Facebook Patent | Dual-side antireflection coatings for broad angular and wavelength bands

Patent: Dual-side antireflection coatings for broad angular and wavelength bands

Drawings: Click to check drawins

Publication Number: 20210199873

Publication Date: 20210701

Applicant: Facebook

Abstract

A waveguide display includes a first substrate having two opposing sides, a grating on a first side of the two opposing sides of the first substrate and configured to couple display light into or out of the first substrate, a first antireflection layer on a first surface of the grating and configured to reduce reflection of visible light at the first surface of the grating, and a second antireflection layer on a second side of the two opposing sides of the first substrate and configured to reduce reflection of the visible light at the second side of the first substrate.

Claims

  1. A waveguide display comprising: a first substrate including two opposing sides; a grating on a first side of the two opposing sides of the first substrate, the grating configured to couple display light into or out of the first substrate; a first antireflection layer on a first surface of the grating and configured to reduce reflection of visible light at the first surface of the grating; and a second antireflection layer on a second side of the two opposing sides of the first substrate and configured to reduce reflection of the visible light at the second side of the first substrate.

  2. The waveguide display of claim 1, wherein at least one of the first antireflection layer or the second antireflection layer includes an array of micro-structures.

  3. The waveguide display of claim 2, wherein the micro-structures include vertical ridges, pillars, tapered ridges, or cones.

  4. The waveguide display of claim 2, wherein the array of micro-structures is in a material layer characterized by a first refractive index lower than a second refractive index of the first substrate.

  5. The waveguide display of claim 2, wherein the array of micro-structures includes a one-dimension or two-dimensional array of micro-structures.

  6. The waveguide display of claim 2, wherein a period of the array of micro-structures is less than a half of a period of the grating.

  7. The waveguide display of claim 1, wherein the first antireflection layer has a reflectivity less than 5% for visible light with incident angles less than 75.degree..

  8. The waveguide display of claim 1, wherein the first antireflection layer or the second antireflection layer includes two or more layers characterized by different respective effective refractive indices less than a refractive index of the first substrate.

  9. The waveguide display of claim 1, wherein the grating includes one or more grating layers configured to cause destructive interference between ambient light diffracted by at least two grating layers or between ambient light diffracted by different portions of one grating layer.

  10. The waveguide display of claim 1, wherein the grating includes: a slanted grating including a plurality of slanted ridges, the slanted grating characterized by a height, a period, and a slant angle of the plurality of slanted ridges configured to cause destructive interference between ambient light diffracted by different portions of the slanted grating; or at least two grating layers, wherein the at least two grating layers are characterized by a same grating period and are offset by a half of the grating period.

  11. The waveguide display of claim 1, further comprising a second grating between the first substrate and the second antireflection layer.

  12. The waveguide display of claim 11, wherein the grating and the second grating are configured to diffract display light of different respective colors or display light for different respective fields of view.

  13. The waveguide display of claim 1, further comprising: a second substrate; a second grating on a first side of the second substrate and configured to couple display light into or out of the second substrate, the grating and the second grating configured to diffract display light of different respective colors or display light for different respective fields of view; a third antireflection layer on a first surface of the second grating and configured to reduce reflection of the visible light at the first surface of the second grating; and a fourth antireflection layer on a second side of the second substrate opposing the second grating and configured to reduce reflection of the visible light at the second side of the second substrate.

  14. The waveguide display of claim 1, further comprising: a second substrate; a second grating on a first side of the second substrate and configured to diffract invisible light; a third antireflection layer on a first surface of the second grating and configured to reduce reflection of the visible light at the first surface of the second grating; and a fourth antireflection layer on a second side of the second substrate opposing the second grating and configured to reduce reflection of the visible light at the second side of the second substrate.

  15. The waveguide display of claim 1, further comprising an angular-selective transmissive layer configured to reflect, diffract, or absorb ambient light incident on the angular-selective transmissive layer with an incidence angle greater than a threshold value.

  16. The waveguide display of claim 1, wherein the first substrate includes a curved substrate.

  17. A near-eye display comprising: a waveguide including a first surface and a second surface opposing the first surface; an input coupler configured to couple display light from an image source into the waveguide; an output coupler coupled to the first surface of the waveguide and configured to: refractively transmit ambient light; and diffractively couple the display light out of the waveguide; a first antireflection layer for visible light on the output coupler; and a second antireflection layer for visible light on the second surface of the waveguide.

  18. The near-eye display of claim 17, wherein the first antireflection layer includes an array of micro-structures in a material layer characterized by a first refractive index lower than a second refractive index of the waveguide or the output coupler.

