Outcoupling Gratings for Augmented Reality Systems

Abstract

The present invention relates to an outcoupling grating for an augmented reality system. An eyepiece for projecting an image to a viewer's eye, the eyepiece comprising a waveguide configured to propagate light, and a diffractive optical element optically coupled to the waveguide. The diffractive optical element comprises a plurality of first ridges protruding from a surface of the waveguide. Each of the plurality of first ridges has a first height and a first width. The diffractive optical element further comprises a plurality of second ridges. Each of the plurality of second ridges protrudes from a corresponding first ridge and has a second height greater than the first height and a second width less than the first width. The diffractive optical element is configured to diffract a first portion of the light propagating in the waveguide toward the eye, and diffract a second portion of the light propagating in the waveguide away from the eye.

Description

[0001] This application is a divisional application of an application with an application date of October 25, 2017, PCT international application number of PCT / US2017 / 058351, Chinese national phase application number of 201780066366.0, and invention name of “Out-coupled grating for augmented reality system”.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This application claims priority benefit to U.S. Provisional Patent Application Serial No. 62 / 413,288, filed on October 26, 2016, the entire disclosure of which is incorporated by reference. Background Art

[0004] Modern computing and display technologies have facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences in which digitally reproduced images, or portions thereof, are presented to a user in a manner that appears or is perceived as real. Virtual reality or "VR" scenarios generally involve presenting digital or virtual image information in a manner that is opaque to other actual real-world visual input; augmented reality or "AR" scenarios generally involve presenting digital or virtual image information as a visual enhancement of the actual world around the viewer.

[0005] Despite these advances in display technology, there remains a need in the art for improved methods and systems related to augmented reality systems. Summary of the invention

[0006] According to some embodiments of the present invention, an eyepiece for projecting an image into a viewer's eye may include: a waveguide having a surface and configured to propagate light in the waveguide; and a diffractive optical element optically coupled to the waveguide. The diffractive optical element may include a plurality of first ridges. The plurality of first ridges protrude from the surface of the waveguide and are arranged in a periodic array having a period. Each of the plurality of first ridges has a first height in a direction perpendicular to the surface of the waveguide and a first width in the direction of the period. The diffractive optical element may further include a plurality of second ridges. Each of the plurality of second ridges protrudes from a corresponding first ridge and has a second height greater than the first height and a second width less than the first width. The diffractive optical element may be configured to diffract a first portion of the light propagating in the waveguide toward the eye as a first order reflection, and diffract a second portion of the light propagating in the waveguide away from the eye as a first order transmission.

[0007] According to some other embodiments of the present invention, an eyepiece for projecting an image into a viewer's eye may include: a waveguide having a surface and configured to propagate light in the waveguide; and a diffractive optical element optically coupled to the waveguide. The diffractive optical element may include a plurality of first ridges. The plurality of first ridges protrude from the surface of the waveguide and are arranged in a periodic array having a period. Each corresponding first ridge has a corresponding first width in the direction of the period, which varies according to the position of the corresponding first ridge in the direction of the period. The diffractive optical element may further include a plurality of second ridges. Each corresponding second ridge protrudes from the corresponding first ridge and has a corresponding second width that is smaller than the corresponding first width of the corresponding first ridge. Each corresponding second width may vary according to the position of the corresponding first ridge in the direction of the period. The diffractive optical element may be configured to diffract a first portion of the light propagating in the waveguide toward the eye as a first-order reflection, and diffract a second portion of the light propagating in the waveguide away from the eye as a first-order transmission.

[0008] According to some further embodiments of the present invention, an eyepiece for projecting an image to a viewer's eye may include: a waveguide having a surface and configured to propagate light in the waveguide; and a diffractive optical element optically coupled to the waveguide. The diffractive optical element may include a plurality of first ridges. The plurality of first ridges protrude from the surface of the waveguide and are arranged in a periodic array having a period. Each corresponding first ridge has a corresponding first width in the direction of the period. The diffractive optical element may further include a plurality of second ridges. Each corresponding second ridge protrudes from the corresponding first ridge and has a corresponding second width that is less than the corresponding first width of the corresponding first ridge. The ratio of the corresponding second width of the corresponding second ridge to the corresponding first width of the corresponding first ridge may vary depending on the position of the corresponding first ridge in the direction of the period. The diffractive optical element may be configured to diffract a first portion of the light propagating in the waveguide toward the eye as a first-order reflection, and diffract a second portion of the light propagating in the waveguide away from the eye as a first-order transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 The optical paths in a viewing optical assembly (VOA) that may be used to present a digital or virtual image to a viewer according to an embodiment of the present invention are schematically shown.

[0010] Figure 2 An example of the path of a single light beam in a waveguide coupled into an eyepiece according to an embodiment of the present invention is shown.

[0011] Figure 3 An example of a bowtie topology for a waveguide according to an embodiment of the invention is shown.

[0012] Figure 4A An example of a waveguide having a combined OPE / EPE region in a single-sided configuration according to an embodiment of the present invention is shown.

[0013] Figure 4B An example of an optical path within a waveguide according to an embodiment of the present invention is shown.

[0014] Figure 5 Schematically shown is a cross-sectional view of a two-stage phase grating that may be used in an eyepiece to couple image light out of a waveguide to a viewer's eye in accordance with an embodiment of the present invention.

[0015] Figure 6 Diffraction efficiency curves of an exemplary two-order grating for first order reflection (1R) and first order transmission (1T) and second order reflection (2R) as a function of incident angle θ according to some embodiments of the present invention are shown.

[0016] 7A to 7F A simulated intensity graph of the diffraction efficiency of each stage of a two-stage grating according to some embodiments is shown.

[0017] Figure 8 An image of an exemplary three-level grating according to an embodiment of the present invention is shown.

[0018] Fig. 9 A schematic cross-sectional view of a three-level grating according to an embodiment of the present invention is shown.

[0019] Fig.10 Simulated diffraction efficiency curves of an exemplary three-level grating for first-order reflection (1R) and first-order transmission (1T) and second-order reflection (2R) according to an incident angle θ according to an embodiment of the present invention are shown.

[0020] Fig.11A and Fig. 11B The embodiment of the present invention shows the s-polarized light (90 degrees polarization, Fig.11A ) according to the grating depth and for p-polarized light (0 degree polarization, Fig. 11B ) of some exemplary three-level gratings according to the grating depth.

[0021] FIG. 12A to FIG. 12F A simulated intensity graph of the diffraction efficiency of each order of a three-order grating according to some embodiments is shown.

[0022] FIG. 13A to FIG. 13F A simulated intensity graph of the diffraction efficiency of each level of a three-level grating according to some other embodiments is shown.

