Patent ID: 12242059

FIG.1is a top view of a known waveguide6.FIG.2is a side view of the same waveguide6. An input diffraction grating1is provided on a surface of the waveguide6for coupling light from a projector2into the waveguide6. Light that is coupled into the waveguide6travels by total internal reflection towards an output grating4. In this arrangement the input and output gratings1,4can be surface relief gratings having grooves that are parallel to one another. The input grating1is typically a blazed grating that preferentially diffracts light in the direction of the output grating4. In this arrangement the grooves of the input grating1and the output element4extend in a direction that is parallel to the x-axis in the Cartesian reference frame ofFIG.1.

Each diffractive optical element comprises a grating vector in the plane of its grooves. A grating vector has a direction that is normal to the grooves and a magnitude which is inversely related to the pitch (i.e. the separation) of the grooves. The direction of the grating vector (positive or negative) is determined by the polarity of the diffracted order of the light.FIG.3shows the grating vectors of the input grating11and the output element14from the perspective of the optical path that couples light towards a viewer. Along the optical path the grating vectors11,14are equal in magnitude but opposite in direction because the grating vector11for the input grating diffracts light into a +1 order and the grating vector14for the output grating14diffracts light into a −1 order (of course, viewed from a different perspective these polarities could equally be reversed). Adding the two grating vectors11,14together produces a resultant vector having substantially zero magnitude. This configuration is chosen so that light outcoupled by the output element4experiences no chromatic or angular dispersion.

Light captured within the waveguide6by total internal reflection interacts with the output grating4multiple times. At each interaction with the output grating4light is either diffracted and coupled out of the waveguide6towards the viewer, or else it is undiffracted in which case the light continues to propagate away from the input grating1in the negative y-direction. The proportion of light that is diffracted versus undiffracted is determined by the diffraction efficiency of the output grating4. The diffraction efficiency is chosen so that light can be coupled out of the waveguide and towards a viewer along the full length of the output grating4in the direction of the y-axis. If the diffraction efficiency of the output grating4is constant along the y-axis then the brightness of light may reduce in the negative y-direction. This is because less and less light remains captured by total internal reflection as light progresses within the waveguide; this phenomenon is indicated schematically by the breadth of the arrows depicting optical paths inFIGS.1and2.

A certain proportion of light remains undiffracted by the output grating4, and continues to propagate in the negative y-direction under total internal reflection. This light is typically scattered by an edge10of the waveguide6. Scattered light can be undesirably directed back towards the output grating4. It has been determined that scattered light can produce background light that reduces the contrast of the augmented reality image that is coupled towards a viewer by the output grating4.

In other known arrangements the output grating4can be replaced by more sophisticated output elements, such as those disclosed in WO 2016/020643, for example. In WO 2016/020643 an arrangement is disclosed where the output element expands light in two dimensions in an augmented reality display. This arrangement has been found to be very effective at simultaneously expanding light in two dimensions and coupling light out of the waveguide. It has been determined that scattering from waveguide edges can similarly reduce the contrast of an augmented reality image in more sophisticated output elements such as these.

For simplicity the arrangement inFIGS.1to3has been described in the context of a single projector and a single waveguide. However, the skilled person will appreciate that multiple waveguides and projectors can be used in different configurations. It is common, for example, to use a stack of three waveguides each of which is optimised for a different primary colour in order to produce a full colour augmented reality image. The same issues can arise in multiple waveguide stacks regarding back scatter from waveguide edges.

FIG.4is a top view of a waveguide106in an embodiment of the invention.FIG.5is a side view of the same waveguide106. The configuration is similar to that ofFIGS.1and2, and an input diffraction grating101is provided on a surface of the waveguide106for coupling light from a projector102into the waveguide106. Light that is coupled into the waveguide106travels by total internal reflection towards an output grating104, and the input and output gratings101,104are surface relief gratings having grooves that are parallel to one another.

