WO2024079470A2

WO2024079470A2 - Image replicating waveguide

Info

Publication number: WO2024079470A2
Application number: PCT/GB2023/052651
Authority: WO
Inventors: Alfred James NEWMAN; Darius Martin Sullivan
Original assignee: Vividq Limited
Priority date: 2022-10-12
Filing date: 2023-10-12
Publication date: 2024-04-18
Also published as: WO2024079470A3; GB202215039D0

Abstract

An image replicating waveguides are described having an In-Coupling, IC, grating having a first k-vector; an Exit Pupil Expanding, EPE, grating having a second k-vector; and an Out- Coupling, OC, grating having a third k-vector. A magnitude of the first k-vector is approximately equal to a magnitude of the third k-vector, and a direction of the second k- vector is approximately horizontal or approximately vertical. Image replicating waveguide systems and display systems comprising one or more such image replicating waveguides are also described.

Description

IMAGE REPLICATING WAVEGUIDE

Technical Field

The present invention relates to image replicating waveguides for use in display systems. In particular, the present invention relates to an image replicating waveguide that generates replications on a rhombic grid.

Background

Image replicating waveguides are optical components used to expand an “eyebox” provided by an image source by generating multiple spatially-separated replications of the images. As used herein, an “eyebox” defines pupil positions in which an image can be viewed; the volume in which a viewer’s pupil can be positioned to view an image from an image source.

A replication may be defined as a real or virtual image of the image-source exit pupil with a given position, orientation and magnification as seen by the viewer’s pupil. In the case of planar image replicating waveguides, the magnification is always magnitude one.

An image replicating waveguide comprises an input surface to receive an input image and an output surface where the multiple replications are extracted. When light rays corresponding to the input image are coincident on the output surface, a portion of the light is refracted through, and extracted from the image replicating waveguide. The portion of light not extracted out undergoes an internal reflection and remains in the image replicating waveguide. This process of partial refraction and partial internal reflection is used to generate multiple replications as viewed through the output surface.

The input surface comprises an Input Coupling (IC) grating that couples incoming light to the waveguide, and the output surface comprises an Out-Coupling (OC) grating that decouples the light from the waveguide. Some image replicating waveguides also comprise an Exit Pupil Expanding (EPE) grating that redirects and expands a volume of the light traversing the waveguide. For example, an image replicating waveguide may have IC, EPE and OC grating arranged such that replications are generated that tile on a rectilinear grid. This configuration minimises the areas of the IC and EPE grating required for a given EPE area and so finds use in such applications as head-mounted displays (HMDs), where reduction in size of the optical components is useful.

However, rectilinear grids also have disadvantages, for example they might not provide efficient tiling for some replication fields and may be more likely to lead to overlapping replication, reducing image quality. It would therefore be desirable to provide an image replicating waveguide that generates replications on a non-rectilinear grid.

Summary

According to a first aspect of the present invention, there is provided an image replicating waveguide comprising: an In-Coupling (IC) grating having a first k-vector; an Exit Pupil Expanding (EPE) grating having a second k-vector; and an Out-Coupling (OC) grating having a third k-vector. A magnitude of the first k-vector is approximately equal to a magnitude of the third k-vector, and a direction of the second k-vector is approximately horizontal or approximately vertical with respect to an outcoupled image axis. The k-vectors express a direction and spacing of grating planes and therefore how the gratings affect the wave vector of light when it interacts with the grating. Horizontal and vertical directions refer to the orientation defined by the output image. That is, the horizontal and vertical directions are understood with respect to the orientation in which an image is intended to be viewed by a user of the image replicating waveguide. This may also be referred to as the outcoupled image axis. For example, the orientation of the image defines an x-y axis by which relative directions can be understood, such as the x-axis corresponding to a horizontal direction and the y axis corresponding to the vertical direction. Put another way, consider the image replicating waveguide in use. For example, for a viewer looking through a headset comprising the image replicating waveguide, an outcoupled image naturally defines vertical (e.g. up and down) and horizontal (e.g. side to side) directions.

These arrangements of k-vectors result in replications that are generated on a rhombic grid and define arrangements that support a given size of rectangular OC grating in combination with reduced vertical extent of the image replicating waveguide. This allows the vertical size of the waveguide to be smaller. This may be beneficial where there are size constraints on a display system comprising the waveguide. Further, the arrangements of k- vectors are appropriate for either the waveguide having the in-coupling grating positioned in use approximately to the side of the eyebox, or above or below the eyebox making it well suited to head-mounted displays. These arrangements are also useful for field of views (FoVs) and eyeboxes that are rectangular and in landscape orientation with respect to a viewer’s eyes (or outcoupled image axis). These properties mean that the image replicating waveguide is particularly beneficial in many holographic displays, such as head-mounted displays (HMDs). In addition, the first and third k-vectors having approximately the same magnitude reduces the range of angles available for light inside the waveguide, reducing the effects of angular spread and so improving image quality.

Image replicating waveguides that replicate on a rhombic grid have been proposed, for example as described in WO2018/178626. However, the architecture of the waveguide described in WO2018/178626 uses a different format in which the function of the EPE and OC grating are combined, there is not a EPE grating or an OC grating with k-vectors as described herein. The architecture of WO2018/178626 uses a cascade approach so that there are multiple paths through the waveguide for each replication. In contrast the waveguides described herein have a 1 : 1 relation for replications, there is only a single path through the waveguide for each replication which can be useful for processing algorithms that consider the path through the waveguide. In addition, the use of IC, EPE, and OC grating as discussed herein may result in a more compact form factor with increased design flexibility for the location of the IC grating relative to the OC grating.

