrared (NIR) light may refer to light with a wavelength between about 750 nm to about 2500 nm. The desired infrared (IR) wavelength range may refer to the wavelength range of IR light that can be detected by a suitable IR sensor (e.g., a complementary metal-oxide semiconductor (CMOS), a charge-coupled device (CCD) sensor, or an InGaAs sensor), such as between 830 nm and 860 nm, between 930 nm and 980 nm, or between about 750 nm to about 1000 nm. 
     As also used herein, a substrate may refer to a medium within which light may propagate. The substrate may include one or more types of dielectric materials, such as glass, quartz, plastic, polymer, poly(methyl methacrylate) (PMMA), crystal, or ceramic. At least one type of material of the substrate may be transparent to visible light and NIR light. A thickness of the substrate may range from, for example, less than about 1 mm to about 10 mm or more. As used herein, a material may be “transparent” to a light beam if the light beam can pass through the material with a high transmission rate, such as larger than 60%, 75%, 80%, 90%, 95%, 98%, 99%, or higher, where a small portion of the light beam (e.g., less than 40%, 25%, 20%, 10%, 5%, 2%, 1%, or less) may be scattered, reflected, or absorbed by the material. The transmission rate (i.e., transmissivity) may be represented by either a photopically weighted or an unweighted average transmission rate over a range of wavelengths, or the lowest transmission rate over a range of wavelengths, such as the visible wavelength range. 
     As also used herein, the term “support matrix” refers to the material, medium, substance, etc., in which the polymerizable component is dissolved, dispersed, embedded, enclosed, etc. In some embodiments, the support matrix is typically a low T g  polymer. The polymer may be organic, inorganic, or a mixture of the two. Without being particularly limited, the polymer may be a thermoset or thermoplastic. 
     As also used herein, the term “polymerizable component” refers to one or more photoactive polymerizable materials, and possibly one or more additional polymerizable materials, e.g., monomers and/or oligomers, that are capable of forming a polymer. 
     As also used herein, the term “photoactive polymerizable material” refers to a monomer, an oligomer and combinations thereof that polymerize in the presence of a photoinitiator that has been activated by being exposed to a photoinitiating light source, e.g., recording light. In reference to the functional group that undergoes curing, the photoactive polymerizable material comprises at least one such functional group. It is also understood that there exist photoactive polymerizable materials that are also photoinitiators, such as N-methylmaleimide, derivatized acetophenones, etc., and that in such a case, it is understood that the photoactive monomer and/or oligomer of the present disclosure may also be a photoinitiator. 
     As also used herein, the term “photopolymer” refers to a polymer formed by one or more photoactive polymerizable materials, and possibly one or more additional monomers and/or oligomers. 
     In the following description, for the purposes of explanation, specific details are set forth in order to provide a thorough understanding of examples of the disclosure. However, it will be apparent that various examples may be practiced without these specific details. For example, devices, systems, structures, assemblies, methods, and other components may be shown as components in block diagram form in order not to obscure the examples in unnecessary detail. In other instances, well-known devices, processes, systems, structures, and techniques may be shown without necessary detail in order to avoid obscuring the examples. The figures and description are not intended to be restrictive. The terms and expressions that have been employed in this disclosure are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof. The word “example” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment or design described herein as “example” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. 
       FIG. 1  is a simplified block diagram of an example of an artificial reality system environment  100  including a near-eye display system  120  in accordance with certain embodiments. Artificial reality system environment  100  shown in  FIG. 1  may include near-eye display system  120 , an optional imaging device  150 , and an optional input/output interface  140  that may each be coupled to an optional console  110 . While  FIG. 1  shows example artificial reality system environment  100  including one near-eye display system  120 , one imaging device  150 , and one input/output interface  140 , any number of these components may be included in artificial reality system environment  100 , or any of the components may be omitted. For example, there may be multiple near-eye display systems  120  monitored by one or more external imaging devices  150  in communication with console  110 . In some configurations, artificial reality system environment  100  may not include imaging device  150 , optional input/output interface  140 , and optional console  110 . In alternative configurations, different or additional components may be included in artificial reality system environment  100 . In some configurations, near-eye display systems  120  may include imaging device  150 , which may be used to track one or more input/output devices (e.g., input/output interface  140 ), such as a handhold controller. 
     Near-eye display system  120  may be a head-mounted display that presents content to a user. Examples of content presented by near-eye display system  120  include one or more of images, videos, audios, or some combination thereof. In some embodiments, audios may be presented via an external device (e.g., speakers and/or headphones) that receives audio information from near-eye display system  120 , console  110 , or both, and presents audio data based on the audio information. Near-eye display system  120  may include one or more rigid bodies, which may be rigidly or non-rigidly coupled to each other. A rigid coupling between rigid bodies may cause the coupled rigid bodies to act as a single rigid entity. A non-rigid coupling between rigid bodies may allow the rigid bodies to move relative to each other. In various embodiments, near-eye display system  120  may be implemented in any suitable form factor, including a pair of glasses. Some embodiments of near-eye display system  120  are further described below. Additionally, in various embodiments, the functionality described herein may be used in a headset that combines images of an environment external to near-eye display system  120  and artificial reality content (e.g., computer-generated images). Therefore, near-eye display system  120  may augment images of a physical, real-world environment external to near-eye display system  120  with generated content (e.g., images, video, sound, etc.) to present an augmented reality to a user. 
     In various embodiments, near-eye display system  120  may include one or more of display electronics  122 , display optics  124 , and an eye-tracking system  130 . In some embodiments, near-eye display system  120  may also include one or more locators  126 , one or more position sensors  128 , and an inertial measurement unit (IMU)  132 . Near-eye display system  120  may omit any of these elements or include additional elements in various embodiments. Additionally, in some embodiments, near-eye display system  120  may include elements combining the function of various elements described in conjunction with  FIG. 1 . 
     Display electronics  122  may display or facilitate the display of images to the user according to data received from, for example, console  110 . In various embodiments, display electronics  122  may include one or more display panels, such as a liquid crystal display (LCD), an organic light emitting diode (OLED) display, an inorganic light emitting diode (ILED) display, a micro light emitting diode (μLED) display, an active-matrix OLED display (AMOLED), a transparent OLED display (TOLED), or some other display. For example, in one implementation of near-eye display system  120 , display electronics  122  may include a front TOLED panel, a rear display panel, and an optical component (e.g., an attenuator, polarizer, or diffractive or spectral film) between the front and rear display panels. Display electronics  122  may include pixels to emit light of a predominant color such as red, green, blue, white, or yellow. In some implementations, display electronics  122  may display a three-dimensional (3D) image through stereo effects produced by two-dimensional panels to create a subjective perception of image depth. For example, display electronics  122  may include a left display and a right display positioned in front of a user&#39;s left eye and right eye, respectively. The left and right displays may present copies of an image shifted horizontally relative to each other to create a stereoscopic effect (i.e., a perception of image depth by a user viewing the image). 
     In certain embodiments, display optics  124  may display image content optically (e.g., using optical waveguides and couplers), magnify image light received from display electronics  122 , correct optical errors associated with the image light, and present the corrected image light to a user of near-eye display system  120 . In various embodiments, display optics  124  may include one or more optical elements, such as, for example, a substrate, optical waveguides, an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, input/output couplers, or any other suitable optical elements that may affect image light emitted from display electronics  122 . 
     Display optics  124  may include a combination of different optical elements as well as mechanical couplings to maintain relative spacing and orientation of the optical elements in the combination. One or more optical elements in display optics  124  may have an optical coating, such as an anti-reflective coating, a reflective coating, a filtering coating, or a combination of different optical coatings. 
     Magnification of the image light by display optics  124  may allow display electronics  122  to be physically smaller, weigh less, and consume less power than larger displays. Additionally, magnification may increase a field of view of the displayed content. The amount of magnification of image light by display optics  124  may be changed by adjusting, adding, or removing optical elements from display optics  124 . In some embodiments, display optics  124  may project displayed images to one or more image planes that may be further away from the user&#39;s eyes than near-eye display system  120 / 
     Display optics  124  may also be designed to correct one or more types of optical errors, such as two-dimensional optical errors, three-dimensional optical errors, or a combination thereof. Two-dimensional errors may include optical aberrations that occur in two dimensions. Example types of two-dimensional errors may include barrel distortion, pincushion distortion, longitudinal chromatic aberration, and transverse chromatic aberration. Three-dimensional errors may include optical errors that occur in three dimensions. Example types of three-dimensional errors may include spherical aberration, comatic aberration, field curvature, and astigmatism. 
     Locators  126  may be objects located in specific positions on near-eye display system  120  relative to one another and relative to a reference point on near-eye display system  120 . In some implementations, console  110  may identify locators  126  in images captured by imaging device  150  to determine the artificial reality headset&#39;s position, orientation, or both. A locator  126  may be a light emitting diode (LED), a corner cube reflector, a reflective marker, a type of light source that contrasts with an environment in which near-eye display system  120  operates, or some combinations thereof. In embodiments where locators  126  are active components (e.g., LEDs or other types of light emitting devices), locators  126  may emit light in the visible band (e.g., about 380 nm to 750 nm), in the infrared (IR) band (e.g., about 750 nm to 1 mm), in the ultraviolet band (e.g., about 10 nm to about 380 nm), in another portion of the electromagnetic spectrum, or in any combination of portions of the electromagnetic spectrum. 
     Imaging device  150  may be part of near-eye display system  120  or may be external to near-eye display system  120 . Imaging device  150  may generate slow calibration data based on calibration parameters received from console  110 . Slow calibration data may include one or more images showing observed positions of locators  126  that are detectable by imaging device  150 . Imaging device  150  may include one or more cameras, one or more video cameras, any other device capable of capturing images including one or more of locators  126 , or some combinations thereof. Additionally, imaging device  150  may include one or more filters (e.g., to increase signal to noise ratio). Imaging device  150  may be configured to detect light emitted or reflected from locators  126  in a field of view of imaging device  150 . In embodiments where locators  126  include passive elements (e.g., retroreflectors), imaging device  150  may include a light source that illuminates some or all of locators  126 , which may retro-reflect the light to the light source in imaging device  150 . Slow calibration data may be communicated from imaging device  150  to console  110 , and imaging device  150  may receive one or more calibration parameters from console  110  to adjust one or more imaging parameters (e.g., focal length, focus, frame rate, sensor temperature, shutter speed, aperture, etc.). 
     Position sensors  128  may generate one or more measurement signals in response to motion of near-eye display system  120 . Examples of position sensors  128  may include accelerometers, gyroscopes, magnetometers, other motion-detecting or error-correcting sensors, or some combinations thereof. For example, in some embodiments, position sensors  128  may include multiple accelerometers to measure translational motion (e.g., forward/back, up/down, or left/right) and multiple gyroscopes to measure rotational motion (e.g., pitch, yaw, or roll). In some embodiments, various position sensors may be oriented orthogonally to each other. 