  19. The near-eye display of claim 18, wherein: the array of micro-structures includes a one-dimensional or two-dimensional array of ridges, pillars, tapered pillars, or cones; and a period of the array of micro-structures is less than a half of a period of the output coupler.

  20. The near-eye display of claim 17, wherein the output coupler comprises one or more grating layers and is configured to cause destructive interference between ambient light diffracted by at least two grating layers or between ambient light diffracted by different portions of one grating layer.

Description

BACKGROUND

[0001] An artificial reality system, such as a head-mounted display (HMD) or heads-up display (HUD) system, generally includes a near-eye display (e.g., in the form of a headset or a pair of glasses) 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’s eyes. The near-eye display 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).

[0002] 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 grating. Light from the surrounding environment may pass through a see-through region of the waveguide and reach the user’s eyes as well.

SUMMARY

[0003] This disclosure relates generally to near-eye display systems, and more specifically to near-eye displays with reduced optical artifacts, such as glare or ghost images. In one embodiment, a waveguide-based near-eye display may include diffraction grating couplers that may diffractively couple display light into or out of a waveguide and refractively transmit ambient light through the waveguide. The grating couplers may include one or more grating layers that can cause destructive interference between ambient light diffracted by at least two grating layers or between ambient light diffracted by different portions of a grating layer to reduced artifacts (e.g., ghost images and chromatic dispersion) caused by ambient light. An antireflection layer may be placed on each of two opposite surfaces of the waveguide to further reduce the artifacts caused by reflected light from external light sources, due to, for example, see-through reflection and small grazing angle reflection. The antireflection layers may transmit light in a broad wavelength range and a broad incident angular range, while allowing (e.g., by refracting) ambient light within the see-through field of view of the near-eye display to pass through and reach user’s eyes with little or no haze or contrast degradation. Various inventive embodiments are described herein, including devices, systems, methods, materials, and the like.

[0004] According to certain embodiments, a waveguide display may include a first substrate including two opposing sides, a grating on a first side of the two opposing sides of the first substrate and configured to couple display light into or out of the first substrate, a first antireflection layer on a first surface of the grating and configured to reduce reflection of visible light at the first surface of the grating, and a second antireflection layer on a second side of the two opposing sides of the first substrate and configured to reduce reflection of the visible light at the second side of the first substrate. In some embodiments, the first antireflection layer or the second antireflection layer may have a reflectivity less than about 5%, such as less than about 3%, for visible light with incident angles less than 75.degree.. In some embodiments, the first substrate may include a curved substrate.

[0005] In some embodiments of the waveguide display, the first antireflection layer or the second antireflection layer may include two or more layers characterized by different respective effective refractive indices less than a refractive index of the first substrate. In some embodiments, at least one of the first antireflection layer or the second antireflection layer may include an array of micro-structures. The micro-structures may include, for example, vertical ridges, pillars, tapered ridges, or cones. The array of micro-structures may be in a material layer characterized by a first refractive index lower than a second refractive index of the first substrate. In some embodiments, the period of the array of micro-structures may be less than a half of a period of the grating.

[0006] In some embodiments, the grating may include one or more grating layers configured to cause destructive interference between ambient light diffracted by at least two grating layers or between ambient light diffracted by different portions of one grating layer. In some embodiments, the grating may include a slanted grating that includes a plurality of slanted ridges, where the slanted grating may be characterized by a height, a period, and a slant angle of the plurality of slanted ridges configured to cause destructive interference between ambient light diffracted by different portions of the slanted grating. In some embodiments, the grating may include at least two grating layers, where the at least two grating layers may be characterized by a same grating period and may be offset horizontally by a half of the grating period. In some embodiments, the waveguide display may also include a second grating between the first substrate and the second antireflection layer, where the grating and the second grating may be configured to diffract display light of different respective colors or display light for different respective fields of view.

[0007] In some embodiments, the waveguide display may further include a second substrate, a second grating on a first side of the second substrate and configured to couple display light into or out of the second substrate, a third antireflection layer on a first surface of the second grating, and a fourth antireflection layer on a second side of the second substrate opposing the second grating. The grating and the second grating may be configured to diffract display light of different respective colors or display light for different respective fields of view. The third antireflection layer may be configured to reduce reflection of the visible light at the first surface of the second grating. The fourth antireflection layer may be configured to reduce reflection of the visible light at the second side of the second substrate.

[0008] In some embodiments, the waveguide display may include a second substrate, a second grating on a first side of the second substrate and configured to diffract invisible light, a third antireflection layer on a first surface of the second grating and configured to reduce reflection of the visible light at the first surface of the second grating, and a fourth antireflection layer on a second side of the second substrate opposing the second grating and configured to reduce reflection of the visible light at the second side of the second substrate. In some embodiments, the waveguide display may include an angular-selective transmissive layer configured to reflect, diffract, or absorb ambient light incident on the angular-selective transmissive layer with an incidence angle greater than a threshold value.