[0023] FIG. 14A to FIG. 14F Shown are simulated intensity graphs of the diffraction efficiency of each level of a three-level grating according to some further embodiments.

[0024] Fig.15 The simulated diffraction efficiency of an exemplary three-level grating for first-order reflection (1R), first-order transmission (1T), and second-order reflection (2R) as a function of incident angle according to some embodiments of the present invention is shown.

[0025] Fig.16 A schematic cross-sectional view of one period of a three-level grating according to an embodiment of the present invention is shown.

[0026] Fig.17 shows the grating parameter h according to an embodiment of the present invention 1 、h 2 、w 1 and w 2 Correlation with the optimization parameter α.

[0027] Fig.18 The power (P) toward the user according to an embodiment of the present invention is shown. user ), power towards the world (P world ) and secondary power (P 2 ) and the correlation with the optimization parameter α.

[0028] Fig.19 A schematic cross-sectional view of a grating formed on a waveguide according to an embodiment of the present invention is shown.

[0029] Fig. 20A and Fig. 20B A simulated contour diagram of average outcoupling power according to parameters a and b in a linear model of grating efficiency according to an embodiment of the present invention is shown ( Fig. 20A ) and the simulated contour plots of the RMS deviation from the average outcoupled power ( Fig. 20B ).

[0030] Fig.21 A simulated graph of normalized outcoupled power g(x)=f(x)y(x) (towards the user and the world) as a function of the normalized distance x relative to the top of the grating is shown for a linear model with parameters a=0.5 and b=1 according to an embodiment of the present invention.

[0031] Fig.22A and Fig. 22B The top of the grating ( Fig.22A ) and the bottom of the grating ( Fig. 22B ) is a schematic cross-sectional view of one period of a three-level grating. DETAILED DESCRIPTION

[0032] The present disclosure generally relates to diffractive optical elements that can be used in virtual reality and augmented reality visualization systems. In VR or AR systems, diffractive optical elements (which may also be referred to as phase gratings or gratings) are used in eyepieces to couple image light out of a waveguide to the viewer's eyes. For clarity, the term "grating" is used herein to describe diffractive optical elements, but the present invention is not limited to grating structures, but may include other forms of diffractive optical elements.

[0033] Figure 1 An optical path in a viewing optical assembly (VOA) that can be used to present a digital or virtual image to a viewer according to an embodiment of the present invention is schematically shown. The VOA includes a projector 101 and an eyepiece 100 that can be worn around the viewer's eyes. The eyepiece 100 can include one or more eyepiece layers. In one embodiment, the eyepiece 100 includes three eyepiece layers, one eyepiece layer for each of the three primary colors (red, green, and blue). In another embodiment, the eyepiece 100 can include six eyepiece layers, that is, a set of eyepiece layers for each of the three primary colors is configured to form a virtual image at one depth plane, and another set of eyepiece layers for each of the three primary colors is configured to form a virtual image at another depth plane. In other embodiments, for three or more different depth planes, the eyepiece 100 can include three or more eyepiece layers for each of the three primary colors. Each eyepiece layer includes a planar waveguide and can include an incoupling grating 107, an orthogonal pupil expander (OPE) region 108, and an exit pupil expander (EPE) region 109.

[0034] Still reference Figure 1 , the projector 101 projects the image light onto the coupling grating 107 in the eyepiece layer 100. The coupling grating 107 couples the image light from the projector 101 into a planar waveguide propagating in a direction toward the OPE region 108. The waveguide propagates the image light in a horizontal direction by total internal reflection (TIR). The OPE region 108 of the eyepiece layer 100 also includes a diffraction element that couples a portion of the image light propagating in the waveguide and redirects the portion of the image light to the EPE region 109. The EPE region 109 includes a diffraction element that couples a portion of the image light propagating in the waveguide in a direction substantially perpendicular to the plane of the eyepiece layer 100 and guides the portion of the image light to the viewer's eye 102. In this way, the viewer's eye 102 can view the image projected by the projector 101.

[0035] The diffraction elements in the EPE region 109 of the eyepiece layer 100 typically include a grating, such as a periodic structure, formed on the surface of a planar waveguide in the eyepiece. When a light beam propagates through the periodic structure, it will be diffracted into multiple orders. The period of the repeating structure determines the angular spacing between the orders. Smaller periods generate larger angular spacings, while larger periods generate closely spaced output beams. The relative power directed to each diffraction order is determined by the shape and characteristics of the surface profile within a single grating period.

[0036] Figure 2 An example of the path of a single beamlet in a waveguide 212 coupled into the eyepiece 200 according to an embodiment of the present invention is shown. The waveguide 212 may include an ICG 220, an OPE 230, and an EPE 240, each of which is disposed on or within a substrate 202, the substrate 202 including a material (typically a dielectric material with a high dielectric constant) capable of guiding light waves by total internal reflection. In some embodiments, the eyepiece 200 may include three waveguides 212, 214, and 216, each corresponding to a particular wavelength of light. Additional or fewer waveguides are possible. Similar to the waveguide 212, each of the waveguides 214 and 216 may include an ICG, an OPE, and an EPE. In some embodiments, the injected light 222 may be coupled to the eyepiece 200 at a wavelength corresponding to the ICG. Figure 2 2 and 3. Injected light 222 may enter eyepiece 200 at ICG 220 in a z-direction orthogonal to the illustration of FIG. 2. Injected light 222 may enter ICG 220, where a grating within ICG 220 may diffract certain wavelengths of light within incoupled light 222, with other wavelengths of incoupled light 222 continuing through subsequent waveguide layers to eyepiece 210. In some embodiments, ICG 220 is a plurality of individual gratings dedicated to specific wavelengths.

[0037] The incoupled light 222 may be diffracted within the waveguide by the ICG 220 in certain directions, spanning a range such as shown by the fan pattern 224 generally in the +x direction toward the OPE 230, but also spanning a fan pattern 226 generally in the -x direction away from the OPE 230. Other light paths spanning other fan patterns are of course possible and depend on the projection optics, as well as the specific grating and diffraction pattern configured by the ICG 220. That is, the light is not diffracted into the waveguide as a diverging beam, but in some embodiments, a progressive distributed sampling of a portion of the image light may create a gradually expanding beamlet distribution pattern across the eyepiece. The coupled light 222 diffracted within the illustrated fan-shaped pattern 224 can generally enter the OPE 230 along the optical path 228 and traverse in the +x direction as it illuminates the diffraction grating that constitutes the OPE 230, accompanied by distributed sampling through the OPE 230, a portion of which is periodically directed downward to the EPE 240 and traverses in the -y direction before being coupled out in the -z direction to the user's eye.