At least one of the IC, EPE and OC grating may be transmissive and / or reflective. In an example, the IC, EPE and OC gratings comprise respective surface relief gratings.

In some examples, the angle between the first and third k-vectors is greater than 90 degrees. This is because the input to the IC grating may be a shape that tessellates on a rhombic grid. Pairing an image replicating waveguide having these first and third k-vectors with an input to the IC grating with such a shape may be used to increase the coverage of the eyebox. Such first and third k-vectors may be beneficial when the image generating unit is mounted to the side of the eyebox. The angle between the first and third k-vectors may be between about 100 and 120 degrees. In some examples, this angle is approximately 112.6 degrees.

In some other examples, the angle between the first and third k-vectors is less than 90 degrees. This may be useful when the image generating unit is positioned above or below the eyebox because in at least one arrangement the IC grating can be vertically displaced from the OC grating.

The image replicating waveguide may have a replication pitch variation of less than 3mm. The replication pitch variation refers to the maximum variation in spacing between nearest neighbouring input-pupil replications across different parts of a field of view. A replication pitch variation of less than 3mm reduces gaps and / or overlaps between replications improving the uniformity of an image as viewed by a viewer. The first k-vector may have a magnitude and orientation such that an angle subtended between a ray of light reflected within the image replicating waveguide and a normal to the image replicating waveguide at the reflection is between a total internal reflection angle of the image replicating waveguide and 60 degrees.

There may be a single (i.e. only one) path for a ray to traverse from an input of the waveguide to each output of the waveguide.

The image replicating waveguide may have a thickness greater than 2mm. A higher thickness can allow for a smaller variation in the replication pitch. In further examples, the thickness of the image replicating waveguide may be greater than 2.5mm, greater than 3mm and about 3.5 mm.

According to a second aspect of the present invention, there is provided an image replicating waveguide system comprising a first image replicating waveguide according to the first aspect and arranged to generate replications at a first replication pitch for light having a first wavelength. The waveguide system also comprises a second image replicating waveguide according to the first aspect and arranged to generate replications at the first replication pitch for light having a second wavelength, different from the first wavelength. The waveguide system therefore has at least two waveguides that are configured to generate replications at a fixed replication pitch for different respective wavelengths of incident light.

The first image replicating waveguide may be further arranged to receive light having a third wavelength, different from the first and second wavelengths, such that light having the first and third wavelengths is transmitted through the first image replicating waveguide above the total internal reflection angle. The first waveguide can be optimised for light of one colour and can receive light of another colour but only be approximately optimised for that colour. The image replicating waveguide system may comprise means to prevent light having the third (and first) wavelength from coupling to the second image replicating waveguide. This allows for the at least two waveguides to handle incident light composed of three different wavelengths. The first wavelength may correspond to green light, the second wavelength may correspond to red light, and the third wavelength may correspond to blue light. Red may have a wavelength between 620nm-750nm such as 635nm. Blue light may have a wavelength around 450nm-495nm, for example, 450nm. Green light may have a wavelength in the range of 495- 570 nm or in the range of 520-560 nm, such as around 520 nm. In this example, two or more colours may be allowed to share a waveguide, with the more visually important colour (green) being replicated at the correct pitch. This can reduce the complexity of the image waveguide system with a reduced impact on image quality.

According to a third aspect of the present invention, there is provided a display system comprising an image generating unit arranged to generate a light field and an image replicating waveguide according to the first aspect or an image replicating waveguide system according to the second aspect. The image generating unit may comprise a light source which is configured to generate at least partially coherent light. The image generating unit may also comprise a display device, such as a spatial light modulator (SLM), arranged to be illuminated by the at least partially coherent light to generate a quantised representation of a target light field. In some examples, the image generating unit further comprises a spatial filter arranged to filter out, or remove, some noise from the quantised representation of the target light field. The image generating unit may be configured to generate a light field comprised of approximately a single wavelength, or it may be configured to generate the light field having more than one wavelength, for example red, blue and green.

An exit pupil of the image generating unit may be arranged to be aligned with the IC grating of the image replicating waveguide. The respective magnitudes and orientations of the first, second and third k-vectors may match a geometry of the exit pupil of the image generating unit. In an example, the exit pupil of the image generating unit has a shape that tiles on a rhombic grid. The rhombic grid may be defined by first and second lattice vectors, and the magnitudes and orientations of the first and third k-vectors may be chosen to match the lattice geometry defined by the first and second lattice vectors.

The IC grating may be arranged to receive light from an area smaller than the area of the exit pupil of the image generating unit. Receiving only a fraction of the total light at the IC grating may reduce the effect of secondary interactions between light that has already been incoupled to the waveguide and the IC grating. This may be achieved by physically changing the area of the IC grating so that it receives less than the total amount of light from the exit pupil of the image generating unit, or there may be a spatial filter in an optical path between the image generating unit and the IC grating to set the area. For example, an initial IC grating arranged, or designed, to receive all light from the exit pupil of the image generating unit. An optimisation process may be performed that is adapted to minimise light loss considering both: light not coupling to the IC grating at all, and second interactions with the IC grating. The result of the optimisation process may be an optimal shape that maximises the amount of light that is transmitted by the waveguide. The shape may be realised by modifying the shape of the initial IC grating, for example by cutting one or more portions off the IC grating. The shape may also be realised by providing a further spatial filter having the optimal shape or modifying the spatial filter of the image generating unit to have the optimal shape.