[0009] According to certain embodiments, a near-eye display may include a waveguide including a first surface and a second surface opposing the first surface, an input coupler configured to couple display light from an image source into the waveguide, an output coupler coupled to the first surface of the waveguide, and a first antireflection layer for visible light on the output coupler, and a second antireflection layer for visible light on the second surface of the waveguide. The output coupler may be configured to refractively transmit ambient light and diffractively couple the display light out of the waveguide.

[0010] In some embodiments of the near-eye display, the first antireflection layer may include an array of micro-structures in a material layer characterized by a first refractive index lower than a second refractive index of the waveguide or the output coupler. The array of micro-structures may include, for example, a one-dimensional or two-dimensional array of ridges, pillars, tapered pillars, or cones. A period of the array of micro-structures may be less than a half of a period of the output coupler. In some embodiments, the output coupler may include one or more grating layers and may be configured to cause destructive interference between ambient light diffracted by at least two grating layers or between ambient light diffracted by different portions of one grating layer.

[0011] 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

[0012] Illustrative embodiments are described in detail below with reference to the following figures.

[0013] FIG. 1 is a simplified block diagram of an example of an artificial reality system environment including a near-eye display according to certain embodiments.

[0014] FIG. 2 is a perspective view of an example of a near-eye display in the form of a head-mounted display (HMD) device for implementing some of the examples disclosed herein.

[0015] FIG. 3 is a perspective view of an example of a near-eye display in the form of a pair of glasses for implementing some of the examples disclosed herein.

[0016] FIG. 4 illustrates an example of an optical see-through augmented reality system including a waveguide display according to certain embodiments.

[0017] FIG. 5 illustrates propagations of display light and external light in an example of a waveguide display.

[0018] FIG. 6A illustrates the propagation of external light in an example of a waveguide display with a grating coupler on the front side of the waveguide display. FIG. 6B illustrates the propagation of external light in an example of a waveguide display with a grating coupler on the back side of the waveguide display.

[0019] FIG. 7 illustrates rainbow artifacts in an example of a waveguide display.

[0020] FIG. 8A illustrates an example of a grating coupler with reduced rainbow artifacts according to certain embodiments. FIG. 8B illustrates an example of a waveguide display including an angular-selective transmissive layer according to certain embodiments.

[0021] FIG. 9A illustrates light reflection at an interface between two example materials.

[0022] FIG. 9B illustrates reflectivity as a function of the light incident angle at the interface between the two example materials.

[0023] FIG. 10A illustrates rainbow artifacts caused by light reflection at a surface of an example of a waveguide display according to certain embodiments. FIG. 10B illustrates an example of a waveguide display having an antireflection layer for reducing rainbow artifacts caused by light reflection at a surface of the waveguide display according to certain embodiments.

[0024] FIG. 11A illustrates rainbow artifacts caused by light reflection at a surface of a grating coupler in an example of a waveguide display according to certain embodiments. FIG. 11B illustrates an example of a waveguide display having an antireflection layer for reducing rainbow artifacts caused by light reflection at a surface of the grating coupler according to certain embodiments.

[0025] FIG. 12A illustrates an example of an antireflection structure according to certain embodiments. FIG. 12B illustrates reflectivity of the example of the antireflection structure shown in FIG. 12A as a function of the light incident angle.

[0026] FIG. 13A illustrates an example of an antireflection structure according to certain embodiments. FIG. 13B illustrates reflectivity of the example of the antireflection structure shown in FIG. 13A as a function of the light incident angle.

[0027] FIG. 14A illustrates an example of an antireflection structure according to certain embodiments. FIG. 14B illustrates reflectivity of the example of the antireflection structure shown in FIG. 14A as a function of the light incident angle.

[0028] FIG. 15A illustrates an example of an antireflection structure according to certain embodiments. FIG. 15B illustrates reflectivity of the example of the antireflection structure shown in FIG. 15A as a function of the light incident angle.

[0029] FIG. 16A illustrates an example of an antireflection structure according to certain embodiments. FIG. 16B illustrates reflectivity of the example of the antireflection structure shown in FIG. 16A as a function of the light incident angle.

[0030] FIG. 17A illustrates rainbow artifacts caused by reflective diffraction of ambient light from the back side of an example of a waveguide display. FIG. 17B illustrates rainbow artifacts in an example of a waveguide display that includes two or more substrates.