In this configuration the device further includes a return grating112. The return grating112is positioned so that it receives light that is undiffracted from the output grating104. The return grating112diffracts light so that it is directed back towards the output grating104in the positive y-direction. Returned light is then diffracted according to the diffraction efficiency of the output grating104. Some of the returned light is diffracted by the output grating104thereby outcoupling the light towards the viewer. The remainder of the light will continue to propagate in the positive y-direction still captured within the waveguide106by total internal reflection; this is indicated schematically by dotted lines inFIGS.4and5. A small proportion of the returned light may remain undiffracted such that it scatters from a top edge of the waveguide106. However, the amount of undiffracted light would be very small and it is believed that its effect on contrast of the augmented reality image would be minimal.

FIG.6is a diagram showing the grating vectors of the input grating111, the output grating114and the return grating122. The grating vectors are chosen so that light that is coupled out of the waveguide106and towards the viewer is diffracted by a number of diffraction gratings having vectors that combine to produce a resultant with zero magnitude. In a first group of optical paths light is diffracted first by the input grating101so that it is coupled into the waveguide to undergo total internal reflection. Light in the first group of optical paths is then diffracted by the output grating104so that it is coupled out of the waveguide106and towards the viewer. The grating vectors111,114are equal in magnitude. In this first group of optical paths the grating vectors111,114are opposite in direction since the optical path involves a positive (+1) diffraction order followed by a negative (−1) diffraction order. As such, the resultant vector has substantially zero magnitude. In the second group of optical paths light is diffracted first by the input grating101(in a +1 order), then by the return grating122(in a −1 order) and then by the output grating104(in a +1 order) so that it is coupled out of the waveguide106and towards the viewer. In this situation the grating vectors111,114of the input grating111and the output grating104are oriented in the same direction and are equal in magnitude. The grating vector of the return grating122has twice the magnitude of the grating vector111of the input grating and acts in the opposite direction. Thus, the grating vectors combine to produce a resultant that has substantially zero magnitude.

The return grating112has a grating vector122with the same orientation but twice the magnitude of the grating vector111of the input grating101. This is achieved by providing the return grating112with grooves in the same orientation as those of the input grating101, and by providing a pitch in the return grating112which is half of the pitch of grooves in the input grating101.

FIG.7is a top view of a waveguide206in another embodiment of the invention. In this arrangement an input diffraction grating201is provided on a surface of the waveguide206. The grooves of the input grating201are oriented parallel to the x-axis in the Cartesian reference frame ofFIG.7. Light from a projector (not shown) is diffracted by the input grating201and coupled into the waveguide206whereupon it undergoes total internal reflection. Light travels within the waveguide206towards an intermediate grating216. The grooves of the intermediate grating216are oriented at +45° to the y-axis, within the x-y plane, which is in the plane of the waveguide206. Light is diffracted by the intermediate grating216towards an output grating204. Light is diffracted upon each interaction with the intermediate grating216as it travels within the waveguide206in the negative y-direction, captured within the waveguide206by total internal reflection. The diffraction efficiency of the intermediate grating216determines the proportion of light that is diffracted towards the output grating204versus the proportion of light that is undiffracted and continues to propagate in the negative y-direction. The diffraction efficiency is chosen to allow effective one-dimensional expansion of the light in the y-axis. Light that is diffracted by the intermediate diffraction grating216travels in the positive x-direction, still captured within the waveguide206by total internal reflection. Light then interacts with the output grating204. The output grating204has grooves that are oriented parallel with the y-axis in the plane of the waveguide206. The diffraction efficiency of the output grating204determines the proportion of light that is diffracted towards a viewer versus the proportion of light that is undiffracted and continues to propagate in the positive x-direction. The diffraction efficiency is chosen to allow effective one-dimensional expansion of the light in the x-axis. This configuration allows two dimensional expansion of light in the y-axis followed by the x-axis so that two-dimensional augmented reality images can be output towards a viewer.

A proportion of light remains undiffracted by the output grating204. The undiffracted light encounters the return grating212which has grooves oriented parallel to the y-axis. Light diffracted by the return grating212extends back towards the output grating204in the negative x-direction so that it has another opportunity to be diffracted by the output grating204and coupled towards a viewer. The return grating212has a high diffraction efficiency so that a high proportion of light is returned towards the output grating204to reduce the possible impact of scatter at the waveguide edge.