In some examples, the image generating unit comprises a spatial filter comprising one or more apertures. The aperture or union of the apertures may form the exit pupil of the image generating unit. The shape of the aperture or union of the apertures may be a shape that tessellates, for example on a rhombic grid. The shape may substantially have the form of an “I” or “ H”. The “I” or “H” shape might be dodecagonal, such as corresponding to an “I” in a serif font and an “H” in a sans serif font. As discussed above, a display system comprising an image generating unit exit pupil having a shape that tessellates on a rhombic grid as well as an image replicating waveguide configured to generate replications on a rhombic grid is able to increase the available eyebox coverage of the system. More generally, the shape may have a two-fold symmetry, such as a two-fold rotational symmetry or a two-fold axis of symmetry. Further details of such spatial filters, including those in the form of an “I” or “H”, is given in UK patent application no. 2211261.9, filed on 2 August 2022, which is hereby incorporated by reference for all purposes.

Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, which is made with reference to the accompanying drawings.

Brief Description of the Drawings

Figure 1 shows an image replicating waveguide according to an example;

Figure 2A shows a first example configuration of the IC, EPE and OC gratings;

Figure 2B shows a second example configuration of the IC, EPE and OC gratings;

Figure 3A shows a landscape eyebox overlaid onto the first example configuration of the IC, EPE and OC gratings;

Figure 3B shows a landscape eyebox overlaid onto the second example configuration of the IC, EPE and OC gratings;

Figure 4 illustrates non-optimal examples of IC, EPE and OC grating configurations;

Figure 5A illustrates a landscape eyebox overlaid onto a first non-optimal example configuration of the IC, EPE and OC gratings;

Figure 5B illustrates a landscape eyebox overlaid onto a second non-optimal example configuration of the IC, EPE and OC gratings;

Figure 6A shows a replication pitch variation in a thick image replicating waveguide; Figure 6B shows a replication pitch variation in a thin image replicating waveguide; Figure 7A shows a k-vector diagram for a thick image replicating waveguide;

Figure 7B shows a k-vector diagram for a thin image replicating waveguide;

Figure 8 shows a k-vector diagram for an image replicating waveguide supporting three different wavelengths of light; Figure 9 shows an image replicating waveguide system comprising different waveguides for different wavelengths of light;

Figure 10A shows a k-vector diagram for blue and green light;

Figure 10B shows a k-vector diagram for red light;

Figure 11 shows an example display system; and

Figure 12 shows a modified IC grating configured to reduce the effect of secondary coupling.

Detailed Description

Image replicating waveguides expand the size of the viewable area of an image for a viewer. Image replicating waveguides according to examples described herein comprise an Input Coupling (IC) grating, also known as an in-coupler or entrance pupil, to receive light rays corresponding to an input image and couple the light rays to the waveguide. The notion of an entrance pupil corresponds to the limiting aperture in an input of the image replicating waveguide. The IC grating is a coupling feature of the image replicating waveguide that couples light waves propagating externally from the waveguide to the inside of the waveguide. The coupling feature may be, for example, a transmissive or reflective grating such as a diffraction grating, or a hologram. Further possible coupling features include micro-prisms, a surface relief slanted grating, a surface relief blazed grating, a surface relief binary grating, a multilevel surface relief grating, a thin volume hologram, a thin photopolymer hologram, a Holographic Polymer Dispersed Liquid Crystal (H-PDLC) volume holographic coupler, a thick photopolymer hologram, a resonant waveguide grating, a metasurface coupler and embedded half-tone mirrors.

Example image replicating waveguides described herein further comprise an Exit Pupil Expanding (EPE) grating which allows for two-di ensional eyebox expansion and may or may not use the same technology as the IC grating. The example image replicating waveguides further comprise an Output Coupling (OC) grating, also called an out-coupler, to output light corresponding to the input image. The OC grating is a further coupling feature of the image replicating waveguide, which may or may not use the same technology as the IC grating. The IC, EPE and OC gratings have, or are described or characterised by, respective k-vectors. The IC, EPE and OC grating, or grating, k-vectors express a direction and spacing of grating planes and therefore how the gratings affect the wave vector of light when it interacts with the grating. Image replicating waveguides may be manufactured from materials with high- refractive indices that support total internal reflection over a wide range of internal incidence angles. Lanthanum dense flint glass, for example N-LASF46 manufactured by Schott™, has a critical angle of ()_c = 31° at wavelength A = 530nm. An image replicating waveguide will propagate waves by total internal reflection at all incident angles above the critical angle.

In an example, an image replicating waveguide takes the form of a substantially planar sheet. The planar sheet may be constructed from a transparent material, such as glass. Furthermore, an image replicating waveguide may take the form of a non-planar sheet. For example, curved waveguides may find use in such applications as spectacles.

The IC grating may be positioned on a surface on which the light is incident and / or may be positioned on the surface adjacent to the surface on which light is incident. The OC grating may be positioned on the same surface as the IC grating (e.g. on the same surface as the IC grating) or may be positioned on a different surface from the IC grating. The particular arrangement of IC and OC gratings may be selected based on a function of the image replicating waveguide.

Replication Geometry

Image replicating waveguides usually generate replications on a rectilinear grid, such as a square grid. This is useful in certain applications because it minimises the areas of the IC and EPE gratings required for a given EPE grating area. Generating replications on a square grid can be achieved by having the k-vectors of the IC and OC gratings at approximately 90 degrees to one another, approximately aligned to the horizontal and vertical directions of a display, and with the EPE vector at approximately 45 degrees to the display.