[0031] FIG. 18A illustrates rainbow artifacts caused by light reflection at a surface of a substrate and reflective diffraction of the reflected light in an example of a waveguide display that includes two or more substrates. FIG. 18B illustrates rainbow artifact reduction in an example of a waveguide display including two or more substrates according to certain embodiments.

[0032] FIG. 19 illustrates an example of a waveguide display including dual-side antireflection coatings according to certain embodiments.

[0033] FIG. 20 illustrates an example of a waveguide display including dual-side antireflection coatings and an angular-selective transmissive layer according to certain embodiments

[0034] FIG. 21 illustrates an example of a waveguide display including two or more substrates each including dual-side antireflection coatings according to certain embodiments.

[0035] FIG. 22 is a simplified block diagram of an example electronic system of an example near-eye display for implementing some of the examples disclosed herein.

[0036] 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.

[0037] 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

[0038] Techniques disclosed herein relate generally to near-eye display systems. More specifically, and without limitation, disclosed herein are near-eye displays with reduced glare or ghost images. The near-eye displays may include grating couplers that cause destructive interference between ambient light diffracted by two or more grating layers of the grating couplers to reduce the diffraction of incident ambient light (e.g., ambient light with large incident angles) by the grating couplers. The near-eye displays may also include antireflection coatings to reduce reflected ambient light that may be diffracted by the grating couplers to user’s eyes to cause optical artifacts. The antireflection coatings may transmit light in a broad wavelength range and a broad incident angular range, while allowing ambient light within the see-through field of view of the near-eye display to pass through without being diffracted and reach user’s eyes with little or no haze or contrast degradation. Various inventive embodiments are described herein, including devices, systems, methods, materials, and the like.

[0039] In some near-eye displays, light may be coupled into or out of the waveguide using a diffractive optical element, such as a grating. The grating may diffract both the light of the projected image and light from the surrounding environment (e.g., from a light source, such as a lamp or the sun). The diffracted portion of the light from ambient light sources and with large incident angles may appear as a ghost image to the user of a near-eye display. In addition, due to the wavelength dependent characteristics of the grating, ghost images of different colors may appear at different locations or angles. These ghost images may negatively impact the user experience of using the near-eye display. Transmissive or reflective gratings used as input or output couplers can be designed to refract ambient light within the field of view, while directing ambient light with large incident angles out of the eyebox of the near-eye display to reduce the optical artifacts. However, the ambient light diffracted, transmitted, or reflected by a grating at one surface of a waveguide may be at least partially reflected by an opposing surface of the waveguide or a surface of another waveguide in a stack due to, for example, Fresnel reflection, and may reach the grating again. The reflected light may be diffracted by the grating towards the user’s eyes to cause rainbow images or other optical artifacts. For example, in some embodiments, a system may include two or more substrates or waveguides, where some ambient light with large incident angles may pass through a first substrate and may then be reflected back to the first substrate when incident on the second substrate, and a grating on the first substrate may diffract the ambient light towards the user’s eyes to cause rainbow images.

[0040] According to certain embodiments, a display system may include a substrate, a grating on one of two opposing surfaces of the substrate, and antireflection layers on the opposing surfaces of the substrate. In some embodiments, the display system may include two or more substrates, where at least one of the two or more substrates may include antireflection layers on two opposing surfaces of the substrate. The antireflection layers may reduce the see-through reflection and the small grazing angle reflection of ambient light within broad wavelength and angular ranges. For example, the antireflection layers may have a low reflectivity (below about 5% or about 3%) for ambient light with wavelengths between 450 nm and 600 nm and with incidence angles within 0-50.degree. (for see-through quality) and a low reflectivity (below about 5% or about 3%) for ambient light with incidence angles within about 50-75 degrees (for rainbow reduction). The antireflection layer may include either multiple uniform layers of different materials or periodic structures (with a small period for large diffraction angles), and may not increase see-through haze or degrade the display contrast.

[0041] In some embodiments, the antireflection layer may be implemented using two or more layers of different materials with different refractive indices, where one or more of the two or more layers may include a material with a low refractive index. In some embodiments, the low refractive index may be achieved using one-dimensional or two-dimensional periodic structures with low filling factors or small duty cycles. In some embodiments, the antireflection layer may be implemented using a multi-layer AR coating with gradient refractive index. In some embodiments, the multi-layer AR coating with gradient refractive index may be achieved using one-dimensional or two-dimensional periodic structures (e.g., tapered ridges or cones), where the width of the ridges or cones (and thus the filling factor and the effective refractive index of the periodic structures) may gradually reduce.