     IMU  132  may be an electronic device that generates fast calibration data based on measurement signals received from one or more of position sensors  128 . Position sensors  128  may be located external to IMU  132 , internal to IMU  132 , or some combination thereof. Based on the one or more measurement signals from one or more position sensors  128 , IMU  132  may generate fast calibration data indicating an estimated position of near-eye display system  120  relative to an initial position of near-eye display system  120 . For example, IMU  132  may integrate measurement signals received from accelerometers over time to estimate a velocity vector and integrate the velocity vector over time to determine an estimated position of a reference point on near-eye display system  120 . Alternatively, IMU  132  may provide the sampled measurement signals to console  110 , which may determine the fast calibration data. While the reference point may generally be defined as a point in space, in various embodiments, the reference point may also be defined as a point within near-eye display system  120  (e.g., a center of IMU  132 ). 
     Eye-tracking system  130  may include one or more eye-tracking systems. Eye tracking may refer to determining an eye&#39;s position, including orientation and location of the eye, relative to near-eye display system  120 . An eye-tracking system may include an imaging system to image one or more eyes and may generally include a light emitter, which may generate light that is directed to an eye such that light reflected by the eye may be captured by the imaging system. For example, eye-tracking system  130  may include a non-coherent or coherent light source (e.g., a laser diode) emitting light in the visible spectrum or infrared spectrum, and a camera capturing the light reflected by the user&#39;s eye. As another example, eye-tracking system  130  may capture reflected radio waves emitted by a miniature radar unit. Eye-tracking system  130  may use low-power light emitters that emit light at frequencies and intensities that would not injure the eye or cause physical discomfort. Eye-tracking system  130  may be arranged to increase contrast in images of an eye captured by eye-tracking system  130  while reducing the overall power consumed by eye-tracking system  130  (e.g., reducing power consumed by a light emitter and an imaging system included in eye-tracking system  130 ). For example, in some implementations, eye-tracking system  130  may consume less than 100 milliwatts of power. 
     Eye-tracking system  130  may be configured to estimate the orientation of the user&#39;s eye. The orientation of the eye may correspond to the direction of the user&#39;s gaze within near-eye display system  120 . The orientation of the user&#39;s eye may be defined as the direction of the foveal axis, which is the axis between the fovea (an area on the retina of the eye with the highest concentration of photoreceptors) and the center of the eye&#39;s pupil. In general, when a user&#39;s eyes are fixed on a point, the foveal axes of the user&#39;s eyes intersect that point. The pupillary axis of an eye may be defined as the axis that passes through the center of the pupil and is perpendicular to the corneal surface. In general, even though the pupillary axis and the foveal axis intersect at the center of the pupil, the pupillary axis may not directly align with the foveal axis. For example, the orientation of the foveal axis may be offset from the pupillary axis by approximately −1° to 8° laterally and about ±4° vertically (which may be referred to as kappa angles, which may vary from person to person). Because the foveal axis is defined according to the fovea, which is located in the back of the eye, the foveal axis may be difficult or impossible to measure directly in some eye-tracking embodiments. Accordingly, in some embodiments, the orientation of the pupillary axis may be detected and the foveal axis may be estimated based on the detected pupillary axis. 
     In general, the movement of an eye corresponds not only to an angular rotation of the eye, but also to a translation of the eye, a change in the torsion of the eye, and/or a change in the shape of the eye. Eye-tracking system  130  may also be configured to detect the translation of the eye, which may be a change in the position of the eye relative to the eye socket. In some embodiments, the translation of the eye may not be detected directly, but may be approximated based on a mapping from a detected angular orientation. Translation of the eye corresponding to a change in the eye&#39;s position relative to the eye-tracking system due to, for example, a shift in the position of near-eye display system  120  on a user&#39;s head, may also be detected. Eye-tracking system  130  may also detect the torsion of the eye and the rotation of the eye about the pupillary axis. Eye-tracking system  130  may use the detected torsion of the eye to estimate the orientation of the foveal axis from the pupillary axis. In some embodiments, eye-tracking system  130  may also track a change in the shape of the eye, which may be approximated as a skew or scaling linear transform or a twisting distortion (e.g., due to torsional deformation). In some embodiments, eye-tracking system  130  may estimate the foveal axis based on some combinations of the angular orientation of the pupillary axis, the translation of the eye, the torsion of the eye, and the current shape of the eye. 
     In some embodiments, eye-tracking system  130  may include multiple emitters or at least one emitter that can project a structured light pattern on all portions or a portion of the eye. The structured light pattern may be distorted due to the shape of the eye when viewed from an offset angle. Eye-tracking system  130  may also include at least one camera that may detect the distortions (if any) of the structured light pattern projected onto the eye. The camera may be oriented on a different axis to the eye than the emitter. By detecting the deformation of the structured light pattern on the surface of the eye, eye-tracking system  130  may determine the shape of the portion of the eye being illuminated by the structured light pattern. Therefore, the captured distorted light pattern may be indicative of the 3D shape of the illuminated portion of the eye. The orientation of the eye may thus be derived from the 3D shape of the illuminated portion of the eye. Eye-tracking system  130  can also estimate the pupillary axis, the translation of the eye, the torsion of the eye, and the current shape of the eye based on the image of the distorted structured light pattern captured by the camera. 
     Near-eye display system  120  may use the orientation of the eye to, e.g., determine an inter-pupillary distance (IPD) of the user, determine gaze directions, introduce depth cues (e.g., blur image outside of the user&#39;s main line of sight), collect heuristics on the user interaction in the VR media (e.g., time spent on any particular subject, object, or frame as a function of exposed stimuli), some other functions that are based in part on the orientation of at least one of the user&#39;s eyes, or some combination thereof. Because the orientation may be determined for both eyes of the user, eye-tracking system  130  may be able to determine where the user is looking. For example, determining a direction of a user&#39;s gaze may include determining a point of convergence based on the determined orientations of the user&#39;s left and right eyes. A point of convergence may be the point where the two foveal axes of the user&#39;s eyes intersect. The direction of the user&#39;s gaze may be the direction of a line passing through the point of convergence and the mid-point between the pupils of the user&#39;s eyes. 
     Input/output interface  140  may be a device that allows a user to send action requests to console  110 . An action request may be a request to perform a particular action. For example, an action request may be to start or to end an application or to perform a particular action within the application. Input/output interface  140  may include one or more input devices. Example input devices may include a keyboard, a mouse, a game controller, a glove, a button, a touch screen, or any other suitable device for receiving action requests and communicating the received action requests to console  110 . An action request received by the input/output interface  140  may be communicated to console  110 , which may perform an action corresponding to the requested action. In some embodiments, input/output interface  140  may provide haptic feedback to the user in accordance with instructions received from console  110 . For example, input/output interface  140  may provide haptic feedback when an action request is received, or when console  110  has performed a requested action and communicates instructions to input/output interface  140 . In some embodiments, imaging device  150  may be used to track input/output interface  140 , such as tracking the location or position of a controller (which may include, for example, an IR light source) or a hand of the user to determine the motion of the user. In some embodiments, near-eye display  120  may include one or more imaging devices (e.g., imaging device  150 ) to track input/output interface  140 , such as tracking the location or position of a controller or a hand of the user to determine the motion of the user. 
     Console  110  may provide content to near-eye display system  120  for presentation to the user in accordance with information received from one or more of imaging device  150 , near-eye display system  120 , and input/output interface  140 . In the example shown in  FIG. 1 , console  110  may include an application store  112 , a headset tracking module  114 , an artificial reality engine  116 , and eye-tracking module  118 . Some embodiments of console  110  may include different or additional modules than those described in conjunction with  FIG. 1 . Functions further described below may be distributed among components of console  110  in a different manner than is described here. 
     In some embodiments, console  110  may include a processor and a non-transitory computer-readable storage medium storing instructions executable by the processor. The processor may include multiple processing units executing instructions in parallel. The computer-readable storage medium may be any memory, such as a hard disk drive, a removable memory, or a solid-state drive (e.g., flash memory or dynamic random access memory (DRAM)). In various embodiments, the modules of console  110  described in conjunction with  FIG. 1  may be encoded as instructions in the non-transitory computer-readable storage medium that, when executed by the processor, cause the processor to perform the functions further described below. 
     Application store  112  may store one or more applications for execution by console  110 . An application may include a group of instructions that, when executed by a processor, generates content for presentation to the user. Content generated by an application may be in response to inputs received from the user via movement of the user&#39;s eyes or inputs received from the input/output interface  140 . Examples of the applications may include gaming applications, conferencing applications, video playback application, or other suitable applications. 
     Headset tracking module  114  may track movements of near-eye display system  120  using slow calibration information from imaging device  150 . For example, headset tracking module  114  may determine positions of a reference point of near-eye display system  120  using observed locators from the slow calibration information and a model of near-eye display system  120 . Headset tracking module  114  may also determine positions of a reference point of near-eye display system  120  using position information from the fast calibration information. Additionally, in some embodiments, headset tracking module  114  may use portions of the fast calibration information, the slow calibration information, or some combination thereof, to predict a future location of near-eye display system  120 . Headset tracking module  114  may provide the estimated or predicted future position of near-eye display system  120  to artificial reality engine  116 . 
     Headset tracking module  114  may calibrate the artificial reality system environment  100  using one or more calibration parameters, and may adjust one or more calibration parameters to reduce errors in determining the position of near-eye display system  120 . For example, headset tracking module  114  may adjust the focus of imaging device  150  to obtain a more accurate position for observed locators on near-eye display system  120 . Moreover, calibration performed by headset tracking module  114  may also account for information received from IMU  132 . Additionally, if tracking of near-eye display system  120  is lost (e.g., imaging device  150  loses line of sight of at least a threshold number of locators  126 ), headset tracking module  114  may re-calibrate some or all of the calibration parameters. 
     Artificial reality engine  116  may execute applications within artificial reality system environment  100  and receive position information of near-eye display system  120 , acceleration information of near-eye display system  120 , velocity information of near-eye display system  120 , predicted future positions of near-eye display system  120 , or some combination thereof from headset tracking module  114 . Artificial reality engine  116  may also receive estimated eye position and orientation information from eye-tracking module  118 . Based on the received information, artificial reality engine  116  may determine content to provide to near-eye display system  120  for presentation to the user. For example, if the received information indicates that the user has looked to the left, artificial reality engine  116  may generate content for near-eye display system  120  that reflects the user&#39;s eye movement in a virtual environment. Additionally, artificial reality engine  116  may perform an action within an application executing on console  110  in response to an action request received from input/output interface  140 , and provide feedback to the user indicating that the action has been performed. The feedback may be visual or audible feedback via near-eye display system  120  or haptic feedback via input/output interface  140 . 
     Eye-tracking module  118  may receive eye-tracking data from eye-tracking system  130  and determine the position of the user&#39;s eye based on the eye-tracking data. The position of the eye may include an eye&#39;s orientation, location, or both relative to near-eye display system  120  or any element thereof. Because the eye&#39;s axes of rotation change as a function of the eye&#39;s location in its socket, determining the eye&#39;s location in its socket may allow eye-tracking module  118  to more accurately determine the eye&#39;s orientation. 