[0038] like Figure 2 As shown, much of the light in the wavelength corresponding to waveguide 212 may be lost due to directional losses such as light diffracted into fan pattern 226 or capture losses due to failure of OPE 230 to properly position or size to capture all of the light within fan pattern 224. Further details regarding the eyepiece are described in U.S. Patent Application No. 15 / 683,624, the contents of which are incorporated by reference for all purposes.

[0039] Figure 3 3 shows an example of a bow-tie topology for waveguide 300 according to another embodiment of the present invention. Waveguide 300 can mitigate losses in other waveguide designs by utilizing light that would normally be diffracted out of a pupil expander. By orienting ICG 320 so that the resulting fan-shaped pattern is aligned with the y-axis and the x-axis (e.g., Figure 3 ), the waveguide 300 may include a first pupil expander 330A and a second pupil expander 330B to capture more diffraction coupled light. In some embodiments, the first pupil expander 330A and the second pupil expander 330B may be OPEs. In some embodiments, the waveguide 300 may further include a third pupil expander 340, such as an EPE.

[0040] The waveguide 300 can reduce the size of a single OPE (such as those described above) because the waveguide 300 can include two smaller pupil expanders (e.g., a first pupil expander 330A and a second pupil expander 330B). In some embodiments, the first pupil expander 330A and the second pupil expander 330B can be similar to the OPE described above with a portion removed (e.g., removing areas 332A and 332B). The first pupil expander 330A and the second pupil expander 330B can multiply the received light and direct the light to the third pupil expander 340 (similar to the above). In some embodiments, the first pupil expander 330A and the second pupil expander 330B can direct the light at a certain angle in the xy plane, rather than directing the light in the general x direction as described above. The angle can cause the first pupil expanders 330A and 330B to send light to the third pupil expander 340 as shown in the optical path 328. In some embodiments, the efficiency of the waveguide 300 can be approximately doubled compared to other waveguides described herein.

[0041] In some embodiments, the waveguide 300 may also include one or more diffusers (e.g., diffuser 332A and diffuser 332B). The one or more diffusers may capture light transmitted directly from the ICG 320 to the center of the third pupil expander 340. The one or more diffusers may include gratings similar to the one or more OPEs described herein. In some embodiments, the gratings of the one or more diffusers may similarly step light into the third pupil expander 340.

[0042] Figure 4A An example of a waveguide 400 having a combined OPE / EPE region 450 in a single-sided configuration according to another embodiment of the present invention is shown. The combined OPE / EPE region 450 includes gratings corresponding to both OPE and EPE that overlap in space in the x-direction and the y-direction. In some embodiments, the gratings corresponding to the OPE and the EPE are located on the same side of the substrate 402 so that the OPE grating is superimposed on the EPE grating or the EPE grating is superimposed on the OPE grating (or both situations exist). In other embodiments, the OPE grating is located on the side opposite to the EPE grating on the substrate 402 so that the gratings overlap in space in the x-direction and the y-direction, but are separated from each other in the z-direction (i.e., located in different planes). Therefore, the combined OPE / EPE region 450 can be implemented in a single-sided configuration or a double-sided configuration.

[0043] Figure 4B An example of an optical path 428 within a waveguide 400 according to an embodiment of the present invention is shown. The optical path 428 includes incident light (denoted as 428A) that is coupled into the substrate 402 at the ICG 420. The coupled-in light (denoted as 428B) propagates toward the gratings 451, 452, and 453 by total internal reflection. When these light rays encounter the first OPE grating 451, the light is diffracted in the +y direction (denoted as 428C) and then diffracted out of the waveguide 400 in the -z direction toward the user's eye by the EPE grating 453 (denoted as 428D). Similarly, the coupled-in light (denoted as 428B) may alternatively encounter the second OPE grating 452 and diffracted in the -y direction (denoted as 428E). The light diffracted in the -y direction may be diffracted out of the waveguide 400 toward the user's eye by the EPE grating 453. Whether light is diffracted in the +y direction (by the first OPE grating 451) or in the -y direction (by the second OPE grating 452) is probabilistic and controlled by the grating structure. Typically, the performance of the combined OPE / EPE region 450 is improved when the probability of the incoupled light (represented as 428B) diffracting in either the +y direction or the -y direction is 50%. In some cases, this is achieved when the first OPE grating 451 and the second OPE grating 452 are perpendicular to each other.

[0044] Although the waveguide 400 is shown as having only a single ICG 420, in some embodiments, the waveguide 400 may preferably include a second ICG on the opposite side of the combined OPE / EPE region 450 (the side opposite the ICG 420). The second ICG may be identical in form and function to the ICG 420, and may be a mirrored version of the ICG 420. For example, when the ICG 420 is configured to diffract the in-coupled light associated with the projected image into the substrate 402, the second ICG 420 may be configured to diffract the in-coupled light associated with a mirrored version of the projected image (e.g., flipped in the x-direction). The optical path associated with the second ICG may include incident light coupled into the substrate 402 at the second ICG, as opposed to the optical path 428 associated with the ICG 420. The in-coupled light propagates toward the gratings 451, 452, and 453 by total internal reflection. When these light rays encounter the first OPE grating 451, the light is diffracted in the -y direction and then diffracted out of the waveguide 400 in the -z direction toward the user's eye by the EPE grating 453. Similarly, the incoupled light may alternatively encounter the second OPE grating 452 and diffracted in the +y direction. The light diffracted in the +y direction may be diffracted out of the waveguide 400b by the EPE grating 453 toward the user's eye.

[0045] Further details regarding other waveguide topologies are described in U.S. Patent Application No. 15 / 683,624, the contents of which are incorporated by reference for all purposes.

[0046] Figure 5 A cross-sectional view of a two-stage phase grating 500 that can be used in an eyepiece to couple image light from a waveguide 502 (located in the XY plane) to a viewer's eye is schematically shown in accordance with an embodiment of the present invention. The two-stage grating 500 may include a ridge array 510 extending along the Y axis (i.e., in a direction perpendicular to the paper) and protruding from the waveguide 502 (along the negative Z direction). The ridge array 510 may be periodically arranged along the X direction. Each ridge 210 may have a height h in the Z direction and a width w in the X direction. For image light incident from the optical waveguide 502 at the grating 500, the two-stage grating 500 may generate a primary reflection (1R) toward the viewer's eye, a primary transmission (1T) toward the world, and a secondary reflection (2R) in a direction substantially opposite to the incident direction, such as Figure 5 The relative diffraction efficiencies between the different diffraction orders may depend on the duty cycle, i.e. the ratio between the feature width w and the period D. They may also depend on the depth of the grating, i.e. the height h of the ridges.