[0042] Techniques disclosed herein may reduce the diffraction of ambient light, reduce see-through reflection, reduce small grazing angle reflection, and thus reduce optical artifacts, such as rainbow images. The antireflection structures may work for broad wavelength and angular ranges, and may not result in see-through haze, and not degrade display contrast.

[0043] 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.

[0044] FIG. 1 is a simplified block diagram of an example of an artificial reality system environment 100 including a near-eye display 120 in accordance with certain embodiments. Artificial reality system environment 100 shown in FIG. 1 may include near-eye display 120, an optional external imaging device 150, and an optional input/output interface 140, each of which may be coupled to an optional console 110. While FIG. 1 shows an example of artificial reality system environment 100 including one near-eye display 120, one external 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 displays 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 external 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.

[0045] Near-eye display 120 may be a head-mounted display that presents content to a user. Examples of content presented by near-eye display 120 include one or more of images, videos, audio, or any combination thereof. In some embodiments, audio may be presented via an external device (e.g., speakers and/or headphones) that receives audio information from near-eye display 120, console 110, or both, and presents audio data based on the audio information. Near-eye display 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 120 may be implemented in any suitable form-factor, including a pair of glasses. Some embodiments of near-eye display 120 are further described below with respect to FIGS. 2 and 3. 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 120 and artificial reality content (e.g., computer-generated images). Therefore, near-eye display 120 may augment images of a physical, real-world environment external to near-eye display 120 with generated content (e.g., images, video, sound, etc.) to present an augmented reality to a user.

[0046] In various embodiments, near-eye display 120 may include one or more of display electronics 122, display optics 124, and an eye-tracking unit 130. In some embodiments, near-eye display 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 120 may omit any of eye-tracking unit 130, locators 126, position sensors 128, and IMU 132, or include additional elements in various embodiments. Additionally, in some embodiments, near-eye display 120 may include elements combining the function of various elements described in conjunction with FIG. 1.

[0047] 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 (.mu.LED) 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 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 stereoscopic 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’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).

[0048] In certain embodiments, display optics 124 may display image content optically (e.g., using optical waveguides and couplers) or 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 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 antireflective coating, a reflective coating, a filtering coating, or a combination of different optical coatings.

[0049] 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’s eyes than near-eye display 120.

[0050] 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 any 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.

[0051] Locators 126 may be objects located in specific positions on near-eye display 120 relative to one another and relative to a reference point on near-eye display 120. In some implementations, console 110 may identify locators 126 in images captured by external imaging device 150 to determine the artificial reality headset’s position, orientation, or both. A locator 126 may be an LED, a corner cube reflector, a reflective marker, a type of light source that contrasts with an environment in which near-eye display 120 operates, or any combination 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.

[0052] External 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 any combination thereof. Additionally, external imaging device 150 may include one or more filters (e.g., to increase signal to noise ratio). External imaging device 150 may be configured to detect light emitted or reflected from locators 126 in a field of view of external imaging device 150. In embodiments where locators 126 include passive elements (e.g., retroreflectors), external 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 external imaging device 150. Slow calibration data may be communicated from external imaging device 150 to console 110, and external 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.).

[0053] Position sensors 128 may generate one or more measurement signals in response to motion of near-eye display 120. Examples of position sensors 128 may include accelerometers, gyroscopes, magnetometers, other motion-detecting or error-correcting sensors, or any combination 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.

[0054] 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 any 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 120 relative to an initial position of near-eye display 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 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 120 (e.g., a center of IMU 132).

[0055] Eye-tracking unit 130 may include one or more eye-tracking systems. Eye tracking may refer to determining an eye’s position, including orientation and location of the eye, relative to near-eye display 120. An eye-tracking system may include an imaging system to image one or more eyes and may optionally 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 unit 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’s eye. As another example, eye-tracking unit 130 may capture reflected radio waves emitted by a miniature radar unit. Eye-tracking unit 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 unit 130 may be arranged to increase contrast in images of an eye captured by eye-tracking unit 130 while reducing the overall power consumed by eye-tracking unit 130 (e.g., reducing power consumed by a light emitter and an imaging system included in eye-tracking unit 130). For example, in some implementations, eye-tracking unit 130 may consume less than 100 milliwatts of power.

[0056] Near-eye display 120 may use the orientation of the eye to, e.g., determine an inter-pupillary distance (IPD) of the user, determine gaze direction, introduce depth cues (e.g., blur image outside of the user’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’s eyes, or any combination thereof. Because the orientation may be determined for both eyes of the user, eye-tracking unit 130 may be able to determine where the user is looking. For example, determining a direction of a user’s gaze may include determining a point of convergence based on the determined orientations of the user’s left and right eyes. A point of convergence may be the point where the two foveal axes of the user’s eyes intersect. The direction of the user’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’s eyes.