     In some embodiments, eye-tracking module  118  may store a mapping between images captured by eye-tracking system  130  and eye positions to determine a reference eye position from an image captured by eye-tracking system  130 . Alternatively or additionally, eye-tracking module  118  may determine an updated eye position relative to a reference eye position by comparing an image from which the reference eye position is determined to an image from which the updated eye position is to be determined. Eye-tracking module  118  may determine eye position using measurements from different imaging devices or other sensors. For example, eye-tracking module  118  may use measurements from a slow eye-tracking system to determine a reference eye position, and then determine updated positions relative to the reference eye position from a fast eye-tracking system until a next reference eye position is determined based on measurements from the slow eye-tracking system. 
     Eye-tracking module  118  may also determine eye calibration parameters to improve precision and accuracy of eye tracking. Eye calibration parameters may include parameters that may change whenever a user dons or adjusts near-eye display system  120 . Example eye calibration parameters may include an estimated distance between a component of eye-tracking system  130  and one or more parts of the eye, such as the eye&#39;s center, pupil, cornea boundary, or a point on the surface of the eye. Other example eye calibration parameters may be specific to a particular user and may include an estimated average eye radius, an average corneal radius, an average sclera radius, a map of features on the eye surface, and an estimated eye surface contour. In embodiments where light from the outside of near-eye display system  120  may reach the eye (as in some augmented reality applications), the calibration parameters may include correction factors for intensity and color balance due to variations in light from the outside of near-eye display system  120 . Eye-tracking module  118  may use eye calibration parameters to determine whether the measurements captured by eye-tracking system  130  would allow eye-tracking module  118  to determine an accurate eye position (also referred to herein as “valid measurements”). Invalid measurements, from which eye-tracking module  118  may not be able to determine an accurate eye position, may be caused by the user blinking, adjusting the headset, or removing the headset, and/or may be caused by near-eye display system  120  experiencing greater than a threshold change in illumination due to external light. In some embodiments, at least some of the functions of eye-tracking module  118  may be performed by eye-tracking system  130 . 
       FIG. 2  is a perspective view of an example of a near-eye display system in the form of a head-mounted display (HMD) device  200  for implementing some of the examples disclosed herein. HMD device  200  may be a part of, e.g., a virtual reality (VR) system, an augmented reality (AR) system, a mixed reality (MR) system, or some combinations thereof. HMD device  200  may include a body  220  and a head strap  230 .  FIG. 2  shows a bottom side  223 , a front side  225 , and a right side  227  of body  220  in the perspective view. Head strap  230  may have an adjustable or extendible length. There may be a sufficient space between body  220  and head strap  230  of HMD device  200  for allowing a user to mount HMD device  200  onto the user&#39;s head. In various embodiments, HMD device  200  may include additional, fewer, or different components. For example, in some embodiments, HMD device  200  may include eyeglass temples and temples tips as shown in, for example,  FIG. 2 , rather than head strap  230 . 
     HMD device  200  may present to a user media including virtual and/or augmented views of a physical, real-world environment with computer-generated elements. Examples of the media presented by HMD device  200  may include images (e.g., two-dimensional (2D) or three-dimensional (3D) images), videos (e.g., 2D or 3D videos), audios, or some combinations thereof. The images and videos may be presented to each eye of the user by one or more display assemblies (not shown in  FIG. 2 ) enclosed in body  220  of HMD device  200 . In various embodiments, the one or more display assemblies may include a single electronic display panel or multiple electronic display panels (e.g., one display panel for each eye of the user). Examples of the electronic display panel(s) may include, for example, a liquid crystal display (LCD), an organic light emitting diode (μLED OLED) display, an inorganic light emitting diode (ILED) display, a micro light emitting diode ( ) display, an active-matrix organic light emitting diode (AMOLED) display, a transparent organic light emitting diode (TOLED) display, some other display, or some combinations thereof. HMD device  200  may include two eye box regions. 
     In some implementations, HMD device  200  may include various sensors (not shown), such as depth sensors, motion sensors, position sensors, and eye-tracking sensors. Some of these sensors may use a structured light pattern for sensing. In some implementations, HMD device  200  may include an input/output interface for communicating with a console. In some implementations, HMD device  200  may include a virtual reality engine (not shown) that can execute applications within HMD device  200  and receive depth information, position information, acceleration information, velocity information, predicted future positions, or some combination thereof of HMD device  200  from the various sensors. In some implementations, the information received by the virtual reality engine may be used for producing a signal (e.g., display instructions) to the one or more display assemblies. In some implementations, HMD device  200  may include locators (not shown, such as locators  126 ) located in fixed positions on body  220  relative to one another and relative to a reference point. Each of the locators may emit light that is detectable by an external imaging device. 
       FIG. 3  is a perspective view of an example of a near-eye display system  300  in the form of a pair of glasses for implementing some of the examples disclosed herein. Near-eye display system  300  may be a specific implementation of near-eye display system  120  of  FIG. 1 , and may be configured to operate as a virtual reality display, an augmented reality display, and/or a mixed reality display. Near-eye display system  300  may include a frame  305  and a display  310 . Display  310  may be configured to present content to a user. In some embodiments, display  310  may include display electronics and/or display optics. For example, as described above with respect to near-eye display system  120  of  FIG. 1 , display  310  may include an LCD display panel, an LED display panel, or an optical display panel (e.g., a waveguide display assembly). 
     Near-eye display system  300  may further include various sensors  350   a ,  350   b ,  350   c ,  350   d , and  350   e  on or within frame  305 . In some embodiments, sensors  350   a - 350   e  may include one or more depth sensors, motion sensors, position sensors, inertial sensors, or ambient light sensors. In some embodiments, sensors  350   a - 350   e  may include one or more image sensors configured to generate image data representing different fields of views in different directions. In some embodiments, sensors  350   a - 350   e  may be used as input devices to control or influence the displayed content of near-eye display system  300 , and/or to provide an interactive VR/AR/MR experience to a user of near-eye display system  300 . In some embodiments, sensors  350   a - 350   e  may also be used for stereoscopic imaging. 
     In some embodiments, near-eye display system  300  may further include one or more illuminators  330  to project light into the physical environment. The projected light may be associated with different frequency bands (e.g., visible light, infra-red light, ultra-violet light, etc.), and may serve various purposes. For example, illuminator(s)  330  may project light in a dark environment (or in an environment with low intensity of infra-red light, ultra-violet light, etc.) to assist sensors  350   a - 350   e  in capturing images of different objects within the dark environment. In some embodiments, illuminator(s)  330  may be used to project certain light pattern onto the objects within the environment. In some embodiments, illuminator(s)  330  may be used as locators, such as locators  126  described above with respect to  FIG. 1 . 
     In some embodiments, near-eye display system  300  may also include a high-resolution camera  340 . Camera  340  may capture images of the physical environment in the field of view. The captured images may be processed, for example, by a virtual reality engine (e.g., artificial reality engine  116  of  FIG. 1 ) to add virtual objects to the captured images or modify physical objects in the captured images, and the processed images may be displayed to the user by display  310  for AR or MR applications. 
       FIG. 4  illustrates an example of an optical see-through augmented reality system  400  using a waveguide display according to certain embodiments. Augmented reality system  400  may include a projector  410  and a combiner  415 . Projector  410  may include a light source or image source  412  and projector optics  414 . In some embodiments, image source  412  may include a plurality of pixels that displays virtual objects, such as an LCD display panel or an LED display panel. In some embodiments, image source  412  may include a light source that generates coherent or partially coherent light. For example, image source  412  may include a laser diode, a vertical cavity surface emitting laser, and/or a light emitting diode. In some embodiments, image source  412  may include a plurality of light sources each emitting a monochromatic image light corresponding to a primary color (e.g., red, green, or blue). In some embodiments, image source  412  may include an optical pattern generator, such as a spatial light modulator. Projector optics  414  may include one or more optical components that can condition the light from image source  412 , such as expanding, collimating, scanning, or projecting light from image source  412  to combiner  415 . The one or more optical components may include, for example, one or more lenses, liquid lenses, mirrors, apertures, and/or gratings. In some embodiments, projector optics  414  may include a liquid lens (e.g., a liquid crystal lens) with a plurality of electrodes that allows scanning of the light from image source  412 . 
     Combiner  415  may include an input coupler  430  for coupling light from projector  410  into a substrate  420  of combiner  415 . Combiner  415  may transmit at least 50% of light in a first wavelength range and reflect at least 25% of light in a second wavelength range. For example, the first wavelength range may be visible light from about 400 nm to about 650 nm, and the second wavelength range may be in the infrared band, for example, from about 800 nm to about 1000 nm. Input coupler  430  may include a volume holographic grating, a diffractive optical elements (DOE) (e.g., a surface-relief grating), a slanted surface of substrate  420 , or a refractive coupler (e.g., a wedge or a prism). Input coupler  430  may have a coupling efficiency of greater than 30%, 50%, 75%, 90%, or higher for visible light. Light coupled into substrate  420  may propagate within substrate  420  through, for example, total internal reflection (TIR). Substrate  420  may be in the form of a lens of a pair of eyeglasses. Substrate  420  may have a flat or a curved surface, and may include one or more types of dielectric materials, such as glass, quartz, plastic, polymer, poly(methyl methacrylate) (PMMA), crystal, or ceramic. A thickness of the substrate may range from, for example, less than about 1 mm to about 10 mm or more. Substrate  420  may be transparent to visible light. 
     Substrate  420  may include or may be coupled to a plurality of output couplers  440  configured to extract at least a portion of the light guided by and propagating within substrate  420  from substrate  420 , and direct extracted light  460  to an eye  490  of the user of augmented reality system  400 . As input coupler  430 , output couplers  440  may include grating couplers (e.g., volume holographic gratings or surface-relief gratings), other DOEs, prisms, etc. Output couplers  440  may have different coupling (e.g., diffraction) efficiencies at different locations. Substrate  420  may also allow light  450  from environment in front of combiner  415  to pass through with little or no loss. Output couplers  440  may also allow light  450  to pass through with little loss. For example, in some implementations, output couplers  440  may have a low diffraction efficiency for light  450  such that light  450  may be refracted or otherwise pass through output couplers  440  with little loss, and thus may have a higher intensity than extracted light  460 . In some implementations, output couplers  440  may have a high diffraction efficiency for light  450  and may diffract light  450  to certain desired directions (i.e., diffraction angles) with little loss. As a result, the user may be able to view combined images of the environment in front of combiner  415  and virtual objects projected by projector  410 . 
     In addition, as described above, in an artificial reality system, to improve user interaction with presented content, the artificial reality system may track the user&#39;s eye and modify or generate content based on a location or a direction in which the user is looking at. Tracking the eye may include tracking the position and/or shape of the pupil and/or the cornea of the eye, and determining the rotational position or gaze direction of the eye. One technique (referred to as Pupil Center Corneal Reflection or PCCR method) involves using NIR LEDs to produce glints on the eye cornea surface and then capturing images/videos of the eye region. Gaze direction can be estimated from the relative movement between the pupil center and glints. Various holographic optical elements may be used in an eye-tracking system for illuminating the user&#39;s eyes or collecting light reflected by the user&#39;s eye. 