[0047] When the grating 500 is used to couple image light out of the waveguide 502 to the viewer's eye in a VR or AR system, several performance characteristics of the grating may be of concern. First, more image light may need to be directed toward the viewer rather than toward the world, because image light directed toward the world is essentially wasted and may also allow others to view what the viewer is viewing. Second, light bounces within the eyepiece can be diffracted back via secondary diffraction and then diffracted out toward the viewer. If the waveguide is not completely flat or if there is a lens function built into the grating, this light may cause angular errors, which can reduce the modulation transfer function (MTF) and contrast. Therefore, it may be desirable to minimize secondary reflections. In addition, light from the world (e.g., overhead lights) may be diffracted toward the viewer, creating a rainbow effect that may obscure the scene and distract the viewer.

[0048] Figure 6 The simulated diffraction efficiency curves of an exemplary two-stage grating for first-order reflection (1R) and first-order transmission (1T) and second-order reflection (2R) are shown as a function of the incident angle θ. As shown, for the incident angle range shown, the diffraction efficiency of the first-order transmission (1T) is comparable to the diffraction efficiency of the first-order reflection (1R). Therefore, approximately the same amount of image light can be delivered to the world and the viewer.

[0049] 7A to 7F 1 shows a simulated intensity graph of the diffraction efficiency of each level of a two-level grating according to some embodiments. Specifically, Fig. 7A and Fig.7D The user-side diffraction efficiency (1R) in terms of characteristic height h (horizontal axis) and characteristic width w (vertical axis) for s-polarization and p-polarization, respectively; Figure 7B and Fig. 7E shows the world-side diffraction efficiency (1T) in terms of h (horizontal axis) and w (vertical axis) for s-polarization and p-polarization, respectively; and Figure 7C and Figure 7F The secondary reflection (2R) according to h (horizontal axis) and w (vertical axis) are shown for s-polarization and p-polarization, respectively. The dashed line indicates the range of w corresponding to the characteristic width with a characteristic height h=60nm, which can cause a relatively low secondary reflection (2R) while having a relatively high primary reflection (1R). Moreover, the primary transmission (1T) is relatively low compared to the primary reflection (1R).

[0050] According to some embodiments of the present invention, improved outcoupling grating performance characteristics may be achieved by using a multi-level grating structure. Figure 8 An image of an exemplary three-level grating 800 is shown in accordance with an embodiment of the present invention. Fig. 98 shows a schematic cross-sectional view of a grating 800. The grating 800 may include a base layer 810 formed on a waveguide 802. The base layer 810 has a thickness (RLT) h 0 In some embodiments, the grating 800 may not have the base layer 810. The grating 800 includes a first layer extending along the Y axis (ie, in a direction perpendicular to the paper) and having a first height h 1 A plurality of first ridges 820 protrude (in the negative Z direction) from the base layer 810. The plurality of first ridges 820 are arranged in a periodic array having a period D defined in the X direction. Each first ridge 820 has a first width w in the X direction. 1 The grating 800 also includes a plurality of second ridges 830. Each second ridge 830 protrudes from the corresponding first ridge 820 by a second height h2 (in the negative Z direction) and has a second width w in the X direction. 2 .

[0051] refer to Fig. 9 , the image light is incident on the grating 800 from the waveguide 802. The grating 800 can generate a zero-order reflected beam (0R) at an angle substantially equal to the incident angle. The grating 800 can also generate a first-order reflected beam (1R) in a direction substantially perpendicular to the waveguide 802 toward the viewer's eyes, and a first-order transmitted beam (1T) in a direction substantially perpendicular to the waveguide toward the world. The grating 800 can also generate a second-order reflected beam (2R) in a direction substantially opposite to the incident beam direction. In addition, world light such as light from a ceiling lamp is incident on the grating 800 from the world side, which can cause the first-order transmitted beam (1T) to pass through the grating 800 toward the viewer's eyes, thereby causing a rainbow effect.

[0052] Compared with the two-stage grating, Figure 8 and Fig. 9 The three-level grating shown may have several advantages. Fig.10 The simulated diffraction efficiency curves of an exemplary three-level grating for p-polarized light (0 degree polarization) according to the incident angle θ in the range between -40 degrees and -60 degrees (the range typically used for image light) are shown. The three-level grating has the following grating parameters: h 0 =30nm, h 1 =54nm, w 1 =0.5D,h 2 =0.0875μm, w 2 =0.25D. As shown, here, for the entire range of incident angles shown, the first order reflection (1R) is significantly greater than the first order transmission (1T). Therefore, a larger portion of the image light can be diffracted toward the viewer rather than toward the world. The ratio of first order reflection (1R) to first order transmission (1T) can be as high as 2:1, and can approach 3:1 at some incident angles. In addition, Figure 6Compared to the two-stage grating shown, the secondary reflection (2R) has also been reduced. In some cases, the diffraction efficiency in the secondary reflection (2R) is reduced to well below 1%. In some cases, the diffraction efficiency of the secondary reflection (2R) is less than 0.5%. Therefore, according to some embodiments of the present invention, undesirable secondary light that can cause image glare in a direction orthogonal to the groove line can be reduced.

[0053] Fig.11A and Fig. 11B For s-polarized light (90 degrees polarization, Fig.11A ) and p-polarized light (0 degree polarization, Fig. 11B ), according to the grating depth (i.e., h 1 With h 2 The simulated diffraction efficiency curves of some exemplary three-level gratings (the sum of ) are shown in the figure. Figure 8 For the entire grating depth range shown, the first-order reflection (1R) is greater than the first-order transmission (1T). It should also be noted that the secondary reflection (2R) shows a clear polarization dependence. For example, the secondary reflection (2R) of p-polarized light is significantly lower than the secondary reflection (2R) of s-polarized light. Therefore, it is feasible to suppress the secondary reflection (2R) by using a polarizer.

[0054] Table 1 summarizes the simulated diffraction efficiency in secondary reflection (2R), first reflection (1R), zero-order reflection (OR), and first-order transmission (1T) of an exemplary two-stage grating at an incident angle (θ) of -50 to -30 degrees for both p-polarized light (0 degree polarization) and s-polarized light (90 degree polarization) for 520 nm wavelength light according to some embodiments. Table 2 summarizes the simulated diffraction efficiency in secondary reflection (2R), first reflection (1R), zero-order reflection (OR), and first-order transmission (1T) of an exemplary three-stage grating at an incident angle (θ) of -30 to -50 degrees for both p-polarized light (0 degree polarization) and s-polarized light (90 degree polarization) according to some embodiments. As shown in the figure, for p-polarized light, the first-order transmission (1T) of the three-stage grating at an incident angle of -30 is only 6.6%, compared to 11% for the first-order transmission (1T) of the two-stage grating at an incident angle of -30. Moreover, for s-polarized light, the first-order transmission (1T) of the three-level grating at an incident angle of -30 is only 0.3%, compared to 1.7% for the two-level grating at an incident angle of -30. Therefore, according to some embodiments, the three-level grating described herein can significantly reduce the undesirable rainbow effect.