[0057] 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, external 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 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.

[0058] Console 110 may provide content to near-eye display 120 for presentation to the user in accordance with information received from one or more of external imaging device 150, near-eye display 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 an 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.

[0059] 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 non-transitory 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.

[0060] 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’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.

[0061] Headset tracking module 114 may track movements of near-eye display 120 using slow calibration information from external imaging device 150. For example, headset tracking module 114 may determine positions of a reference point of near-eye display 120 using observed locators from the slow calibration information and a model of near-eye display 120. Headset tracking module 114 may also determine positions of a reference point of near-eye display 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 any combination thereof, to predict a future location of near-eye display 120. Headset tracking module 114 may provide the estimated or predicted future position of near-eye display 120 to artificial reality engine 116.

[0062] Artificial reality engine 116 may execute applications within artificial reality system environment 100 and receive position information of near-eye display 120, acceleration information of near-eye display 120, velocity information of near-eye display 120, predicted future positions of near-eye display 120, or any 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 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 120 that mirrors the user’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 120 or haptic feedback via input/output interface 140.

[0063] Eye-tracking module 118 may receive eye-tracking data from eye-tracking unit 130 and determine the position of the user’s eye based on the eye tracking data. The position of the eye may include an eye’s orientation, location, or both relative to near-eye display 120 or any element thereof. Because the eye’s axes of rotation change as a function of the eye’s location in its socket, determining the eye’s location in its socket may allow eye-tracking module 118 to more accurately determine the eye’s orientation.

[0064] FIG. 2 is a perspective view of an example of a near-eye display in the form of an HMD device 200 for implementing some of the examples disclosed herein. HMD device 200 may be a part of, e.g., a VR system, an AR system, an MR system, or any combination 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 left 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’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 temple tips as shown in, for example, FIG. 3 below, rather than head strap 230.

[0065] 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), audio, or any combination 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, an LCD, an OLED display, an ILED display, a .mu.LED display, an AMOLED, a TOLED, some other display, or any combination thereof. HMD device 200 may include two eye box regions.

[0066] 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 any 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.

[0067] FIG. 3 is a perspective view of an example of a near-eye display 300 in the form of a pair of glasses for implementing some of the examples disclosed herein. Near-eye display 300 may be a specific implementation of near-eye display 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 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 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).

[0068] Near-eye display 300 may further include various sensors 350a, 350b, 350c, 350d, and 350e on or within frame 305. In some embodiments, sensors 350a-350e may include one or more depth sensors, motion sensors, position sensors, inertial sensors, or ambient light sensors. In some embodiments, sensors 350a-350e may include one or more image sensors configured to generate image data representing different fields of views in different directions. In some embodiments, sensors 350a-350e may be used as input devices to control or influence the displayed content of near-eye display 300, and/or to provide an interactive VR/AR/MR experience to a user of near-eye display 300. In some embodiments, sensors 350a-350e may also be used for stereoscopic imaging.

[0069] In some embodiments, near-eye display 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 350a-350e in capturing images of different objects within the dark environment. In some embodiments, illuminator(s) 330 may be used to project certain light patterns 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.

[0070] In some embodiments, near-eye display 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.

[0071] FIG. 4 illustrates an example of an optical see-through augmented reality system 400 including 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, light source or image source 412 may include one or more micro-LED devices described above. 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, an LED, and/or a micro-LED described above. In some embodiments, image source 412 may include a plurality of light sources (e.g., an array of micro-LEDs described above), 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 three two-dimensional arrays of micro-LEDs, where each two-dimensional array of micro-LEDs may include micro-LEDs configured to emit light of 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. For example, in some embodiments, image source 412 may include one or more one-dimensional arrays or elongated two-dimensional arrays of micro-LEDs, and projector optics 414 may include one or more one-dimensional scanners (e.g., micro-mirrors or prisms) configured to scan the one-dimensional arrays or elongated two-dimensional arrays of micro-LEDs to generate image frames. 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.

[0072] 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 element (DOE) (e.g., a surface-relief grating), a slanted surface of substrate 420, or a refractive coupler (e.g., a wedge or a prism). For example, input coupler 430 may include a reflective volume Bragg grating or a transmissive volume Bragg grating. 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.

[0073] Substrate 420 may include or may be coupled to a plurality of output couplers 440, each 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 eyebox 495 where an eye 490 of the user of augmented reality system 400 may be located when augmented reality system 400 is in use. The plurality of output couplers 440 may replicate the exit pupil to increase the size of eyebox 495 such that the displayed image is visible in a larger area. As input coupler 430, output couplers 440 may include grating couplers (e.g., volume holographic gratings or surface-relief gratings), other diffraction optical elements (DOEs), prisms, etc. For example, output couplers 440 may include reflective volume Bragg gratings or transmissive volume Bragg gratings. Output couplers 440 may have different coupling (e.g., diffraction) efficiencies at different locations. Substrate 420 may also allow light 450 from the 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 very 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 in 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 images of virtual objects projected by projector 410.