     One example of the holographic optical elements used in an artificial reality system for eye tracking or image display may be a holographic volume Bragg grating, which may be recorded on a holographic material layer by exposing the holographic material layer to light patterns generated by the interference between two or more coherent light beams. 
       FIG. 5A  illustrates an example of a volume Bragg grating (VBG)  500 . Volume Bragg grating  500  shown in  FIG. 5A  may include a transmission holographic grating that has a thickness D. The refractive index n of volume Bragg grating  500  may be modulated at an amplitude n 1 , and the grating period of volume Bragg grating  500  may be Λ. Incident light  510  having a wavelength λ may be incident on volume Bragg grating  500  at an incident angle θ, and may be refracted into volume Bragg grating  500  as incident light  520  that propagates at an angle θ n  in volume Bragg grating  500 . Incident light  520  may be diffracted by volume Bragg grating  500  into diffraction light  530 , which may propagate at a diffraction angle θ d  in volume Bragg grating  500  and may be refracted out of volume Bragg grating  500  as diffraction light  540 . 
       FIG. 5B  illustrates the Bragg condition for volume Bragg grating  500  shown in  FIG. 5A . Vector  505  represents the grating vector {right arrow over (G)}, where |{right arrow over (G)}|=2π/Λ. Vector  525  represents the incident wave vector {right arrow over (k l )}, and vector  535  represents the diffract wave vector {right arrow over (k d )}, where |{right arrow over (k l )}|=|{right arrow over (k d )}|=2πn/λ. Under the Bragg phase-matching condition, {right arrow over (k l )}−{right arrow over (k d )}={right arrow over (G)}. Thus, for a given wavelength λ, there may only be one pair of incident angle θ (or θ n ) and diffraction angle θ d  that meets the Bragg condition perfectly. Similarly, for a given incident angle θ, there may only be one wavelength λ that meets the Bragg condition perfectly. As such, the diffraction may only occur in a small wavelength range and a small incident angle range. The diffraction efficiency, the wavelength selectivity, and the angular selectivity of volume Bragg grating  500  may be functions of thickness D of volume Bragg grating  500 . For example, the full-width-half-magnitude (FWHM) wavelength range and the FWHM angle range of volume Bragg grating  500  at the Bragg condition may be inversely proportional to thickness D of volume Bragg grating  500 , while the maximum diffraction efficiency at the Bragg condition may be a function sin 2 (a×n 1 ×D), where a is a coefficient. For a reflection volume Bragg grating, the maximum diffraction efficiency at the Bragg condition may be a function of tan h 2 (a×n 1 ×D). 
     In some embodiments, a multiplexed Bragg grating may be used to achieve the desired optical performance, such as a high diffraction efficiency and a large field of view (FOV) for the full visible spectrum (e.g., from about 400 nm to about 700 nm, or from about 440 nm to about 650 nm). Each part of the multiplexed Bragg grating may be used to diffract light from a respective FOV range and/or within a respective wavelength range. Thus, in some designs, multiple volume Bragg gratings each recorded under a respective recording condition may be used. 
     The holographic optical elements described above may be recorded in a holographic material (e.g., photopolymer) layer. In some embodiments, the HOEs can be recorded first and then laminated on a substrate in a near-eye display system. In some embodiments, a holographic material layer may be coated or laminated on the substrate and the HOEs may then be recorded in the holographic material layer. 
     In general, to record a holographic optical element in a photosensitive material layer, two coherent beams may interfere with each other at certain angles to generate a unique interference pattern in the photosensitive material layer, which may in turn generate a unique refractive index modulation pattern in the photosensitive material layer, where the refractive index modulation pattern may correspond to the light intensity pattern of the interference pattern. The photosensitive material layer may include, for example, silver halide emulsion, dichromated gelatin, photopolymers including photo-polymerizable monomers suspended in a polymer matrix, photorefractive crystals, and the like. One example of the photosensitive material layer for holographic recording is two-stage photopolymers. 
       FIG. 6  illustrates an example of a holographic recording material including two-stage photopolymers. The raw material  610  of the two-stage photopolymers may be a resin including matrix precursors  612  and imaging components  614 . Matrix precursors  612  in raw material  610  may include monomers that may be thermally or otherwise cured at the first stage to polymerize and to form a photopolymer film  620  that includes a cross-linked matrix formed by polymeric binders  622 . Imaging components  614  may include writing monomers and polymerization initiating agents, such as photosensitizing dyes, initiators, and/or chain transfer agents. Thus, photopolymer film  620  may include polymeric binders  622 , writing monomers (e.g., acrylate monomers), and initiating agents, such as photosensitizing dyes, initiators, and/or chain transfer agents. Polymeric binders  622  may act as the backbone or the support matrix for the writing monomers and initiating agents. For example, in some embodiments, polymeric binders  622  may include a low refractive index (e.g., &lt;1.5) rubbery polymer (e.g., a polyurethane), which may provide mechanical support during the holographic exposure and ensure the refractive index modulation by the light pattern is permanently preserved. 
     Imaging components  614  including the writing monomers and the polymerization initiating agents may be dispersed in the support matrix. The writing monomers may serve as refractive index modulators. For example, the writing monomers may include high refractive index acrylate monomers which can react with the initiators and polymerize. The photosensitizing dyes may be used to absorb light and interact with the initiators to produce active species, such as radicals, cations (e.g., acids), or anion (e.g., bases). The active species (e.g., radicals) may initiate the polymerization by attacking a monomer. For example, in some monomers, one electron pair may be held securely between two carbons in a sigma bond and another electron pair may be more loosely held in a pi bond, and the free radical may use one electron from the pi bond to form a more stable bond with a first carbon atom in the two carbon atoms. The other electron from the pi bond may return to the second carbon atom in the two carbon atoms and turn the whole molecule into another radical. Thus, a monomer chain (e.g., a polymer) may be formed by adding additional monomers to the end of the monomer chain and transferring the radical to the end of the monomer chain to attack and add more monomers to the chain. 
     During the recording process (e.g., the second stage), an interference pattern generated by the interference between two coherent beams may cause the photosensitizing dyes and the initiators in the bright fringes to generate active species, such as radicals, cations (e.g., acids), or anion (e.g., bases), from the initiators, where the active species (e.g., radicals) may transfer from the initiators to monomers and cause the polymerization of the monomers in the bright fringes as described above. The initiators or radicals may be bound to the polymer matrix when abstracting the hydrogen atoms on the polymer matrix. The radicals may be transferred to the ends of the chains of monomers to add more monomers to the chains. While the monomers in the bright fringes are attached to chains of monomers, monomers in the unexposed dark regions may diffuse to the bright fringes to enhance the polymerization. As a result, polymerization concentration and density gradients may be formed in photopolymer film  620 , resulting in refractive index modulation in photopolymer film  620  due to the higher refractive index of the writing monomers. For example, areas with a higher concentration of monomers and polymerization may have a higher refractive index. Thus, a hologram or a holographic optical element  630  may be formed in photopolymer film  620 . 
     During the exposure, a radical at the end of one monomer chain may combine with a radical at the end of another monomer chain to form a longer chain and terminate the polymerization. In addition to the termination due to radical combination, the polymerization may also be terminated by disproportionation of polymers, where a hydrogen atom from one chain may be abstracted to another chain to generate a polymer with a terminal unsaturated group and a polymer with a terminal saturated group. The polymerization may also be terminated due to interactions with impurities or inhibitors (e.g., oxygen). In addition, as the exposure and polymerization proceed, fewer monomers may be available for diffusion and polymerization, and thus the diffusion and polymerization may be suppressed. The polymerization may stop until there are no more monomers or until the monomer chains terminate for an exposure. After all or substantially all monomers have been polymerized, no more new holographic optical elements  630  (e.g., gratings) may be recorded in photopolymer film  620 . 
     In some embodiments, the recorded holographic optical elements in the photosensitive material layer may be UV cured or thermally cured or enhanced, for example, for dye bleaching, completing polymerization, permanently fixing the recorded pattern, and enhancing the refractive index modulation. At the end of the process, a holographic optical element, such as a holographic grating, may be formed. The holographic grating may be a volume Bragg grating with a thickness of, for example, a few, or tens, or hundreds of microns. 
     To generate the desired light interference pattern for recording the HOEs, two or more coherent beams may generally be used, where one beam may be a reference beam and another beam may be an object beam that may have a desired wavefront profile. When the recorded HOEs are illuminated by the reference beam, the object beam with the desired wavefront profile may be reconstructed. 
     In some embodiments, the holographic optical elements may be used to diffract light outside of the visible band. For example, IR light or NIR light (e.g., at 940 nm or 850 nm) may be used for eye-tracking. Thus, the holographic optical elements may need to diffract IR or NIR light, but not the visible light. However, there may be very few holographic recording materials that are sensitive to infrared light. As such, to record a holographic grating that can diffract infrared light, recording light at a shorter wavelength (e.g., in visible or UV band, such as at about 660 nm, about 532 nm, about 514 nm, or about 457 nm) may be used, and the recording condition (e.g., the angles of the two interfering coherent beams) may be different from the reconstruction condition. 
       FIG. 7A  illustrates the recording light beams for recording a volume Bragg grating  700  and the light beam reconstructed from volume Bragg grating  700 . In the example illustrated, volume Bragg grating  700  may include a transmission volume hologram recorded using a reference beam  720  and an object beam  710  at a first wavelength, such as 660 nm. When a light beam  730  at a second wavelength (e.g., 940 nm) is incident on volume Bragg grating  700  at a 0° incident angle, the incident light beam  730  may be diffracted by volume Bragg grating  700  at a diffraction angle as shown by a diffracted beam  740 . 
       FIG. 7B  is an example of a holography momentum diagram  705  illustrating the wave vectors of recording beams and reconstruction beams and the grating vector of the recorded volume Bragg grating.  FIG. 7B  shows the Bragg matching conditions during the holographic grating recording and reconstruction. The length of wave vectors  750  and  760  of the recording beams (e.g., object beam  710  and reference beam  710 ) may be determined based on the recording light wavelength λ c  (e.g., 660 nm) according to 2πn/λ c , where n is the average refractive index of holographic material layer. The directions of wave vectors  750  and  760  of the recording beams may be determined based on the desired grating vector K ( 770 ) such that wave vectors  750  and  760  and grating vector K ( 770 ) can form an isosceles triangle as shown in  FIG. 7B . Grating vector K may have an amplitude 2π/Λ, where Λ is the grating period. Grating vector K may in turn be determined based on the desired reconstruction condition. For example, based on the desired reconstruction wavelength λ r  (e.g., 940 nm) and the directions of the incident light beam (e.g., light beam  730  at 0°) and the desired diffracted light beam (e.g., diffracted beam  740 ), grating vector K ( 770 ) of volume Bragg grating  700  may be determined based on the Bragg condition, where wave vector  780  of the incident light beam (e.g., light beam  730 ) and wave vector  790  of the diffracted light beam (e.g., diffracted beam  740 ) may have an amplitude 2πn/λ r , and may form an isosceles triangle with grating vector K ( 770 ) as shown in  FIG. 7B . 