It is desirable in some applications to have an image replicating waveguide that replicates on a non-rectilinear grid, such as a rhombic grid. For example, a circular exit pupil benefits from replications tiled on a rhombic grid rather than a rectilinear grid because more replications on a rhombic grid can be covered by the circular exit pupil. Replications generated on a rhombic grid would also be desirable to enlarge the coverage of an eyebox where the exit pupil of an image generating unit used to drive the waveguide has a geometry that also tiles on a rhombic grid.

An image replicating waveguide according to examples described herein is configured to generate replications on a rhombic grid by modifying the lattice vectors that characterize the IC, EPE and OC gratings of the waveguide. That is, varying the relative angles and magnitudes of the IC, EPE and OC k-vectors can result in replications being generated on a rhombic grid. Most combinations of IC, EPE and OC k-vectors result in unacceptable image quality or undesirable form factors, and the inventors have found that determining an optimal set of k- vectors is a non-trivial exercise. Some examples of IC, EPE and IC gratings resulting in less than optimal image quality or form factor will be discussed further with regards to Figures 4, 5 A and 5B. However, the present disclosure relates to a subset of all the possible IC, EPE and OC geometries that result in replications that tile on a rhombic grid which result in improved image quality and waveguide design.

Figure 1 shows a diagrammatic representation of an image replicating waveguide 100 that generates replications on a rhombic grid according to an example. The image replicating waveguide 100 has an IC grating 102, an EPE grating 104, and an OC grating 106. The IC grating 102 is described by a first k-vector 108, the EPE grating 104 is described by a second k-vector 110, and the OC grating 106 is described by a third k-vector 112. The magnitude of the first k-vector 108 is approximately equal to the magnitude of the third k-vector 112 and in this example, the direction of the second k-vector 110 is approximately vertical. In other examples, the direction of the second k-vector 110 may be approximately horizontal as shown in Fig. 2B, for example. In Figure 1, vertical and horizontal directions are defined by the orientation of the image replicating waveguide 100, which determines the orientation of an out- coupled image and hence an out-coupled image axis.

The result of the image replicating waveguide 100 having the first, second and third k- vectors 108, 110, 112 with these properties is that replications are generated on a rhombic grid. These arrangements of k-vectors define optimal arrangements that support a given size of rectangular OC grating with reduced vertical extent of the image replicating waveguide 100. Further, these are appropriate for either an image generating unit being positioned approximately to the side of the eyebox, or an image generating unit mounted above or below the eyebox. These arrangements are also useful for field of views (FoVs) and eyeboxes that are rectangular and in landscape orientation with respect to a viewer’s eyes (or outcoupled image axis). Examples of IC, EPE and OC gratings with these k-vectors will now be discussed with reference to Figures 2 A and 2B.

Figure 2A is an example of a grating configuration 200 according to the example discussed above with regards to Figure 1. The grating configuration 200 comprises an IC grating (e.g. grating) 202 having an IC grating k-vector shown by line 208. The grating configuration 200 further comprises an EPE grating 204 and an OC grating having an OC grating k-vector shown by line 210. The magnitudes of the IC and OC grating k-vectors 208, 210 are approximately equal and the direction of the EPE grating k-vector is vertical. The direction and relative spacing of the gratings are shown by the direction and spacing of hatching in the three gratings 202, 204, 206. Also shown in Figure 2 A is the effect of the grating configuration 200 on a circular beam of light. An incoming light beam couples into a waveguide via the IC grating 202 and is directed towards the EPE grating 204. By partial internal reflection of part of the light field traversing the waveguide, three copies of the input field are shown in the EPE grating 204. The EPE grating 204 is such that light from these gratings is directed downward towards the OC grating 206 where two further total internal reflections are shown for each of the three copies. The result is that the nine (shown) replications extracted at the OC grating 206 are approximately positioned on a rhombic grid. This can be understood by joining the centres of neighbouring replications with lines and inspecting the resulting lattice.

This grating configuration 200 works well when an image generating unit is mounted to the side of the eyebox as can be seen by the relative positioning of the IC grating 202 with respect to the OC grating 206. As can be seen from the grating configuration 200, the IC grating k-vector 208 is approximately equal in magnitude to the OC grating k-vector 210. In addition, the angle between the IC and OC grating k-vectors is greater than 90 degrees. The EPE grating k-vector can be determined using the k-vector closure relation and can therefore be understood to be directed vertically with respect to the Figure (i.e. perpendicular in the plane of the Figure to the grating directions). In the example grating configuration 200 shown in Figure 2A, the angle between IC and OC grating k-vectors 208, 210 is approximately 112.6 degrees. Certain image generating unit are configured to have an exit pupil with a shape that tessellates on a rhombic grid, wherein the angle between lines joining the centres of neighbouring contiguous shapes is 112.6 degrees. Using the grating configuration 200 with such an image generating unit in a display system can therefore increase an addressable eyebox coverage of the system.

Figure 2B is an example grating configuration 250 according to a further example. The grating configuration 250 comprises an IC grating 252 having a further IC grating k-vector shown by line 258. The grating configuration 250 further comprises an EPE grating 254 and an OC grating 256 having a further OC grating k-vector shown by line 260. The magnitudes of the IC and OC grating k-vectors 258, 260 are approximately equal and the direction of the EPE grating k-vector is horizontal. Again, the relative direction and spacing of the gratings are indicated by the direction and spacing of the hatching in each of the IC, EPE and OC gratings 252, 254, 256. Light traverses the grating configuration 250 in a similar way to how it traverses the grating configuration 200. A light field is coupled into the waveguide via the IC grating 252 and is directed towards the EPE grating 254. The light field undergoes a series of partial internal reflections at the EPE grating 254 whereby copies of the light field are directed towards the OC grating 256. At the OC grating 256, light not partially internally reflected is extracted from the waveguide forming a series of replications as shown in the Figure. Again, the replications approximately have the geometry of a rhombic grid.