[0074] FIG. 5 illustrates propagations of display light 540 and external light 530 in an example waveguide display 500 including a waveguide 510 and a grating coupler 520. Waveguide 510 may be a flat or curved transparent substrate with a refractive index n.sub.2 greater than the free space refractive index n.sub.1 (e.g., 1.0). Grating coupler 520 may be, for example, a Bragg grating or a surface-relief grating.

[0075] Display light 540 may be coupled into waveguide 510 by, for example, input coupler 430 of FIG. 4 or other couplers (e.g., a prism or slanted surface) described above. Display light 540 may propagate within waveguide 510 through, for example, total internal reflection. When display light 540 reaches grating coupler 520, display light 540 may be diffracted by grating coupler 520 into, for example, a 0.sup.th order diffraction (i.e., reflection) light 542 and a -1st order diffraction light 544. The 0.sup.th order diffraction may propagate within waveguide 510, and may be reflected by the bottom surface of waveguide 510 towards grating coupler 520 at a different location. The -1st order diffraction light 544 may be coupled (e.g., refracted) out of waveguide 510 towards the user’s eye, because a total internal reflection condition may not be met at the bottom surface of waveguide 510 due to the diffraction angle.

[0076] External light 530 may also be diffracted by grating coupler 520 into, for example, a 0.sup.th order diffraction light 532 and a -1st order diffraction light 534. Both the 0.sup.th order diffraction light 532 and the -1st order diffraction light 534 may be refracted out of waveguide 510 towards the user’s eye. Thus, grating coupler 520 may act as an input coupler for coupling external light 530 into waveguide 510, and may also act as an output coupler for coupling display light 540 out of waveguide 510. As such, grating coupler 520 may act as a combiner for combining external light 530 and display light 540. In general, the diffraction efficiency of grating coupler 520 (e.g., a surface-relief grating coupler) for external light 530 (i.e., transmissive diffraction) and the diffraction efficiency of grating coupler 520 for display light 540 (i.e., reflective diffraction) may be similar or comparable.

[0077] FIG. 6A illustrates the propagation of external light 630 in an example of a waveguide display 600 with a grating coupler 620 on the front side of a waveguide 610. External light 630 may be diffracted by grating coupler 620 into a 0.sup.th order diffraction light 632 and a -1st order diffraction light 634. The 0.sup.th order diffraction light 632 may be refracted out of waveguide 610 in a direction shown by a light ray 636, which may not reach the eyebox or user’s eyes. The -1.sup.st order diffraction light 634 may be refracted out of waveguide 610 in a direction shown by a light ray 638, which may reach the eyebox and user’s eyes. For different wavelengths (colors), the 0.sup.th order diffraction light may have a same diffraction angle, but the -1st order diffraction light may be wavelength dependent and thus may have different diffraction angles for light of different wavelengths to cause rainbow images.

[0078] FIG. 6B illustrates the propagation of external light 680 in an example of a waveguide display 650 with a grating coupler 670 on the back side of a waveguide 660. External light 680 may be refracted into waveguide 660 as refracted light 682. Refracted light 682 may then be diffracted out of waveguide 660 by grating coupler 670 into a 0.sup.th order diffraction light 684 and a -1st order diffraction light 686. The propagation direction of the 0.sup.th order diffraction light 684 may be similar to the propagation direction of light ray 636, and thus may not reach the eyebox or user’s eyes. The propagation direction of the -1st order diffraction light 686 may be similar to the propagation direction of light ray 638, and thus may reach the eyebox or user’s eyes. For different wavelengths (colors), the 0.sup.th order diffraction light may have a same diffraction angle, but the -1st order diffraction light may be wavelength dependent and thus may have different diffraction angles for light of different wavelengths to cause rainbow images.

[0079] FIG. 7 illustrates rainbow artifacts in an example of a waveguide display 700. As described above, waveguide display 700 may include a waveguide 710, a grating coupler 720, and a projector 730. Display light 732 from projector 730 may be coupled into waveguide 710, and may be partially coupled out of waveguide 710 at different locations by grating coupler 720 to reach a user’s eye 790. External light 742 from an external light source 740, such as the sun or a lamp, may also be diffracted by grating coupler 720 into waveguide 710 and may then propagate through waveguide 710 to reach user’s eye 790.