     As described above, for a given wavelength, there may only be one pair of incident angle and diffraction angle that meets the Bragg condition perfectly. Similarly, for a given incident angle, there may only be one wavelength that meets the Bragg condition perfectly. When the incident angle of the reconstruction light beam is different from the incident angle that meets the Bragg condition of the volume Bragg grating or when the wavelength of the reconstruction light beam is different from the wavelength that meets the Bragg condition of the volume Bragg grating, the diffraction efficiency may be reduced as a function of the Bragg mismatch factor caused by the angular or wavelength detuning from the Bragg condition. As such, the diffraction may only occur in a small wavelength range and a small incident angle range. 
       FIG. 8  illustrates an example of a holographic recording system  800  for recording holographic optical elements. Holographic recording system  800  includes a beam splitter  810  (e.g., a beam splitter cube), which may split an incident collimated laser beam  802  into two light beams  812  and  814  that are coherent and have similar intensities. Light beam  812  may be reflected by a first mirror  820  towards a plate  830  as shown by the reflected light beam  822 . On another path, light beam  814  may be reflected by a second mirror  840 . The reflected light beam  842  may be directed towards plate  830 , and may interfere with light beam  822  at plate  830  to generate an interference pattern that may include bright fringes and dark fringes. In some embodiments, plate  830  may also be a mirror. A holographic recording material layer  850  may be formed on plate  830  or on a substrate mounted on plate  830 . The interference pattern may cause the holographic optical element to be recorded in holographic recording material layer  850  as described above. 
     In some embodiments, a mask  860  may be used to record different HOEs at different regions of holographic recording material layer  850 . For example, mask  860  may include an aperture  862  for the holographic recording and may be moved to place aperture  862  at different regions on holographic recording material layer  850  to record different HOEs at the different regions under different recording conditions (e.g., recording beams with different angles). 
     Holographic recording materials can be selected for specific applications based on some parameters of the holographic recording materials, such as the spatial frequency response, dynamic range, photosensitivity, physical dimensions, mechanical properties, wavelength sensitivity, and development or bleaching method for the holographic recording material. 
     The dynamic range indicates the refractive index change that can be achieved in a holographic recording material. The dynamic range may affect, for example, the thickness of the device to achieve a high efficiency, and the number of holograms that can be multiplexed in a holographic material layer. The dynamic range may be represented by the refractive index modulation (RIM), which may be one half of the total change in refractive index. In generally, a large refractive index modulation in the holographic optical elements is desired in order to improve the diffraction efficiency and record multiple holographic optical elements in a same holographic material layer. However, for holographic photopolymer materials, due to the solubility limitation of the monomers in the holographic photopolymer materials, the maximum achievable refractive index modulation or dynamic range may be limited. 
     The spatial frequency response is a measure of the feature size that the holographic material can record and may dictate the types of Bragg conditions that can be achieved. The spatial frequency response can be characterized by a modulation transfer function, which may be a curve depicting the sinusoidal waves of varying frequencies. In general, a single spatial frequency value may be used to represent the frequency response, which may indicate the spatial frequency value at which the refractive index modulation begins to drop or at which the refractive index modulation is reduced by 3 dB. The spatial frequency response may also be represented by lines/mm, line pairs/mm, or the period of the sinusoid. 
     The photosensitivity of the holographic recording material may indicate the photo-dosage used to achieve a certain efficiency, such as 100% (or 1% for photo-refractive crystals). The physical dimensions that can be achieved in a particular holographic material may affect the aperture size as well as the spectral selectivity of the HOE device. Physical parameters of holographic recording materials may include, for example, damage thresholds and environmental stability. The wavelength sensitivity may be used to select the light source for the recording setup and may also affect the minimum achievable period. Some materials may be sensitive to light in a wide wavelength range. Many holographic materials may need post-exposure development or bleaching. Development considerations may include how the holographic material is developed or otherwise processed after the recording. 
     To record holographic optical elements for artificial reality system, it may be desirable that the photopolymer material is sensitive to visible light, can produce a large refractive index modulation Δn (e.g., high dynamic range), and have temporally and spatially controllable reaction and/or diffusion of the monomers and/or polymers such that chain transfer and termination reactions can be suppressed. 
       FIG. 9  illustrates an example of a grating  900 . The grating  900  includes two substrate layers  910 ,  915  and a polymer layer  920 . The grating  900  may correspond to a volume Bragg grating and/or a multiplexed volume Bragg grating. 
     In some embodiments, the first substrate  910  is disposed on a first side of the polymer layer  920 . The first substrate  910  may be composed of, for example, glass, quartz, plastic, polymer, or any other suitable material which is transparent to visible light and NIR light. A thickness of the first substrate  910  may range from about 0.1 mm to about 10 mm. In some embodiments, the first substrate  910  may not be included and/or may be substituted with another component. 
     In some embodiments, second substrate  915  is disposed on a second side of the polymer layer  920 . The second substrate  915  may be composed of, for example, glass, quartz, plastic, polymer, or any other suitable material which is transparent to visible light and NIR light. A thickness of the second substrate  915  may range from about 0.1 mm to about 10 mm. In some embodiments, the second substrate  915  may not be included and/or may be substituted with another component. 
     The polymer layer  920  includes first regions  922  having a first refractive index (n1), and second regions  924  having a second refractive index (n2). The second regions may have a refractive index higher than the first regions (or vice versa). The refractive index difference between the regions (e.g., |n1−n2|) may be between approximately 0 and about 0.2. 
     In addition to the refractive indexes of the regions  922 ,  924 , the grating  900  is characterized by the slant angle θ ( 940 ) of the fringes and the pitch  950 . The slant angle θ ( 940 ) of the fringes may be between approximately 0 degrees and about 90 degrees. The pitch  950 , may be between approximately 0.1 and about 1.5 μm. 
     The parameters θ ( 940 ) and pitch  950  may affect the behavior of incident light  960  approaching the grating  900 . Based on these parameters, along with other parameters such as the relative refractive indexes in the grating, diffracted light  970  may have certain power and may be in a certain direction. The diffraction efficiency of the grating  900  is the ratio between power of diffracted light and power of incident light. 
       FIGS. 10A-10B  illustrate examples of gratings with a modified refractive index modulation according to some embodiments. The diffractive efficiency may increase as the refractive index difference between regions in the grating increases within a certain range. Similarly, the diffractive efficiency may decrease as the refractive index difference between regions in the grating decreases within a certain range. In some cases, it may be desirable to increase the refractive index difference between the regions. This can be achieved by modifying the refractive indexes in the regions, as illustrated in  FIGS. 10A and 10B . 
       FIG. 10A  illustrates a grating  1000  with a certain initial refractive index modulation and diffraction efficiency. The grating  1000  includes two substrate layers  1010  and  1020  and a polymer layer  1030  which includes regions  1032  and  1034 . Each region  1032  is a region of relatively high refractive index (as compared to each region  1034 ). Each region  1034  is a region of relatively low refractive index (as compared to each region  1032 ). When incident light  1040  passes through the grating  1000 , some percentage of the incident light  1040  is diffracted as diffracted light  1045 , according to the diffraction efficiency of the grating  1000 . 
       FIG. 10B  illustrates a grating  1050  with a modified refractive index modulation and increased diffraction efficiency. The grating  1050  includes two substrate layers  1060 ,  1070  and a polymer layer  1080  which includes regions  1082  and  1084 . Each region  1082  is a region of relatively high refractive index (as compared to each region  1084 ). Each region  1084  is a region of relatively low refractive index (as compared to the first region  1082 ). 
     There are several ways to modify the refractive index modulation of the grating  1050  by modifying the refractive index of the polymer layer  1080 , in whole or in part. For example, the refractive index modulation of the grating  1050  can be increased by decreasing the refractive index in region  1084  while the refractive index of region  1082  remains substantially constant. The refractive index modulation of the grating  1050  can alternatively be increased by increasing the refractive index in region  1082  while the refractive index of region  1084  remains substantially constant. The refractive index modulation of the grating  1050  can also be increased by decreasing the refractive index in both regions, but decreasing the refractive index more in region  1084 . The refractive index modulation of the grating  1050  can be increased by increasing the refractive index in both regions, but increasing the refractive index more in region  1082 . 
     When incident light  1090  passes through the grating  1050 , some percentage of the incident light  1090  is diffracted as diffracted light  1095 , according to the diffraction efficiency of the grating  1050 . As the diffraction efficiency of the grating  1050  in  FIG. 10B  has been increased, as compared to the diffraction efficiency of grating  1000  of  FIG. 10A , a larger fraction of the incident light is diffracted in diffracted light  1095  in comparison to diffracted light  1045 . 
       FIGS. 11A-11C  illustrate an example technique for modifying the refractive index modulation in a holographic grating.  FIG. 11A  illustrates the grating after recording,  FIG. 11B  illustrates the grating with a substrate replaced by a resin layer that includes nanoparticles (e.g., monomers), and  FIG. 11C  illustrates the grating after the nanoparticles diffuse into the grating from the resin layer. 
       FIG. 11A  illustrates a recorded holographic grating  1100 . The grating  1100  includes a first substrate  1102  disposed on a bottom side of a polymer layer. The polymer layer includes regions of relatively high refractive index  1104  and regions of relatively low refractive index  1106 . The polymer layer may, for example, have been exposed to a holographic recording light pattern to record a refractive index modulation pattern in the polymer layer. The grating  1100  further includes a second substrate  1103  disposed on a top side of the polymer layer. 
       FIG. 11B  illustrates a grating  1120  including a resin layer  1123  that includes nanoparticles. Similarly to the grating  1100  of  FIG. 11A , the grating  1120  includes a first substrate  1122  disposed on a bottom side of a polymer layer and regions of differing refractive index  1124  and  1126 . The second substrate (e.g., second substrate  1103  shown in  FIG. 11A ) has been removed and replaced with resin layer  1123 . The resin layer  1123  includes a support layer or matrix, filled with high refractive index nanoparticles (e.g., with a higher refractive index than the high refractive index region of the polymer layer). The resin layer filled with nanoparticles is also referred to herein as a “monomer reservoir buffer layer.” Alternatively, low or moderate refractive index nanoparticles may be used, depending on the modification desired. In some embodiments, the nanoparticles may be monomers. In some embodiments, the nanoparticles may be in the form of a liquid. The resin layer  1123  is disposed on the top side of the polymer layer, such that the resin layer  1123  and the polymer layer are in contact with one another. The sponge layer may be a polymer film, typically an elastomer. Typical elastomers include crosslinked films of polyesters, polyethers, polyurethanes, or polysiloxanes. 
     When the resin layer  1123  and the polymer layer are placed in contact, the nanoparticles may diffuse from the resin layer  1123  into the polymer layer. As indicated by the gradients in regions  1124 ,  1126 , the introduction of the nanoparticles in the polymer layer modifies the refractive index of regions  1124 ,  1126 . 
       FIG. 11C  illustrates a grating  1140  with modified refractive index modulation. Grating  1140  includes a substrate  1142 , a nanoparticle-filled resin layer  1143 , and a polymer layer which includes regions of different refractive index  1144 ,  1146 . The nanoparticles have further diffused into the polymer layer, creating a change in the refractive indexes in regions  1144 ,  1146 . 