This grating configuration 250 works well when an image generating unit is mounted above the eyebox as can be seen by the relative positioning of the IC grating 252 with respect to the OC grating 256. In this grating configuration 250, the IC grating k-vector 258 is approximately equal in magnitude to the OC grating k-vector 260. In addition, the angle between the IC and OC grating k-vectors is less than 90 degrees. The EPE grating k-vector can again be determined using the k-vector closure relation and can be readily determined to be directed horizontally with respect to the Figure (i.e. perpendicular in the plane of the Figure to the grating directions).

An image replicating waveguide having grating configurations 200, 250 has the property that there is a single path for a ray to traverse from an input of the image replicating waveguide to each output of the image replicating waveguide.

Figures 3 A and 3B show landscape eyeboxes 300, 310 overlaid onto the grating configurations 200, 250 shown in Figures 2A and 2B having IC gratings 202, 252, EPE gratings 204, 254 and OC gratings 206, 256 respectively. Increasing eyebox coverage is a goal of image replicating waveguides. The size of the eyebox is set by the exit pupil of the display system and may be arranged so that it covers a sufficiently large area to cover all possible pupil positions for the display. As can be seen from Figures 3A and 3B, almost five circular replications can be fitted within the eyebox 300, 310 while keeping the grating configurations 250, 254 in a landscape orientation. This is important when the display system in which the image replicating waveguide is used extends substantially in a horizontal direction (e.g. the frames of a pair of spectacles or a head-mounted display) to minimise the vertical extent of the system’s components.

The grating configurations 200, 250 provide improved image quality for rhombic grid replication compared to other IC, EPE and OC grating k-vector configurations. Figure 4 shows a plurality of examples of grating configurations 400-414 that generate replications on a rhombic grid, but which have one or more disadvantages compared to the grating configurations 200, 250 illustrated in Figures 2A and 2B respectively. For example, the grating configurations 200, 250 both support a given size of rectangular OC grating with reduced vertical extent of the waveguide as compared to grating configurations 400, 406, 408, 414 Further, the magnitude of the k-vectors for the IC and OC gratings of grating configurations 402, 404, 410, 412 are greatly different, meaning that the range of angles inside the waveguide is very large, which causes issues in terms of angular spread within the waveguide. Effects of angular spread lead to distortion and stretching in the replicated images, and will be discussed further in the following section.

Figures 5 A and 5B show landscape eyeboxes 500, 510 overlaid onto the grating configurations 400, 414 shown in Figure 4. The grating configurations 400, 414 are capable of a similar replication density to the grating configurations 200, 250 but they extend substantially in a vertical direction causing an image replicating waveguide having these configurations to extend unsatisfactorily in the vertical direction. This may be a problem where a horizontal arrangement of system components is desired.

Waveguide Internal Angles

It is desirable to reduce excessive gaps and / or overlaps between replications of an image replicating waveguide. This is controlled by the replication pitch of the waveguide, which refers to the spacing between nearest neighbouring input-pupil replications. The replication pitch is equal to 2t tanfOmtemai), where t is the thickness of the waveguide and (Eternal is the internal angle of a ray traversing the waveguide and is a function of the incident angle on the waveguide and the IC grating k-vector according to equation 1.

Equation 1

wherein k_x internal k_x incident kx IC? ky internal ky incident ky IC \kinternal\ 2jt/( /?), 3U(1 wherein: k_x incident and k_y incident 3 6 the x and y components of the wavevector of incident light, kxic and k_yic are the x and y components of the IC grating k-vector, z is the wavelength of light and n is the refractive index of the waveguide. This functional relationship means that the replication pitch varies very rapidly with internal angle (Ointemai) as it approaches 7t/2. To minimise the variation in replication pitch, it is useful to keep Otntemai small (i.e. significantly lower than 7t/2) whilst still meeting the conditions for total internal reflection (TIR) within the waveguide. This can be achieved in several ways. One such method is to increase the thickness of the waveguide. In general, there is a trade-off between this reduction in replication pitch variation and having a waveguide in the display system that is too thick, which may be a problem for HUDs, HMDs etc. Typically, thinner waveguides are preferred but having a balance between thickness and replication pitch reduction can have a positive effect on image quality while not having a substantial effect on the size and / or weight of the display system comprising the waveguide. An optimisation scheme may be performed to optimise the image quality in terms of replication pitch against the size and / or weight of the waveguide.

For a given replication pitch, the IC grating k-vector needs to be adjusted based on the thickness of the waveguide. Thicker waveguides need a smaller k-vector to achieve a given pitch replication than thinner waveguides. This results in thinner waveguides having a larger spread in variation pitch for incident rays having a fixed incident angle. This is illustrated in Figures 6A and 6B.

Figure 6A shows an example waveguide 600 having a thickness ti indicated by the length 604, and an IC grating 606 having a first k-vector. The distance 608 illustrates the distance between the point of incidence of a perpendicular incident ray at the IC grating 606 and a point at which the ray is incident on the same surface as the IC grating 606 after having undergone one total internal reflection. This defines the replication pitch for incident rays arriving at the waveguide 600 normal to the IC grating 606. Due to the angular dependence on replication pitch, one can see that a ray incident at an incident angle 602 has a different replication pitch from the perpendicular ray. The result is a variation in the replication pitch, illustrated by the distance 610.