[0055] Table 1

[0056] polarization 2R 1R 0R 1T θ 0.0000 0.0063315115 0.042606835 0.889826498 0.061251511 -50 90.000 0.012548442 0.024650098 0.931271532 0.031529927 -50 0.0000 0 0.050533856 0.004828623 0.109664217 -30 90.000 0 0.029522560 0.035912803 0.016903517 -30

[0057] Table 2

[0058] polarization 2R 1R 0R 1T θ 0.0000 0.000594872 0.050695651 0.928987394 0.019722082 -50 90.000 0.008069904 0.018196041 0.965302811 0.008431243 -50 0.0000 0.080741167 0.022736306 0.065726994 -30 90.000 0.042537267 0.020530137 0.002793524 -30

[0059] It has been demonstrated that gratings with more preferred properties, such as a higher ratio of first order reflection (1R) to first order transmission (1T) and lower second order reflection (2R), can follow certain parameter patterns. Fig. 9 Typically, the first width w of each first ridge 820 is 1 The second width w of each second ridge 830 may be advantageously selected to be approximately 0.5D±0.1D. 2 The first height h of each first ridge 820 may be advantageously selected to be less than or equal to about 0.25 D. 1 can be advantageously selected to be smaller than the second height h of each second ridge 830 2 In some embodiments, the second height h 2 With the first height h 1 The ratio of can be advantageously selected to be about 8:5. In some embodiments, the following grating parameters of the three-level grating can be advantageously selected: 0 =0.03μm, h 1 =0.054μm, w 1 =0.5D,h 2 = 0.0875 μm, and w 2 =0.2D.

[0060] Insofar as the tertiary cross-sectional shape can be regarded as approximately triangular sawtooth, Fig. 9 The three-level grating shown can be regarded as a blazed grating. For light incident at an angle close to normal to the blazed surface (e.g. Fig. 9 ), the grating may be referred to as "blazed". For incident light at an angle close to parallel to the blazed surface (i.e. Fig. 9 Table 3 compares the diffraction efficiencies of an exemplary two-level grating, an exemplary three-level blazed grating, and an exemplary three-level anti-blazed grating according to some embodiments of the present invention. As shown, the two-level grating has comparable diffraction efficiencies for the viewer (first-level reflection 1R) and the world (first-level transmission 1T). The three-level blazed grating may have a higher diffraction efficiency for the viewer than the diffraction efficiency for the world. On the other hand, the three-level anti-blazed grating may have a higher diffraction efficiency for the world than the diffraction efficiency for the viewer. Therefore, the three-level blazed grating may be superior to both the two-level grating (binary grating) and the three-level anti-blazed grating.

[0061] Table 3

[0062]

[0063] refer to Fig. 9 , the optimization algorithm may allow for the first height h of each first ridge 820 to be 1 and the first width w 1 , the second height h of each second ridge 830 2 and the second width w 2 The grating period D may be assumed to have a value of D=380 nm, and h may be assumed to have a value of 1R. 1 and h 2 With h 1 =50nm and h 1 =75nm, and assuming that w 1 and w 2 The nominal value is w 1 =210nm and w 2 = 170nm. Then w can be changed and optimized 1 and w 2 To obtain a higher first order reflection (1R).

[0064] In the exemplary optimization simulation, it is assumed that the incident angle is 50 degrees and the thickness of the base layer 810 is h 0 =20nm, and h 1 and h 2 With h 1 =50nm and h 1 =75nm. Assume further that the grating has n 1 =1.54, and waveguide 802 has a refractive index of n 2 =Refractive index of 1.8. 1 From 2m to Dm, where m is the minimum feature size and D is the grating period. In one embodiment, assume D = 380nm, m = 30nm (feature size of electron beam lithography). 2 From m to w1-m. In some cases, w 2 can be equal to w 1 , or w 2 can be equal to zero (which corresponds to a two-level grating without a second ridge).

[0065] FIG. 12A to FIG. 12F 1 shows a simulated intensity graph of the diffraction efficiency of each level of a three-level grating according to some embodiments. Specifically, Fig. 12A and Fig.12D For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) user-side diffraction efficiency (1R); Fig. 12B and Fig.12EFor s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 World-side diffraction efficiency (1T) (vertical axis); and Fig. 12C and Fig.12F For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) of the secondary reflection (2R). Fig. 12C and Fig.12F As shown, for w in the dotted ellipse area 1 and w 2 The parameter space of the secondary reflection (2R) can be relatively low. Fig. 12A and Fig.12D As shown, w in the dotted ellipse area 1 and w 2 In the same parameter space, the user-side diffraction efficiency (1R) is quite high.

[0066] FIG. 13A to FIG. 13F 1 shows a simulated intensity diagram of the diffraction efficiency of each level of a three-level grating according to some other embodiments. Assuming h 1 =60nm,h 2 =75nm, and h 0 =20nm. Specifically, Fig.13A and Fig.13D For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) user-side diffraction efficiency (1R); Fig. 13B and 13E For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) world-side diffraction efficiency (1T); Fig. 13C and Fig.13F For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) of the secondary reflection (2R).

[0067] FIG. 14A to FIG. 14F 1 shows a simulated intensity diagram of the diffraction efficiency of each level of a three-level grating according to some further embodiments. Assuming h 1 =60nm,h 2 =75nm, and h 0 =30nm. Specifically, Fig.14A and Fig.14D For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2(vertical axis) user-side diffraction efficiency (1R); Fig. 14B and 14E For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) world-side diffraction efficiency (1T); Fig. 14C and Fig.14F For s-polarization and p-polarization, the w 1 (horizontal axis) and w 2 (vertical axis) of the secondary reflection (2R).

[0068] In general, it can be observed that the diffraction efficiency of s-polarized light is higher than that of p-polarized light. Therefore, s-polarization leaks faster than p-polarization. Therefore, it can be assumed that the light propagating in the waveguide is mostly p-polarized.