       FIGS. 12A-12D  illustrate an example of refractive index modulation modification in a holographic grating, according to some embodiments. Depending on the properties of the nanoparticles in the resin layer, the diffusion of the nanoparticles and the resulting refractive index modulation modification may vary. The diffusion properties may be controlled based on the properties of the nanoparticles in the resin layer, such as the refractive index and the solubility in the different regions of the polymer layer. The solubility of the nanoparticles in a given region may be controlled, e.g., based on the size of the nanoparticle and/or the affinity between the nanoparticle and the material in the region of interest. 
       FIG. 12A  illustrates a first example of a grating  1200  with refractive index modulation modification using a monomer (or other nanoparticles) reservoir buffer layer  1202 . The grating  1200  includes a polymer layer which includes regions of relatively low refractive index  1204  (with initial refractive index n1) and regions of relatively high refractive index  1206  (with initial refractive index n2). A substrate layer  1201  is disposed on a bottom side of the polymer layer. Monomer reservoir buffer layer  1202  is disposed on a top side of the polymer layer. 
     In  FIG. 12A , the monomer reservoir buffer layer  1202  includes a monomer with a relatively large refractive index n3 (&gt;n2). Further, the monomer is more soluble in low refractive index fringes (e.g., in regions  1204 ) than in high refractive index fringes (e.g., in regions  1206 ). Accordingly, the impact on the refractive index modulation is most pronounced with respect to dips in the initial refractive index modulation profile, as indicated in refractive index modulation plot  1208 . The plot  1208  shows the refractive index of the grating  1200  as a function of position from left to right across the polymer layer. Initially, before addition of the monomer reservoir buffer layer  1202 , the refractive index of the grating  1200  varies between n1 and n2 (as shown by a curve  1209 A). With the refractive index modification introduced by the monomer reservoir buffer layer, the refractive index modulation profile changes as shown by a curve  1209 B, due to the increase in the refractive index of low refractive index regions  1204  (corresponding to the dips in the refractive index modulation profile). 
       FIG. 12B  illustrates a second example of a grating  1210  with refractive index modulation modification using a monomer reservoir buffer layer  1212 . The grating  1210  includes a polymer layer which includes regions of relatively low refractive index  1214  (with refractive index n1) and regions of relatively high refractive index  1216  (with a refractive index n2). A substrate layer  1211  is disposed on a bottom side of the polymer layer. The monomer reservoir buffer layer  1212  is disposed on a top side of the polymer layer. 
     In  FIG. 12B , the monomer reservoir buffer layer  1212  includes a monomer with a relatively large refractive index n3 (&gt;n2). Further, the monomer is more soluble in high refractive index fringes (e.g., in regions  1216 ) than in low refractive index fringes (e.g., in regions  1214 ). Accordingly, the impact on the refractive index is most pronounced with respect to peaks in the refractive index modulation profile, as indicated in refractive index modulation plot  1218  (showing an initial refractive index modulation  1219 A and a modified refractive index modulation  1219 B). In particular, by introducing a larger refractive index material into the regions of relatively high refractive index  1216  via the monomer reservoir buffer layer  1212 , the refractive index in the regions of relatively high refractive index  1216  increases. This increase in refractive index causes the peaks in refractive index plot  1219 B to increase above the initial level of n2. 
       FIG. 12C  illustrates a third example of a grating  1220  with a refractive index modulation modification using a monomer reservoir buffer layer  1222 . Grating  1220  includes a polymer layer which includes regions of relatively low refractive index  1224  (with refractive index n1) and regions of relatively high refractive index  1226  (with refractive index n2). A substrate layer  1221  is disposed on a bottom side of the polymer layer. The monomer reservoir buffer layer  1222  is disposed on a top side of the polymer layer. 
     In  FIG. 12C , the monomer reservoir buffer layer  1222  includes a monomer with a relatively small refractive index n4 (&lt;n1). Further, the monomer is more soluble in low refractive index fringes (e.g., in regions  1224 ) than in high refractive index fringes (e.g., in regions  1226 ). Accordingly, the impact on refractive index modulation is most pronounced with respect to dips in the refractive index modulation profile, as indicated in refractive index modulation plot  1228  (showing initial refractive index modulation  1229 A and modified refractive index modulation  1229 B). By introducing a lower refractive index material into the lower refractive index regions  1224  via the monomer reservoir buffer layer  1222 , the refractive index in the regions of relatively low refractive index  1224  decreases, causing refractive index at low points in plot  1229 B to dip below n1. 
       FIG. 12D  illustrates a fourth example of a grating  1230  with refractive index modulation modification using a monomer reservoir buffer layer  1232 . Grating  1230  includes a polymer layer which includes regions of relatively low refractive index  1234  (with refractive index n1) and regions of relatively high refractive index  1236  (with refractive index n2). A substrate layer  1231  is disposed on a bottom side of the polymer layer. Monomer reservoir buffer layer  1232  is disposed on a top side of the polymer layer. 
     In  FIG. 12D , the monomer reservoir buffer layer  1232  includes a monomer with a relatively small refractive index n4 (&lt;n1). Further, the monomer is more soluble in high refractive index fringes (e.g., in regions  1236 ) than in low refractive index fringes (e.g., in regions  1234 ). Accordingly, the impact on the refractive index is most pronounced with respect to the peaks in the refractive index modulation profile, as indicated in refractive index modulation plot  1238  (peaks reduced as-modified  1239 B, as compared to initial refractive index modulation  1239 A). By introducing a lower refractive index material into the higher refractive index regions  1236  via the monomer reservoir buffer layer  1232 , the refractive index in the higher refractive index regions  1236  decreases, causing refractive index at high points in plot  1239 B to dip below n2. 
       FIGS. 13A-13B  illustrate variations on refractive index modulation modification in a grating, according to some embodiments. In  FIG. 13A , the refractive index modulation modification is substantially constant across the thickness of a region of the polymer layer, while in  FIG. 13B , the refractive index modification varies across the thickness of a region of the polymer layer. The “thickness” represents the z-direction from bottom to top of the polymer layer. 
       FIG. 13A  shows a grating  1300  which includes a first region  1302  with an initial refractive index n1 and a second region  1304  with an initial refractive index n2. In the grating  1300 , the refractive index modification has occurred through the whole thickness of the polymer layer. Refractive index modulation graphs  1306 ,  1308  illustrate the refractive index modulation across the polymer layer. Refractive index modulation graph  1306  illustrates the refractive index modulation as a function of position through a cross-section  1305  towards the upper side of the polymer layer. Refractive index modulation graph  1308  illustrates the refractive index modulation as a function of position through a cross-section  1307  towards the lower side of the polymer layer. In the grating  1300 , the refractive index modulation modification profile is substantially the same at the cross-sections  1305 ,  1307 . This corresponds to a concentration of nanoparticles (e.g., monomers) being in a substantially constant concentration across the thickness of the polymer layer in a given region. Substantially constant concentration may correspond to some small variations, such as 0.1%, 0.5%, 1%, or 5%. 
       FIG. 13B  shows a grating  1350  which includes a first region  1352  with an initial refractive index n1 and a second region  1354  with an initial refractive index n2. In the grating  1350 , the refractive index modulation modification has occurred in a portion of the polymer layer. Refractive index modulation graphs  1356 ,  1358  illustrate the refractive index modulation across the polymer layer. Refractive index modulation graph  1356  illustrates the refractive index modulation as a function of position through a cross-section  1355  towards the upper side of the polymer layer. Refractive index modulation graph  1358  illustrates the refractive index modulation as a function of position through a cross-section  1357  towards the lower side of the polymer layer. In the grating  1350 , the refractive index modulation at cross-section  1355  has been modified. Monomers of refractive index n3, which is greater than n1, have diffused preferentially into region  1352  near a top surface of the polymer layer, which causes the refractive index in region  1352  to shift upward from n1 in plot  1356 . In contrast, at cross-section  1357 , the monomers have not diffused to this point of the polymer layer, so the refractive index modulation has not been modified as shown in graph  1358 ). The refractive index modulation modification shown in  FIG. 13B  corresponds to the monomers or other nanoparticles being more highly concentrated in proximity to the upper edge of the polymer layer (e.g., the top surface of the polymer layer shown in  FIG. 13B ). 
     Accordingly, based on the position and contents of the monomer reservoir buffer layer(s), the refractive index modulation modification can be customized to taper as a function of the thickness within the polymer layer. The refractive index modulation modification may happen only across a certain diffusion depth. The refractive index modulation may be tapered to smooth the refractive index modulation from the upper and/or lower edges of the polymer layer towards the center of the polymer layer. This tapered refractive index modulation can be used to reduce sidelobes of the diffracted order and improve performance of the waveguide display. 
       FIG. 14  illustrates a grating  1400  with a refractive index modulation profile that is tapered on both a top and a bottom edge of the grating. Region  1402  has an initial refractive index of n1 and region  1402  has an initial refractive index of n2. The refractive index across the grating has been modulated (e.g., by affixing monomer reservoir buffer layers to the upper and lower edges of the polymer layer). The modulation affects the grating most strongly at the top and the bottom, where the monomer is more concentrated in proximity to the upper and lower edges of the polymer layer. Graph  1430  shows the refractive index modulation across the grating at cross-section  1432  at the center of the grating  1400  in terms of thickness. The refractive index modulation modification from the monomer reservoir buffer layers does not reach to the center. Accordingly, at cross-section  1432  the refractive index modulation remains at an initial level. 
     Graph  1410  shows the refractive index modulation across the grating at cross-section  1412  near the bottom of the grating  1400 . The refractive index modulation modification from the monomer reservoir buffer layer at the bottom of the grating has reached the depth level indicated by cross-section  1412 . Accordingly, at cross-section  1412  the refractive index modulation has been modified such that the refractive index in regions  1402  is increased, as indicated in graph  1410 . In comparison with graph  1430 , in graph  1410 , the lowest points in refractive index have shifted upwards from n1. 
     Graph  1420  shows the refractive index modulation across the grating at cross-section  1422  near the top of the grating  1400 . The refractive index modulation modification from the monomer reservoir buffer layer at the top of the grating has reached the depth level indicated by cross-section  1422 . Accordingly, at cross-section  1422  the refractive index modulation has been modified such that the refractive index in regions  1402  is increased, as indicated in graph  1420 . In comparison with graph  1430 , in graph  1420 , the lowest points in refractive index have shifted upwards from n1. 
       FIGS. 15A-15B  illustrate an example of refractive index modulation in an apodized grating in accordance with some embodiments.  FIG. 15A  shows the refractive index modulation as a function of grating depth z (as illustrated in  FIG. 15B ), with and without refractive index modification. 
     In  FIG. 15A , a refractive index modulation profile in an apodized grating is shown. This apodized grating may be used in a 1-D or 2-D pupil expander in a waveguide-based near-eye display system, as shown in  FIG. 15B . Refractive index modulation without index profile modulation  1502  has a constant profile with respect to normalized grating depth z. A refractive index modulation with index profile modulation  1504  can be used to reduce or eliminate sidelobes, as illustrated in  FIGS. 16A-16B . 