Figure 6B shows a further example waveguide 650 having a thickness C that is smaller than the thickness ti of the waveguide 600, and illustrated by the length 654. The waveguide 650 has an IC grating 656 having a second k-vector arranged to result in the same replication pitch 658 for perpendicular incident rays as the waveguide 600. Due to the thinner design of the waveguide 650, a ray incident on the waveguide 650 at the incident angle 652 (the same as the incident angle 602) has a larger replication pitch than the equivalent ray incident on the waveguide 600. The resulting replication pitch variation 660 is therefore larger than the replication pitch variation 610.

Thicknesses of greater than, for example, 2mm may be used to reduce the replication pitch variation. In further examples, the thickness may be greater than 2.5mm, greater than 3mm and greater than 3.5 mm. In any case, it may be useful to keep the internal angle between the TIR angle and around 50-70 degrees (for example, around 60 degrees). This can be used to cause the variation in replication pitch to be less than 8mm, less than 6mm, less than 4mm, less than 2mm or even less than 1mm. While thicker waveguides allow for reductions in replication pitch variation, design constraints may put an upper limit on what is acceptable in terms of waveguide thickness. For example, a thicker waveguide is larger and heavier than a thinner waveguide made of the same material and may be harder to include in a display system, especially for head mounted displays where size and weight are important. Some examples may have an upper limit on the thickness, so that it is less than 10mm, less than 7.5mm, less than 5mm or less than 4mm thick. The range 2.5mm to 5mm may provide a good balance between reducing replication pitch variation and size/weight.

Figure 7A shows a k-vector diagram 700 for a waveguide having a refractive index of 2.04 for green light (around 520 nm) and a thickness of 3.75mm. The diagram 700 illustrates the allowable x and y wave vector components of light within the waveguide. No light having a wave vector inside the inside edge is coupled into the waveguide due to it not satisfying the TIR condition, which is a function of the refractive indices of the waveguide and the medium in which the waveguide is located. The outside edge represents the waveguide cut-off corresponding to a reflection angle of 7t/2. Only light having wave vectors (k-vectors), or equivalently angles, that fall within these limits can be transmitted by the waveguide.

The range of wave vectors for light being coupled in via the IC grating forms a subset of the total possible allowable wave vectors due to the geometry of the IC grating and the thickness of the waveguide, essentially because light can only enter the waveguide at a range of angles. A box 702 illustrates the variation in the wave vector of light coupled into a waveguide via the IC grating for the waveguide having a thickness of 3.75mm, for a particular field of view, in this case 18 x 11 degrees. As can be seen from the Figure, the box 702 is near the inside edge of the annulus representing the allowable angles supported by the waveguide, which is possible because of the thickness of the waveguide. The dotted lines in Figure 7A represent contours at 1mm increments of replication pitch. The box 702 therefore cuts a relatively low number of replication pitch increments, meaning that replication pitch variation is relatively low for this waveguide with green light.

In contrast to this, Figure 7B shows a k-vector diagram 750 for a waveguide having a refractive index of 2.04 for green light and a thickness of 1.5mm, and configured to have the same replication pitch for light of a given wavelength as the waveguide discussed with regards to Figure 7A. A box 752 illustrating the variation in the wave vector of light coupled into a waveguide via the IC grating is relatively far from the inside edge of the annulus. This can be understood from Figure 6B showing how a thinner waveguide 650 admits rays reflected from the IC grating 656 at a shallower reflection angle compared to a thicker waveguide. The box 752 cuts a relatively high number of replication pitch increments indicating that the replication pitch variation of this waveguide is high.

The variation in replication pitch of the waveguide used in Figure 7B is 7mm, meaning that the sum of the maximum gaps between replications and the maximum overlap of replications over the entire eyebox will be 7mm. For example, setting the gap to zero at the minimum replication pitch means that there will be a 7mm gap at the maximum replication pitch, or vice versa. Similarly, zero overlap at the maximum replication pitch will result in 7mm of overlap at the minimum replication pitch. Typically, this variation would be shared equally between gap and overlap, for example to have 3.5mm of maximum gap and 3.5mm of maximum overlap.

Supporting Multiple Wavelengths

A single image replicating waveguide may support a plurality of wavelengths. This can lead to problems due to the wavelength dependency in Equation 1 resulting in different replication pitches and variations for light of different wavelengths. This is illustrated in Figure 8 which shows a k-vector diagram 800 for a waveguide having a thickness of 3mm and supporting light having three different wavelengths, here being red (620nm-750nm such as 635nm), blue (450nm-495nm, such as 450nm) and green (495-570 nm or in the range of 520- 560 nm such as around 520 nm).

The variation in k-vector angles for blue, illustrated by the box 802, is near to the inside edge of the annulus and so blue light has a minimal replication pitch variation (around 2mm) resulting in good image quality due to low angular spread. The variation in k-vector angles for green, illustrated by the box 804, is slightly further from the inside edge of the annulus than the box 802 for blue. This may still be acceptable for image quality so that the waveguide may effectively be used to transmit both blue and green.