[0069] It may be necessary to adjust the eyepiece (e.g. Figure 1 and Figure 2 The invention provides a method of having a uniform light output from the grating across the entire EPE portion of the eyepiece (shown in FIG. 1 ). As light propagates from top to bottom in the waveguide, more and more light is diffracted out of the waveguide by the grating. Thus, the diffraction efficiency of the grating can be advantageously increased with increasing distance from the top of the grating, so that as the amount of light remaining in the waveguide decreases, a greater and greater percentage of the light is coupled out, resulting in a relatively uniform light output across the entire EPE portion.

[0070] In some embodiments, a 100 nm linewidth grating near the top of the waveguide (i.e., w 1 =100nm, w 2 = 0) can conserve light within the waveguide by keeping the outcoupling efficiency low so that enough light remains in the waveguide to be emitted near the end of the EPE. The 260 / 150nm linewidth grating near the bottom of the waveguide (i.e., w 1 =260nm, w 2 =150nm) can couple most of the remaining light out of the waveguide.

[0071] Fig.15 The simulated diffraction efficiency for first-order reflection (1R), first-order transmission (1T), and second-order reflection (2R) as a function of the incident angle is shown. Assuming h 1 =50nm,h 2 =75nm, w 1 = 200nm, and w 2= 120 nm. As shown in the figure, for decreasing angle of incidence, both first-order reflection (1R) and first-order transmission (1T) increase. Therefore, first-order reflection (1R) has a larger value at lower angles of incidence (corresponding to the bottom of the field of view) than its value at higher angles of incidence (corresponding to the top of the field of view). Therefore, light at the bottom of the field of view (FOV) (with the shortest bounce interval) is coupled out fastest.

[0072] Anti-blaze gratings may be better for field uniformity. However, as described above, blazed gratings have better user-side efficiency. In some embodiments, a two-stage grating may achieve a better balance. In one embodiment, the two-stage grating may be configured so that its duty cycle (i.e., the ratio of characteristic width to period w / D) increases with increasing distance x from the top of the grating, so that the grating efficiency increases with increasing distance x.

[0073] In some embodiments, the optimization may be performed using a merit function as the optimization objective. Assume that the power diffracted toward the user is P user , the power diffracted toward the world is P world , the power of the second level is P 2 , and the power of the zeroth order is P 0 ,like Fig.16 In one embodiment, the merit function can be expressed as:

[0074] J = α(P 2 +P world )-P user ,

[0075] Among them, α is related to the term P user Compared with the given item (P 2 +P world ). In one embodiment, h is allowed to 1 、h 2 、w 1 and w 2 changes to minimize the merit function J. Therefore, the optimization goal can be to minimize P 2 and P world , and maximize P user The parameter α determines the relative weight given to the two objectives. Fig.17 The variable h is shown 1 、h 2 、w 1 and w 2 The correlation between each item in and the weight α. Fig.18 It shows that P user , P world and P 2 Correlation with weight α.

[0076] As described above, it may be advantageous to increase the diffraction efficiency of the grating with increasing distance from the top of the grating in order to achieve relatively uniform light output from the grating across the entire EPE portion of the eyepiece. Fig.19 A grating 1900 formed on a waveguide 1902 is schematically shown. Let x be the normalized distance from the top of the grating (i.e., at the top of the grating, x=0, at the bottom of the grating, x=1). Let f(x) be the normalized diffraction efficiency of the grating 1900 at position x. f(x) can be expressed as:

[0077] f(x)=u(x)+w(x),

[0078] Where u(x) and w(x) are the light emitted to the user (i.e., first order reflection 1R) and the light emitted to the world (i.e., first order transmission 1T), respectively. Note that f(x) represents the efficiency of the grating 1900 for coupling light out of the grating 1900. Since the light in the second order reflection (2R) remains in the waveguide 1902, the second order reflection (2R) is not included in f(x). In some embodiments, f(x) can be normalized to a predetermined constant.

[0079] Let y(x) be the normalized light intensity within waveguide 1902 at position x, and let y(0) = 1. The outcoupled power at position x (i.e., the dimensionless fraction of light coupled out of waveguide 1902) can be expressed as:

[0080] y'(x)=-f(x)y(x),

[0081] The solution to this differential equation can be expressed as:

[0082]

[0083] Using a simple linear model, we assume that the normalized diffraction efficiency f(x) can be expressed as:

[0084] f(x)=a+bx,

[0085] Where a and b are constants. The average outcoupling power through the grating 1900 can be expressed as:

[0086]

[0087] The root mean square (RMS) deviation from the average outcoupled power can be expressed as:

[0088]

[0089] The RMS deviation represents the average deviation from the average outcoupled power. Lower RMS deviation values ​​mean higher uniformity of the outcoupled power according to x.

[0090] Fig. 20A Simulated contour plots of the average outcoupled power according to a and b are shown. Fig. 20B The simulated contour plots of the RMS deviation from the average outcoupled power according to a and b are shown. Fig. 20B As shown, the area within the dashed ellipse can represent the parameter space of a and b, which forms a relatively uniform outcoupling power across the grating. In some embodiments, a can be advantageously selected in the range of about 0.5 to 0.7, and b can be advantageously selected in the range of about 1.0 to about 1.5.

[0091] As an example, assume that a=0.5 and b=1.0, so f(x)=0.5+x. Assume that light bounces N times from top to bottom in waveguide 1902. Assuming f(x) is normalized to 1 / N, the initial outcoupling rate of grating 1900 (i.e., at x=0) can be 0.5 / N. The final outcoupling rate of grating 1900 after N bounces (i.e., at x=1) can be 1.5 / N. As an example, assume that waveguide 1902 has a thickness of approximately 325 μm. For an incident angle of 50 degrees, the bounce interval can be approximately 0.77 mm. Assume that the total width of grating 1900 from top to bottom is L=21 mm. Therefore, light can bounce 27 times from the top of waveguide 1902 to the bottom of waveguide 1902. The initial outcoupling efficiency of the grating 1900 at the top of the grating (towards the user and the world) may be about 1.8%, and the final outcoupling efficiency of the grating 1900 at the bottom of the grating (towards the user and the world) may be about 5.4%.

[0092] Fig.21 A graph of normalized outcoupled power g(x)=f(x)y(x) (towards the user and the world) as a function of normalized distance x from the top of the grating 1900 is shown for a linear model with parameters a=0.5 and b=1 according to an embodiment of the present invention. As shown, the normalized outcoupled power is relatively uniform across the grating 1900.

[0093] Typically, in order to have a more uniform outcoupled power across the grating, the diffraction efficiency of the grating can be varied from top to bottom by a factor ranging from about 2 to about 3. Higher factors can result in more light output, but may end up with lower uniformity. The highest diffraction efficiency achievable at the bottom of the grating can determine the overall outcoupled efficiency. This is true for gratings where the user-side diffraction efficiency (i.e., 1R) and the world-side diffraction efficiency (i.e., 1T) are roughly proportional to each other. This may not be the case for deep gratings.