       FIGS. 16A-16B  illustrate sidelobe reduction using an apodized grating in accordance with some embodiments. In  FIG. 16A , normalized diffraction efficiency for a single grating is shown as a function of wavelength. Plot  1602  may correspond to a grating without apodization. Sidelobes  1606  are visible. These sidelobes are undesirable, particularly in multiplexed gratings. In multiplexed gratings, the sidelobes in diffraction pattern cause crosstalk, reducing the image contrast. To avoid such crosstalk, the number of gratings multiplexed may be limited, which limits the efficiency achievable. 
     Plot  1604 , on the other hand, corresponds to a grating with variable refractive index across the thickness of the grating, reducing the sidelobes. To reduce the sidelobes, the refractive index of the grating should be modified so that the refractive index modulation is higher at the center of the grating and lower at one or more sides of the grating, as illustrated in  FIGS. 13B and 14 . In some embodiments, a bell-shaped refractive index modulation profile across the z-direction in the grating may be generated, as illustrated in  FIGS. 15A-15B . Accordingly, varying the refractive index across the thickness of the grating can reduce sidelobes and crosstalk in multiplexed gratings. This improves the image contrast and enables a larger number of gratings to be multiplexed, increasing the overall efficiency. 
     In  FIG. 16B , the normalized diffraction efficiency vs wavelength plots  1602  and  1604  are shown on a logarithmic scale, further highlighting the sidelobes  1606  and reduction thereof. 
       FIG. 17  is a simplified flow chart  1700  illustrating an example of a method of fabricating a holographic optical element according to certain embodiments. The operations described in flow chart  1700  are for illustration purposes only and are not intended to be limiting. In various implementations, modifications may be made to flow chart  1700  to add additional operations, omit some operations, combine some operations, split some operations, or reorder some operations. 
     At block  1710 , a holographic recording material layer may be obtained. The holographic recording material layer may include a mixture of matrix monomers and writing monomers. The matrix monomers may be configured to polymerize (e.g., via thermal treatment) to form a polymer matrix. The writing monomers may be dispersed in the matrix monomers and may be configured to polymerize when the holographic recording material is exposure to recording light. The matrix monomers may have different refractive index(es) from the writing monomers. For example, the writing monomers may have a higher refractive index than the matrix monomers. 
     In some embodiments, the layer of the holographic recording material may be cured, for example, thermally or optically, to polymerize the matrix monomers and form a polymer matrix. The writing monomers may not polymerize under the curing condition and may be dispersed in the formed polymer matrix. The polymer matrix may function as a support matrix or backbone of the layer of the holographic recording material. 
     At block  1720 , the layer of holographic recording material may be exposed to a recording light pattern to polymerize the writing monomers in selected regions, such as the bright fringes of the recording light pattern, as described above with respect to, for example,  FIGS. 7A-8 . The recording light pattern may correspond to a grating, a lens, a diffuser, and the like. The recording light pattern may cause the polymerization and diffusion of the writing monomers to form a holographic optical element corresponding to the recording light pattern. The exposure to the recording light pattern creates a first region having a first refractive index and a second region having a second refractive index. 
     At block  1730 , a resin layer comprising nanoparticles may be applied to the holographic recording material layer. For example, the layer of the holographic recording material may be deposited or laminated on a first resin layer. In some embodiments, the holographic recording material layer may be laminated on a substrate, which is removed before applying the resin layer. In some embodiments, the holographic recording material layer may be sandwiched between two resin layers. Alternatively, the holographic recording material layer may be laminated on a substrate (e.g., glass or plastic) layer on one side, and a resin layer is applied to the holographic recording material layer on the other side. Application of the resin layer causes diffusion of nanoparticles from the resin layer into the holographic recording material layer. Particles will further diffuse from the holographic recording material layer into the resin layer. If unreacted monomer from the initial holographic film is not present in the resin layer, the monomer will diffuse from the holographic film to the resin layer just because there is a natural concentration gradient between the two films. Accordingly, the refractive index in the holographic recording material layer is modified due to the diffusion of particles. The concentration of nanoparticles in the resin layer may be controlled so that, after a time, no nanoparticles are available to diffuse into the holographic recording material layer. Alternatively, or additionally, the removal of the resin layer may be timed to tailor the nanoparticle concentration in the holographic recording material layer. The concentration of the nanoparticles may be tailored to achieve any of the configurations for increasing the diffractive efficiency or apodizing the grating described above. 
     Optionally, at block  1740 , the resin layer(s) may be removed from the layer of the holographic recording material. The holographic recording material layer may then be laminated on one or more substrates. For example, the resin layer may comprise a flexible polyester film or plastic sheeting. Such a flexible resin layer may be peeled off of the holographic recording material layer. The layer of the holographic recording material on one substrate may then be laminated on a substrate, such as an optical component (e.g., a quartz, glass, crystal plate, or lens). 
     Removal of the resin layer and/or a substrate without damaging the holographic recording material layer can be achieved in multiple ways. The use of a pliable material such as flexible plastic may facilitate low impact layer removal. Alternatively, or additionally, a resin layer or substrate may be treated with an anti-adhesion component to make the layer remove easily. 
       FIG. 18  is a schematic diagram showing another HOE fabrication method  1800 , according to some embodiments. HOE fabrication method  1800  is similar to the method described above with respect to  FIG. 7 , but the resin layer(s) are applied before holographic exposure. 
     At  1802 , a resin layer  1810 , filled with nanoparticles such as monomers with some predetermined refractive index, is applied to a first substrate  1820 . The resin layer  1810  may be bonded to, or deposited on, the first substrate  1820 . A holographic recording material layer  1830  is applied to a second substrate  1840 . Similarly, the holographic recording material layer  1830  may be bonded to, or deposited on, the second substrate  1840 . In some embodiments, the resin layer and the holographic recording material layer have similar properties. For example the resin layer and the holographic recording material layer may both comprise a polymer matrix. However, the holographic recording material layer may differ in the addition of photoinitiators for holographic recording. 
     At  1804 , resin layer  1810  and first substrate  1820  are disposed on the holographic recording material layer  1830  and second substrate  1840 . The resin layer  1810  is placed in contact with the holographic recording material layer  1830 . The resin layer  1810  is laminated or bonded to the holographic recording material layer  1830 . Nanoparticles may diffuse from the resin layer  1810  to the holographic recording material layer  1830 . Species may also diffuse into the resin layer  1810  from the holographic recording material layer  1830 . The dispersion of the nanoparticles may be tailored to achieve any of the configurations for increasing the diffractive efficiency or apodizing the grating described above. 
     At  1806 , a hologram is recorded in the holographic recording material layer  1830 . A recoding light pattern is applied to at least the recording material layer, as described above with respect to  FIG. 17 . 
     At  1808 , the hologram has been recorded in holographic recording material layer  1830 . The resin layer  1810  may remain affixed to the holographic recording material layer  1830 . Diffusion may continue for a time after the hologram is recorded. As nanoparticles diffuse from the resin layer  1810  into the holographic recording material layer  1830 , or vice versa, the refractive index modulation may continue to change. The amount of diffusion, and the corresponding refractive index change, may be controlled by controlling the number of nanoparticles in the resin layer  1810  (e.g., so that only a desired number of nanoparticles are available). The speed of the diffusion process (and the solubility of the monomer in the grating) can be controlled by increasing/decreasing the temperature. In addition, the diffusion process could be stopped by flood exposing both films to polymerize the diffused monomer. Further, the support layer of the resin layer may be selected so as to be transparent to visible light (e.g., similar to a substrate layer), to avoid affecting performance of the holographic optical element. 
     Embodiments may be used to fabricate components of an artificial reality system or may be implemented in conjunction with an artificial reality system. Artificial reality is a form of reality that has been adjusted in some manner before presentation to a user, which may include, for example, a virtual reality (VR), an augmented reality (AR), a mixed reality (MR), a hybrid reality, or some combination and/or derivatives thereof. Artificial reality content may include completely generated content or generated content combined with captured (e.g., real-world) content. The artificial reality content may include video, audio, haptic feedback, or some combination thereof, and any of which may be presented in a single channel or in multiple channels (such as stereo video that produces a three-dimensional effect to the viewer). Additionally, in some embodiments, artificial reality may also be associated with applications, products, accessories, services, or some combination thereof, that are used to, for example, create content in an artificial reality and/or are otherwise used in (e.g., perform activities in) an artificial reality. The artificial reality system that provides the artificial reality content may be implemented on various platforms, including a head-mounted display (HMD) connected to a host computer system, a standalone HMD, a mobile device or computing system, or any other hardware platform capable of providing artificial reality content to one or more viewers. 
       FIG. 19  is a simplified block diagram of an example of an electronic system  1900  of a near-eye display system (e.g., HMD device) for implementing some of the examples disclosed herein. Electronic system  1900  may be used as the electronic system of an HMD device or other near-eye displays described above. In this example, electronic system  1900  may include one or more processor(s)  1910  and a memory  1920 . Processor(s)  1910  may be configured to execute instructions for performing operations at a number of components, and can be, for example, a general-purpose processor or microprocessor suitable for implementation within a portable electronic device. Processor(s)  1910  may be communicatively coupled with a plurality of components within electronic system  1900 . To realize this communicative coupling, processor(s)  1910  may communicate with the other illustrated components across a bus  1940 . Bus  1940  may be any subsystem adapted to transfer data within electronic system  1900 . Bus  1940  may include a plurality of computer buses and additional circuitry to transfer data. 
     Memory  1920  may be coupled to processor(s)  1910 . In some embodiments, memory  1920  may offer both short-term and long-term storage and may be divided into several units. Memory  1920  may be volatile, such as static random access memory (SRAM) and/or dynamic random access memory (DRAM) and/or non-volatile, such as read-only memory (ROM), flash memory, and the like. Furthermore, memory  1920  may include removable storage devices, such as secure digital (SD) cards. Memory  1920  may provide storage of computer-readable instructions, data structures, program modules, and other data for electronic system  1900 . In some embodiments, memory  1920  may be distributed into different hardware modules. A set of instructions and/or code might be stored on memory  1920 . The instructions might take the form of executable code that may be executable by electronic system  1900 , and/or might take the form of source and/or installable code, which, upon compilation and/or installation on electronic system  1900  (e.g., using any of a variety of generally available compilers, installation programs, compression/decompression utilities, etc.), may take the form of executable code. 
     In some embodiments, memory  1920  may store a plurality of application modules  1922  through  1924 , which may include any number of applications. Examples of applications may include gaming applications, conferencing applications, video playback applications, or other suitable applications. The applications may include a depth sensing function or eye tracking function. Application modules  1922 - 1924  may include particular instructions to be executed by processor(s)  1910 . In some embodiments, certain applications or parts of application modules  1922 - 1924  may be executable by other hardware modules  1980 . In certain embodiments, memory  1920  may additionally include secure memory, which may include additional security controls to prevent copying or other unauthorized access to secure information. 
     In some embodiments, memory  1920  may include an operating system  1925  loaded therein. Operating system  1925  may be operable to initiate the execution of the instructions provided by application modules  1922 - 1924  and/or manage other hardware modules  1980  as well as interfaces with a wireless communication subsystem  1930  which may include one or more wireless transceivers. Operating system  1925  may be adapted to perform other operations across the components of electronic system  1900  including threading, resource management, data storage control and other similar functionality. 