An issue arises when the waveguide is also used to transmit red light. Here, it is apparent that the box 806 representing the variation in k-vector angles for red is far from the inside edge of the annulus resulting in a large replication pitch variation (around 6mm). This will result in a noticeable colour non-uniformity / banding. The effect of replication pitch variation between light having different wavelengths can be reduced by using separate waveguides for each wavelength. The inventors have shown that separate waveguides having a thickness of 2.5mm result in acceptable image quality. The result of using separate waveguides would be, at a minimum, a 7.5mm thick stack, which may not be overly thick for most purposes. One way to achieve such a stack is design the waveguide so that light of at least one wavelength does not couple to a waveguide due to moving the box in the k-vector diagram beyond the limits defined by the annulus. As can be seen from Figure 8, blue and green light have a large overlap so it is difficult to remove blue without also removing green. Further, removing red by making it beyond the waveguide cut-off results in blue and green getting pushed towards the outer edge of the annulus, resulting in higher replication pitch variations for these colours. A further solution may implement a coupler technology that allows only a single wavelength of light to be in-coupled per waveguide.

An alternative solution is illustrated in Figure 9, which shows an image replicating waveguide system 900 comprising first and second waveguides 902, 904. Each waveguide 902, 904 may have a thickness of around 3mm (as discussed above, this reduces replication pitch variation for at least monochromatic light). The first waveguide 902 is configured to in-couple red light 910 (shown by the long dashed lines) while allowing blue (shown by the solid lines) and green (shown by the dashed lines) light to be transmitted without in-coupling. This can be achieved with a dichroic mirror that back-reflects red light onto an in-coupler designed to be illuminated back-to-front.

The second waveguide 904 is then configured to in-couple blue and green light. The k- vector diagrams 1000, 1050 for the first and second waveguides 902, 904 are shown in Figures 10A and 10B respectively. The k-vector diagram 1000 is similar to the k-vector diagram 800 but wherein red light 1006 is not in-coupled and so the waveguide does not have the problems of transmitting red light discussed above. The variation of k-vectors of blue 1002 and green 1004 light result in an acceptable replication pitch variation. The k-vector diagram 1050 for the red transmitting waveguide illustrates that neither blue 1052 nor green 1054 are in-coupled and that red light 1056 has a relatively low variation in replication pitch. The result is that the image replicating waveguide system has a low replication pitch variation for the three colours transmitted. Note that light of different wavelengths transmitted through a single image replicating waveguide needs to be above the total internal reflection angle for all wavelengths that are desired to be transmitted. This can be achieved by varying the IC grating k-vectors, for example. Of course, the waveguide system may support light of more or fewer wavelengths; three colours have been shown for illustration only. Example Display System

The example image replicating waveguides that have been discussed throughout may have particular use in holographic display systems. Figure 11 shows a holographic display system 1100 according to an example. The holographic display system 1100 comprises an image generating unit 1102 configured to generate an input light field 1110. The image generating unit 1102 may also be referred to as an optical engine, an Optical Engine Module or a Picture Generating Unit (PGU). The holographic display system 1100 further comprises an image replicating waveguide 1104, which may be any of the image replicating waveguides 100, 902, 904 shown in Figures 1 and 9 and may therefore have any of the grating configurations 200, 250 shown in Figures 2A and 2B. As discussed, the image replicating waveguide 1104 is configured to generate a plurality of replications 1112, 1114, 1116 of the input light field 1110 incident at the entrance pupil 1106 of the waveguide 1104. The replications are extracted at an output surface 1108 of the waveguide 1104 and (at least one is) received at a viewer’s eye 1124.

The image generating unit 1102 may comprise a light source configured to generate at least partially coherent light at approximately one or more wavelengths. The image generating unit 1102 may further comprise a display device to be illuminated by the light source. Any suitable display device can be used, such as a spatial light modulator (SLM). The SLM may be a digital micromirror device (DMD). In other examples, the SLM is a Liquid Crystal on Silicon, LCoS, device.

An exit pupil of the image generating unit 1102 may be arranged to be aligned with an IC grating of the image replicating waveguide 1104. With this in mind, the IC grating of the waveguide 1104 may be designed to factor in a shape of the exit pupil of the image generating unit 1102. The exit pupil of the image generating unit 1102 may have a shape that approximately tessellates upon replication by the image replicating waveguide 1104. That is, if the exit pupil tiles on a rhombic grid defined by a first and second lattice vector, the first magnitudes and orientations of the IC and OC k-vectors of the combiner may be chosen to match the lattice geometry of the exit pupil. Image replicating waveguides that replicate on a rhombic grid have been described. This is achieved by selecting certain properties for the IC, EPE and OC grating k-vectors. In an example then, the exit pupil of the image generating unit 1102 may have a shape that tiles on a rhombic grid. This can be achieved by ensuring that the shape of the aperture(s) defined by the filter has this shape. Secondary Interactions with the IC Grating

Light in-coupled to an image replicating waveguide via an IC grating may undergo a second interaction with the IC grating whereby a portion will be extracted without having traversed the waveguide, resulting in a loss of light at the eyebox of the waveguide. This effect can be decreased by reducing the area of the IC grating, or in other words arrange the IC grating to receive light from an area smaller than the area of the exit pupil of the image generating unit. There is a compromise between the loss of light that never couples due to the missing portion of IC and the loss of light due to the second interaction with the IC. The optimal configuration could be arrived at using a suitable optimisation scheme. An example optimisation scheme models the amount of light in-coupled by a given point in the IC grating vs the amount of light out-coupled, and removes any points from the IC grating that have a net loss. Other schemes are envisaged such as machine learning algorithms adapted to find the optimal balance between light lost to secondary coupling vs light lost to never coupling in the first place due to the reduced effective size of the IC grating.