[0094] It should be understood that although a grating having a diffraction efficiency that varies linearly with position is discussed above, such variation is not required and other variation patterns are possible. According to some other embodiments, a grating may be designed to have a diffraction efficiency that varies with a quadratic function or other nonlinear function. In some other embodiments, a grating may be designed to have a diffraction efficiency that varies non-monotonically from one edge of the grating to the other edge. For example, for a grating having Figure 3 For an eyepiece with the bow-tie topology shown (in which light is injected into the waveguide at the middle portion of the waveguide), the grating can be designed so that the diffraction efficiency of the grating is low in the middle portion of the grating and high at the two edges of the grating on either side of the middle portion.

[0095] The optimization can be performed with a three-level grating where the diffraction efficiency increases with increasing distance from the top of the grating. Fig.22A and Fig. 22B The top of the grating ( Fig.22A ) and the bottom of the grating ( Fig. 22B ) is a schematic cross-sectional view of one period of a three-level grating. The first height h of each first ridge 1 and the second height h of each second ridge 2 Fixed at h 1 =50nm and h 2 =75nm. In some embodiments, w 1 and w 2 The value of each of increases with the distance from the top of the grating. For example, the first width w of the first ridge at the top of the grating 1 Can have w 1 =180nm, the first width w of the first ridge at the bottom of the grating 1 Can have w 1 = a value of 220 nm; the second width w of the second ridge at the top of the grating 2 Can have w 2 =60nm, the second width w of the second ridge at the bottom of the grating 2 Can have w 2 =180nm value, such as Fig.22A and 22B In some other embodiments, the ratio w of the first width to the second width 1 / w 2 As the distance from the top of the grating increases, the first width w 1 , the second width w 2 and / or ratio w 1 / w 2 It can be varied across the grating in other ways. For example, the ratio w 1 / w2 It may be lower in the middle portion of the grating and become higher towards the two edges of the grating.

[0096] It should also be understood that the examples and embodiments described herein are for illustrative purposes only and that those skilled in the art are advised to make slight modifications or changes to the present invention that are included within the spirit and scope of the present application and the scope of the appended claims.

Claims

1. An eyepiece for use in front of a viewer's eyes, the eyepiece comprising: a waveguide having a surface; as well as a diffractive optical element optically coupled to the waveguide, the diffractive optical element comprising: a plurality of first ridges protruding from the surface of the waveguide and arranged in a periodic array having a period, each respective first ridge of the plurality of first ridges having a first height in a direction perpendicular to the surface of the waveguide and a respective first width in the direction of the period; and a plurality of second ridges, each respective second ridge of the plurality of second ridges protruding from a respective first ridge and having a second height greater than the first height and a respective second width less than the respective first width; wherein the diffractive optical element is configured to diffract a first portion of the light beam propagating in the waveguide toward the eye as a first-order reflection, and to diffract a second portion of the light beam propagating in the waveguide away from the eye as a first-order transmission, and wherein the light beam propagating in the waveguide is incident on the diffractive optical element at an incident angle ranging from -40 degrees to -60 degrees.

2. The eyepiece according to claim 1, wherein: The diffractive optical element has a first-order reflection efficiency greater than a first-order transmission efficiency, and wherein the corresponding first width ranges from 0.4 times the period to 0.6 times the period.

3. The eyepiece according to claim 2, wherein: The corresponding second width is less than 0.25 times the period.

4. The eyepiece according to claim 1, wherein: The diffractive optical element has a first-order reflection efficiency greater than a first-order transmission efficiency, and wherein a ratio of the second height to the first height ranges from 8:7 to 8:

3.

5. The eyepiece according to claim 1, wherein: The diffractive optical element has a first-order reflection efficiency greater than a first-order transmission efficiency, and wherein the first height ranges from 45 nm to 65 nm, and the second height ranges from 70 nm to 80 nm.

6. The eyepiece according to claim 1, wherein: The diffractive optical element has a first-order reflection efficiency greater than a first-order transmission efficiency, and wherein a ratio of the first-order reflection efficiency to the first-order transmission efficiency is greater than 2.

7. The eyepiece according to claim 1, wherein: The diffractive optical element is configured to diffract a third portion of the light beam propagating in the waveguide in a direction substantially opposite to the incident direction as a secondary reflection, and the corresponding first width and the corresponding second width are selected so that the diffractive optical element has a secondary reflection efficiency of less than one percent.

8. The eyepiece of claim 1, wherein: the respective first width of each respective first ridge varies according to the position of the respective first ridge in the direction of the period; as well as The respective second width of each respective second ridge varies according to the position of the corresponding first ridge in the direction of the period.

9. The eyepiece according to claim 8, wherein: Each respective first width of the respective first ridges and each respective second width of the respective second ridges are changed so that the primary reflection efficiency of the diffractive optical element is changed according to the position of the surface of the waveguide in a direction across the period.

10. The eyepiece according to claim 9, wherein: The primary reflection efficiency of the diffractive optical element increases from a first edge of the diffractive optical element to a second edge of the diffractive optical element.

11. The eyepiece according to claim 10, wherein: The first-order reflection efficiency of the diffractive optical element increases substantially linearly from the first edge of the diffractive optical element to the second edge of the diffractive optical element.

12. The eyepiece of claim 9, wherein: The first-order reflection efficiency of the diffractive optical element increases from a central portion of the diffractive optical element toward edges of the diffractive optical element on either side of the central portion.

13. The eyepiece of claim 1, wherein: A ratio of the respective second width of the respective second ridge to the respective first width of the respective first ridge varies according to a position of the respective first ridge in the direction of the period.

14. The eyepiece according to claim 13, wherein: A ratio of the corresponding second width of the corresponding second ridge to the corresponding first width of the corresponding first ridge changes depending on the position of the corresponding first ridge in the direction of the period, so that the first-order reflection efficiency of the diffractive optical element changes depending on the position of the surface of the waveguide in the direction across the period.

15. The eyepiece of claim 14, wherein: The primary reflection efficiency of the diffractive optical element increases from a first edge of the diffractive optical element to a second edge of the diffractive optical element.

16. The eyepiece of claim 15, wherein: The first-order reflection efficiency of the diffractive optical element increases substantially linearly from the first edge of the diffractive optical element to the second edge of the diffractive optical element.

17. The eyepiece of claim 14, wherein: The first-order reflection efficiency of the diffractive optical element increases from a central portion of the diffractive optical element toward edges of the diffractive optical element on either side of the central portion.