     Wireless communication subsystem  1930  may include, for example, an infrared communication device, a wireless communication device and/or chipset (such as a Bluetooth® device, an IEEE 802.11 device, a Wi-Fi device, a WiMax device, cellular communication facilities, etc.), and/or similar communication interfaces. Electronic system  1900  may include one or more antennas  1934  for wireless communication as part of wireless communication subsystem  1930  or as a separate component coupled to any portion of the system. Depending on desired functionality, wireless communication subsystem  1930  may include separate transceivers to communicate with base transceiver stations and other wireless devices and access points, which may include communicating with different data networks and/or network types, such as wireless wide-area networks (WWANs), wireless local area networks (WLANs), or wireless personal area networks (WPANs). A WWAN may be, for example, a WiMax (IEEE 802.16) network. A WLAN may be, for example, an IEEE 802.11x network. A WPAN may be, for example, a Bluetooth network, an IEEE 802.15x, or some other types of network. The techniques described herein may also be used for any combination of WWAN, WLAN, and/or WPAN. Wireless communications subsystem  1930  may permit data to be exchanged with a network, other computer systems, and/or any other devices described herein. Wireless communication subsystem  1930  may include a means for transmitting or receiving data, such as identifiers of HMD devices, position data, a geographic map, a heat map, photos, or videos, using antenna(s)  1934  and wireless link(s)  1932 . Wireless communication subsystem  1930 , processor(s)  1910 , and memory  1920  may together comprise at least a part of one or more of a means for performing some functions disclosed herein. 
     Embodiments of electronic system  1900  may also include one or more sensors  1990 . Sensor(s)  1990  may include, for example, an image sensor, an accelerometer, a pressure sensor, a temperature sensor, a proximity sensor, a magnetometer, a gyroscope, an inertial sensor (e.g., a module that combines an accelerometer and a gyroscope), an ambient light sensor, or any other similar module operable to provide sensory output and/or receive sensory input, such as a depth sensor or a position sensor. For example, in some implementations, sensor(s)  1990  may include one or more inertial measurement units (IMUs) and/or one or more position sensors. An IMU may generate calibration data indicating an estimated position of the HMD device relative to an initial position of the HMD device, based on measurement signals received from one or more of the position sensors. A position sensor may generate one or more measurement signals in response to motion of the HMD device. Examples of the position sensors may include, but are not limited to, one or more accelerometers, one or more gyroscopes, one or more magnetometers, another suitable type of sensor that detects motion, a type of sensor used for error correction of the IMU, or some combination thereof. The position sensors may be located external to the IMU, internal to the IMU, or some combination thereof. At least some sensors may use a structured light pattern for sensing. 
     Electronic system  1900  may include a display module  1960 . Display module  1960  may be a near-eye display, and may graphically present information, such as images, videos, and various instructions, from electronic system  1900  to a user. Such information may be derived from one or more application modules  1922 - 1924 , virtual reality engine  1926 , one or more other hardware modules  1980 , a combination thereof, or any other suitable means for resolving graphical content for the user (e.g., by operating system  1925 ). Display module  1960  may use liquid crystal display (LCD) technology, light-emitting diode (LED) technology (including, for example, OLED, ILED, μLED, AMOLED, TOLED, etc.), light emitting polymer display (LPD) technology, or some other display technology. 
     Electronic system  1900  may include a user input/output module  1970 . User input/output module  1970  may allow a user to send action requests to electronic system  1900 . An action request may be a request to perform a particular action. For example, an action request may be to start or end an application or to perform a particular action within the application. User input/output module  1970  may include one or more input devices. Example input devices may include a touchscreen, a touch pad, microphone(s), button(s), dial(s), switch(es), a keyboard, a mouse, a game controller, or any other suitable device for receiving action requests and communicating the received action requests to electronic system  1900 . In some embodiments, user input/output module  1970  may provide haptic feedback to the user in accordance with instructions received from electronic system  1900 . For example, the haptic feedback may be provided when an action request is received or has been performed. 
     Electronic system  1900  may include a camera  1950  that may be used to take photos or videos of a user, for example, for tracking the user&#39;s eye position. Camera  1950  may also be used to take photos or videos of the environment, for example, for VR, AR, or MR applications. Camera  1950  may include, for example, a complementary metal-oxide-semiconductor (CMOS) image sensor with a few millions or tens of millions of pixels. In some implementations, camera  1950  may include two or more cameras that may be used to capture 3-D images. 
     In some embodiments, electronic system  1900  may include a plurality of other hardware modules  1980 . Each of other hardware modules  1980  may be a physical module within electronic system  1900 . While each of other hardware modules  1980  may be permanently configured as a structure, some of other hardware modules  1980  may be temporarily configured to perform specific functions or temporarily activated. Examples of other hardware modules  1980  may include, for example, an audio output and/or input module (e.g., a microphone or speaker), a near field communication (NFC) module, a rechargeable battery, a battery management system, a wired/wireless battery charging system, etc. In some embodiments, one or more functions of other hardware modules  1980  may be implemented in software. 
     In some embodiments, memory  1920  of electronic system  1900  may also store a virtual reality engine  1926 . Virtual reality engine  1926  may execute applications within electronic system  1900  and receive position information, acceleration information, velocity information, predicted future positions, or some combination thereof of the HMD device from the various sensors. In some embodiments, the information received by virtual reality engine  1926  may be used for producing a signal (e.g., display instructions) to display module  1960 . For example, if the received information indicates that the user has looked to the left, virtual reality engine  1926  may generate content for the HMD device that mirrors the user&#39;s movement in a virtual environment. Additionally, virtual reality engine  1926  may perform an action within an application in response to an action request received from user input/output module  1970  and provide feedback to the user. The provided feedback may be visual, audible, or haptic feedback. In some implementations, processor(s)  1910  may include one or more GPUs that may execute virtual reality engine  1926 . 
     In various implementations, the above-described hardware and modules may be implemented on a single device or on multiple devices that can communicate with one another using wired or wireless connections. For example, in some implementations, some components or modules, such as GPUs, virtual reality engine  1926 , and applications (e.g., tracking application), may be implemented on a console separate from the head-mounted display device. In some implementations, one console may be connected to or support more than one HMD. 
     In alternative configurations, different and/or additional components may be included in electronic system  1900 . Similarly, functionality of one or more of the components can be distributed among the components in a manner different from the manner described above. For example, in some embodiments, electronic system  1900  may be modified to include other system environments, such as an AR system environment and/or an MR environment. 
     The methods, systems, and devices discussed above are examples. Various embodiments may omit, substitute, or add various procedures or components as appropriate. For instance, in alternative configurations, the methods described may be performed in an order different from that described, and/or various stages may be added, omitted, and/or combined. Also, features described with respect to certain embodiments may be combined in various other embodiments. Different aspects and elements of the embodiments may be combined in a similar manner. Also, technology evolves and, thus, many of the elements are examples that do not limit the scope of the disclosure to those specific examples. 
     Specific details are given in the description to provide a thorough understanding of the embodiments. However, embodiments may be practiced without these specific details. For example, well-known circuits, processes, systems, structures, and techniques have been shown without unnecessary detail in order to avoid obscuring the embodiments. This description provides example embodiments only, and is not intended to limit the scope, applicability, or configuration of the invention. Rather, the preceding description of the embodiments will provide those skilled in the art with an enabling description for implementing various embodiments. Various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the present disclosure. 
     Also, some embodiments were described as processes depicted as flow diagrams or block diagrams. Although each may describe the operations as a sequential process, many of the operations may be performed in parallel or concurrently. In addition, the order of the operations may be rearranged. A process may have additional steps not included in the figure. Furthermore, embodiments of the methods may be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the associated tasks may be stored in a computer-readable medium such as a storage medium. Processors may perform the associated tasks. 
     It will be apparent to those skilled in the art that substantial variations may be made in accordance with specific requirements. For example, customized or special-purpose hardware might also be used, and/or particular elements might be implemented in hardware, software (including portable software, such as applets, etc.), or both. Further, connection to other computing devices such as network input/output devices may be employed. 
     With reference to the appended figures, components that can include memory can include non-transitory machine-readable media. The term “machine-readable medium” and “computer-readable medium” may refer to any storage medium that participates in providing data that causes a machine to operate in a specific fashion. In embodiments provided hereinabove, various machine-readable media might be involved in providing instructions/code to processing units and/or other device(s) for execution. Additionally or alternatively, the machine-readable media might be used to store and/or carry such instructions/code. In many implementations, a computer-readable medium is a physical and/or tangible storage medium. Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Common forms of computer-readable media include, for example, magnetic and/or optical media such as compact disk (CD) or digital versatile disk (DVD), punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read instructions and/or code. A computer program product may include code and/or machine-executable instructions that may represent a procedure, a function, a subprogram, a program, a routine, an application (App), a subroutine, a module, a software package, a class, or any combination of instructions, data structures, or program statements. 
     Those of skill in the art will appreciate that information and signals used to communicate the messages described herein may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof. 
     Terms, “and” and “or” as used herein, may include a variety of meanings that are also expected to depend at least in part upon the context in which such terms are used. Typically, “or” if used to associate a list, such as A, B, or C, is intended to mean A, B, and C, here used in the inclusive sense, as well as A, B, or C, here used in the exclusive sense. In addition, the term “one or more” as used herein may be used to describe any feature, structure, or characteristic in the singular or may be used to describe some combination of features, structures, or characteristics. However, it should be noted that this is merely an illustrative example and claimed subject matter is not limited to this example. Furthermore, the term “at least one of” if used to associate a list, such as A, B, or C, can be interpreted to mean any combination of A, B, and/or C, such as A, AB, AC, BC, AA, ABC, AAB, AABBCCC, etc. 
     Further, while certain embodiments have been described using a particular combination of hardware and software, it should be recognized that other combinations of hardware and software are also possible. Certain embodiments may be implemented only in hardware, or only in software, or using combinations thereof. In one example, software may be implemented with a computer program product containing computer program code or instructions executable by one or more processors for performing any or all of the steps, operations, or processes described in this disclosure, where the computer program may be stored on a non-transitory computer readable medium. The various processes described herein can be implemented on the same processor or different processors in any combination. 
     Where devices, systems, components or modules are described as being configured to perform certain operations or functions, such configuration can be accomplished, for example, by designing electronic circuits to perform the operation, by programming programmable electronic circuits (such as microprocessors) to perform the operation such as by executing computer instructions or code, or processors or cores programmed to execute code or instructions stored on a non-transitory memory medium, or any combination thereof. Processes can communicate using a variety of techniques, including, but not limited to, conventional techniques for inter-process communications, and different pairs of processes may use different techniques, or the same pair of processes may use different techniques at different times. 
     The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that additions, subtractions, deletions, and other modifications and changes may be made thereunto without departing from the broader spirit and scope as set forth in the claims. Thus, although specific embodiments have been described, these are not intended to be limiting. Various modifications and equivalents are within the scope of the following claims.