This will now be discussed with reference to Figure 12 which shows an improved IC grating shape 1202 for a given image generating unit exit pupil shape 1204. Here, the image generating unit exit pupil shape 1204 substantially has the form of an “I”. This shape can be tessellated on a rhombic grid and so has particular advantages when paired with an image replicating waveguide according to the present disclosure. The “I” shape having a dotted outline represents the in-coupled light field after having undergone a single total internal reflection 1206 within the waveguide. Spatial filters comprising a union of apertures having a shape substantially in the form of an “I” are described in UK patent application no. 2211261.9 which was incorporated by reference above.

An initial shape for the IC grating may be approximately a square and arranged to overlay and include the entirety of the image generating unit exit pupil shape 1204. As can be seen in Figure 12, this initial configuration for the IC grating is non-optimal in that a relatively high proportion of the light that is in-coupled at the IC grating is out-coupled due to a secondary interaction with the IC grating following a total internal reflection inside the waveguide. In other words, a high fraction of the reflection 1206 is covered by the initial IC grating, and so some of this reflected light will be extracted out upon interaction with the IC grating. It may be beneficial to modify the initial IC grating shape so that less light undergoes a secondary interaction with the IC grating at the expense of reducing the amount of light from the image generating unit exit pupil 1204 that is in-coupled in the first place. Here, the improved IC grating shape is essentially the initial IC grating shape with a rectangular cut taken from a comer, in this case the top right edge. This shape can be realised using a variety of means, such as manufacturing the waveguide with an IC grating having this shape, or providing a filter at, or near to, the IC grating so as to limit the amount of light that is incident on the IC grating.

A similar procedure can be applied where a waveguide / IC grating is arranged to receive light of more than one wavelength. That is, a similar optimisation scheme can be applied across the multiple wavelengths to determine an optimal IC grating shape. This may be important because light having different wavelengths will be reflected at slightly different positions within the waveguide. An optimal configuration may allow for a maximum amount of light of each wavelength to be transmitted by the waveguide.

The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. For example, although the description above refers to image replicating waveguides, it is of course understood that it similarly applies to image replicating waveguide combiners.

It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.

Claims

1. An image replicating waveguide comprising: an In-Coupling, IC, grating having a first k-vector; an Exit Pupil Expanding, EPE, grating having a second k-vector; and an Out-Coupling, OC, grating having a third k-vector, wherein a magnitude of the first k-vector is approximately equal to a magnitude of the third k-vector, and wherein a direction of the second k-vector is approximately horizontal or approximately vertical with respect to an outcoupled image axis.

2. The image replicating waveguide according to claim 1, wherein the angle between the first and third k-vectors is greater than 90 degrees.

3. The image replicating waveguide according to claim 2, wherein the angle between the first and third k-vectors is between about 100 and 120 degrees.

4. The image replicating waveguide according to any preceding claim having a replication pitch variation of less than 3mm.

5. The image replicating waveguide according to any preceding claim, wherein the first k-vector has a magnitude and orientation such that an angle subtended between a ray of light reflected within the image replicating waveguide and a normal to the image replicating waveguide at the reflection is between a total internal reflection angle of the image replicating waveguide and 60 degrees.

6. The image replicating waveguide according to any preceding claim, wherein there is a single path for a ray to traverse from an input of the image replicating waveguide to each output of the image replicating waveguide.

7. The image replicating waveguide according to any preceding claims, which is configured to replicate on a rhombic grid.

8. The image replicating waveguide according to any preceding claim, having a thickness greater than 2mm.

9. An image replicating waveguide system comprising: a first image replicating waveguide according to any of claims 1 to 8 and arranged to generate replications at a first replication pitch for light having a first wavelength; and a second image replicating waveguide according to any of claims 1 to 8 and arranged to generate replications at the first replication pitch for light having a second wavelength, different from the first wavelength.

10. The image replicating waveguide system according to claim 9, wherein the first image replicating waveguide is further arranged to receive light having a third wavelength, different from the first and second wavelengths, such that light having the first and third wavelengths is transmitted through the first image replicating waveguide above the total internal reflection angle.

11. The image replicating waveguide system according to claim 10, wherein the first wavelength corresponds to green light, the second wavelength corresponds to red light, and the third wavelength corresponds to blue light.

12. A display system comprising: an image generating unit arranged to generate a light field; and an image replicating waveguide according to any of claims 1 to 8 or an image replicating waveguide system according to any of claims 9 to 11.

13. The display system according to claim 12, wherein respective magnitudes and orientations of the first, second and third k-vectors match a geometry of an exit pupil of the image generating unit.

14. The display system according to claim 12 or 13, wherein the exit pupil of the image generating unit has a shape that tiles on a rhombic grid.

15. The display system according to any of claims 12 to 14, wherein the exit pupil of the image generating unit has a shape that tiles on a rhombic grid defined by first and second lattice vectors, and the magnitudes and orientations of the first and third k-vectors are chosen to match the lattice geometry defined by the first and second lattice vectors.

16. The display system according to any of claims 12 to 15, wherein the IC grating is arranged to receive light from an area smaller than the area of the exit pupil of the image generating unit.

17. The display system according to claim 16, wherein the area is determined to minimise the total light loss due to the combined effect of a portion of light not coupling to the IC grating and of a second interaction with the IC grating.

18. The display system according to any of claims 12 to 17, wherein the image generating unit comprises a spatial filter comprising a plurality of apertures, and wherein the union of the plurality of apertures forms the exit pupil of the image generating unit.

19. The display system according to claim 18, wherein the union of the plurality of apertures forms a shape that substantially has the form of an “I” or “H”.