18. The eyepiece of claim 1, wherein: The diffractive optical element is further configured to diffract a portion of the second light beam incident on the diffractive optical element towards the eye as a first order transmission.

19. The eyepiece of claim 18, wherein: The second light beam comprises natural light incident on the diffractive optical element in a direction from the world toward the eye.

20. An eyepiece for projecting an image into an eye of a viewer, the eyepiece comprising: a waveguide having a first surface; as well as an incoupling grating optically coupled to a first region of the waveguide, the incoupling grating being configured to diffract image light incident on the waveguide in a direction substantially perpendicular to the first surface into the waveguide to propagate therein in a first direction; a first diffractive optical element (DOE) optically coupled to a second region of the waveguide, the first DOE being configured to diffract the image light propagating in the waveguide toward a second direction different from the first direction; as well as a second DOE optically coupled to the second region of the waveguide, the second DOE comprising: a plurality of first ridges protruding from the first surface of the waveguide and arranged in a periodic array having a period, each of the plurality of first ridges having a first height in a direction perpendicular to the first surface of the waveguide and a first width in a direction of the period; and a plurality of second ridges, each of the plurality of second ridges protruding from a corresponding first ridge and having a second height greater than the first height and a second width less than the first width; Wherein, the second DOE is configured to diffract a first portion of the image light diffracted by the first DOE toward the eye as a first-order reflection, and to diffract a second portion of the image light diffracted by the first DOE away from the eye as a first-order transmission.

21. The eyepiece of claim 20, wherein: The first DOE is optically coupled to the first surface of the waveguide.

22. The eyepiece of claim 20, wherein: The waveguide has a second surface opposite the first surface, and the first DOE is optically coupled to the second surface of the waveguide.

23. The eyepiece of claim 20, wherein: A ratio of the second height to the first height ranges from 8:7 to 8:

3.

24. The eyepiece of claim 20, wherein: The first width and the second width are selected such that the second DOE has a first order reflection efficiency greater than a first order transmission efficiency.

25. The eyepiece of claim 24, wherein: A ratio of the primary reflection efficiency to the primary transmission efficiency is greater than 2.

26. The eyepiece of claim 20, wherein: The first width ranges from 0.4 times the period to 0.6 times the period, and the second width is less than 0.25 times the period.

27. An eyepiece for projecting an image into an eye of a viewer, the eyepiece comprising: a waveguide having a first surface; as well as an incoupling grating optically coupled to a first region of the waveguide, the incoupling grating being configured to diffract image light incident on the waveguide in a direction substantially perpendicular to the first surface into the waveguide to propagate therein in a first direction; a first diffractive optical element (DOE) optically coupled to a second region of the waveguide, the first DOE being configured to diffract the image light propagating in the waveguide toward a second direction different from the first direction; as well as a second DOE optically coupled to the second region of the waveguide, the second DOE comprising: a plurality of first ridges protruding from the first surface of the waveguide and arranged in a periodic array having a period, each respective first ridge having a respective first width in a direction of the period, the respective first width varying according to a position of the respective first ridge in the direction of the period; and a plurality of second ridges, each respective second ridge protruding from the respective first ridge and having a respective second width that is smaller than the respective first width of the respective first ridge, each respective second width varying according to a position of the respective first ridge in the direction of the period; Wherein, the second DOE is configured to diffract a first portion of the image light diffracted by the first DOE toward the eye as a first-order reflection, and to diffract a second portion of the image light diffracted by the first DOE away from the eye as a first-order transmission.

28. The eyepiece of claim 27, wherein: Each first ridge has a first height, and each second ridge has a second height greater than the first height.

29. The eyepiece of claim 28, wherein: The first height ranges from 45 nm to 65 nm, and the second height ranges from 70 nm to 80 nm.

30. The eyepiece of claim 27, wherein: Each respective first width of the respective first ridges and each respective second width of the respective second ridges are varied such that a primary reflection efficiency of the second DOE varies according to a position of the first surface of the waveguide in a direction across the period.

31. The eyepiece of claim 30, wherein: The primary reflection efficiency of the second DOE increases from a first edge of the second DOE to a second edge of the second DOE.

32. The eyepiece of claim 31, wherein: The first-order reflection efficiency of the second DOE increases substantially linearly from the first edge of the second DOE to the second edge of the second DOE.

33. The eyepiece of claim 30, wherein: The waveguide has a second surface opposite to the first surface, and the first DOE is optically coupled to the first surface or the second surface of the waveguide.

34. An eyepiece for projecting an image into an eye of a viewer, the eyepiece comprising: a waveguide having a first surface; as well as an incoupling grating optically coupled to a first region of the waveguide, the incoupling grating being configured to diffract image light incident on the waveguide in a direction substantially perpendicular to the first surface into the waveguide to propagate therein in a first direction; a first diffractive optical element (DOE) optically coupled to a second region of the waveguide, the first DOE being configured to diffract the image light propagating in the waveguide toward a second direction different from the first direction; as well as a second DOE optically coupled to the second region of the waveguide, the second DOE comprising: a plurality of first ridges protruding from the first surface of the waveguide and arranged in a periodic array having a period, each respective first ridge having a respective first width in a direction of the period; and a plurality of second ridges, each respective second ridge protruding from a respective first ridge and having a respective second width that is less than a respective first width of the respective first ridge; wherein a ratio of the corresponding second width of the corresponding second ridge to the corresponding first width of the corresponding first ridge varies depending on the position of the corresponding first ridge in the direction of the period, and wherein the second DOE is configured to diffract a first portion of the image light diffracted by the first DOE toward the eye as a first-order reflection, and to diffract a second portion of the image light diffracted by the first DOE away from the eye as a first-order transmission.

35. The eyepiece of claim 34, wherein: A ratio of the corresponding second width of the corresponding second ridge to the corresponding first width of the corresponding first ridge changes according to the position of the corresponding first ridge in the direction of the period, so that the first-order reflection efficiency of the second DOE changes according to the position of the first surface of the waveguide in the direction across the period.

36. The eyepiece of claim 35, wherein: The primary reflection efficiency of the second DOE increases from a first edge of the second DOE to a second edge of the second DOE.

37. The eyepiece of claim 36, wherein: The first-order reflection efficiency of the second DOE increases substantially linearly from the first edge of the second DOE to the second edge of the second DOE.

38. The eyepiece of claim 35, wherein: The waveguide has a second surface opposite to the first surface, and the first DOE is optically coupled to the first surface or the second surface of the waveguide.

39. The eyepiece of claim 34, wherein: Each first ridge has a first height, and each second ridge has a second height greater than the first height.

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