[0080] As described above with respect to FIG. 5 and FIGS. 6A and 6B, the grating coupler may not only diffract the display light, but also diffract the external light. In addition, as described above with respect to FIGS. 6A-6B, due to the chromatic dispersion of the grating, lights of different colors may be diffracted at different angles for diffraction orders greater or less than zero. As such, the -1st order diffractions of external light of different colors that reach the user’s eye (e.g., diffraction light 686 or light ray 638) may appear as ghost images located at different locations (or directions), which may be referred to as a rainbow artifact or rainbow ghost 744. Rainbow ghost 744 may appear on top of the displayed image or the image of the environment, and disrupt the displayed image or the image of the environment. Rainbow ghost 744 may significantly impact the user experience. In some cases, rainbow ghost 744 may also be dangerous to user’s eye 790 when the light from external light source 740 (e.g., the sun) is directed to user’s eye 790 with a high efficiency.

[0081] The rainbow ghost caused by the diffraction of external light by a grating coupler of a waveguide display may be reduced using certain techniques disclosed herein. For example, in some embodiments, a slanted grating including a plurality of slanted ridges may be used as the grating coupler, where a height of the slanted ridges may be equal to or close to an integer multiple of the period of the slanted grating divided by the tangent of the slant angle of the slanted ridges. In one example, the height and slant angle of the slanted ridges of the slanted grating may be designed so that the height of the grating is equal to or close to the period of the slanted grating divided by the tangent of the slant angle of the slanted ridges. In other words, a top left (or right) point on a first ridge of the slanted grating may be vertically aligned with a bottom left (or right) point of a second ridge of the slanted grating. Thus, the slanted grating may be considered as including two overlapped slanted gratings with an offset of about a half of the grating period between the two slanted gratings. As a result, external light diffracted by the two offset slanted gratings (e.g., the -1st order diffraction) may be out of phase by about 180.degree., and thus may destructively interfere with each other such that most of the external light may enter the waveguide as the 0.sup.th order diffraction, which may not be wavelength dependent. In this way, the rainbow ghost caused by the -1st order diffraction of external light by the grating coupler may be reduced or eliminated. Thus, the efficiency of the -1st order transmissive diffraction of the grating coupler for the external light can be much lower than that of the -1st order reflective diffraction of the grating coupler for the display light. For example, the efficiency for the -1st order diffraction of the display light may be greater than about 5%, about 20%, about 30%, about 50%, about 75%, about 90%, or higher, while the efficiency for the -1st order diffraction of the external light may be less than about 2%, less than about 1%, less than about 0.5%, or lower. In some implementations, an antireflection coating may be used to reduce the reflection of the external light at a surface of the waveguide or the grating coupler, where the external light, if reflected back to the grating coupler and then diffracted by the grating coupler, may cause rainbow ghosts and/or other artifacts.

[0082] FIG. 8A is a simplified diagram illustrating external light diffraction (e.g., transmissive diffraction) by a grating coupler 820 in a waveguide display 800 with reduced rainbow artifacts according to certain embodiments. Waveguide display 800 may include a waveguide 810 and grating coupler 820 on one side of waveguide 810. Grating coupler 820 may be formed on a waveguide 810 (e.g., a transparent substrate with a refractive index n.sub.2) of waveguide display 800. Grating coupler 820 may include a plurality of periods in the x (horizontal) direction. Each period may include a first slanted region formed of a material with a refractive index n.sub.g1, and a second slanted region formed of a material with a refractive index n.sub.g2. In various embodiments, the difference between n.sub.g1 and n.sub.g2 may be greater than 0.1, 0.2, 0.3, 0.5, 1.0, or higher. In some implementations, one of first slanted region and second slanted region may be an air gap with a refractive index of about 1.0. First slanted region and second slanted region may have a slant angle .alpha. with respect to the z (vertical) direction. The height (H) of first slanted region and second slanted region may be equal or close to (e.g., within about 5% or 10% of) an integer multiple (m) of the grating period p divided by the tangent of the slant angle .alpha., i.e., [0083] H.times.tan(.alpha.).apprxeq.m.times.p. In the example shown in FIG. 8A, m is equal to 1. Thus, the top left point of a first slanted region in a grating period may align vertically with the bottom left point of another first slanted region in a different grating period. Grating coupler 820 may thus include a first (top) slanted grating 822 and a second (bottom) slanted grating 824 each having a height of H/2. First slanted grating 822 and a second slanted grating 824 may be offset from each other in the x direction by p/2. In other embodiments, m may be equal to or greater than 2. For example, grating coupler 820 may include four overlapped slanted gratings each having a height of H/4 and offset from each other by a half grating period (p/2) in the x direction.

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