The input, intermediate, output and return gratings201,216,204,212are surface relief gratings.FIG.8is a diagram showing the grating vectors of the input grating211, the output grating214, the intermediate grating217and the return grating222. In a first group of optical paths light is diffracted first by the input grating201so that it is coupled into the waveguide206to undergo total internal reflection. Light in the first group of optical paths is then diffracted by the intermediate grating216and subsequently by the output grating204so that it is coupled out of the waveguide206and towards the viewer. The grating vectors211,217,214can be combined in a right angled triangle so that the resultant has substantially zero magnitude. This is achieved because the pitch of the input grating201is equal to the pitch of the output grating204. The intermediate grating216has a pitch equal to d·cos (45°), where d is the pitch of the input grating201and the output grating204.

In a second group of optical paths light is diffracted first by the input grating201so that it is coupled into the waveguide to undergo total internal reflection. Light is then diffracted by the intermediate grating216towards the output grating204. Light is undiffracted by the output grating204and it encounters the return grating212which diffracts the light back towards the output grating204so that it can be coupled out of the waveguide206towards a viewer. Light in the second group of optical paths is therefore diffracted by four gratings before it is coupled towards a viewer. The grating vectors for these gratings211,217,214,222can be combined to produce a resultant vector having substantially zero magnitude. This is achieved because the return grating212has grooves that are parallel to those in the output grating204, but the pitch of the grooves in the return grating212is half that of the output grating204; thus, the grating vector222for the return grating has twice the magnitude of the output grating vector214.

FIG.9is a top view of a waveguide306in another embodiment of the invention. In this arrangement an input diffraction grating301is provided on a surface of the waveguide306. The grooves of the input grating301are oriented parallel to the x-axis in the Cartesian reference frame ofFIG.9. Light from a projector (not shown) is diffracted by the input grating301and coupled into the waveguide306whereupon it undergoes total internal reflection. Light travels within the waveguide306towards an output element304. In this arrangement the output element304is a pair of crossed gratings or a photonic crystal as described in WO 2016/020643. Thus, the output element304comprises first and second diffractive optical elements overlaid on one another in or on the waveguide306. The first diffractive optical element is arranged with rows of diffractive optical structures oriented at an angle of −30° to the y-axis. The second diffractive optical element is arranged with rows of diffractive optical structures oriented at an angle of +30° to the y-axis, within the x-y plane. The first diffractive optical element is configured to receive light from the input grating301and to diffract it into an order that extends in a direction angled at +120° to the y-axis. These orders can then be diffracted by the second output diffractive optical element which is orthogonal to the diffracted order extending at +120° to the y-axis so that it can provide outcoupled orders towards a viewer. Similarly, the second output diffractive optical element is configured to receive light from the input grating301and diffract it into an order that extends in a direction angled at −120° to the y-axis. These diffracted orders can then be diffracted by the first output diffractive optical element which is orthogonal to the diffracted orders and can provide outcoupled orders towards a viewer. The diffraction efficiencies of the first and second output diffractive optical elements within the output element304are chosen to allow the light to simultaneously expand in two-dimensions while providing outcoupled orders towards a viewer as augmented reality images.

The device shown inFIG.9also includes first, second and third return gratings307,309,312. The first return grating307has grooves oriented at −30° to the y-axis. The second return grating309has grooves oriented at +30° to the y-axis. The third return grating312has grooves oriented parallel to the x-axis. Each return grating307,309,312can receive light which has not been coupled towards a viewer by the output element304and return the light towards the output element304.

There is a very large number of possible optical paths within the output element304, but this can be simplified by considering four options for light upon its first interaction with the output element304, following diffraction by the input grating301. First, the light may be undiffracted such that it continues to propagate in the negative y-direction, still captured within the waveguide306by total internal reflection. Second, the light may be diffracted by the first diffractive optical element with grooves angled at −30° to the y-axis so that light extends in a direction at +120° to the y-axis. Third, the light may be diffracted by the second diffractive optical element with grooves angled at +30° to the y-axis so that light extends in a direction at −120° to the y-axis. Fourth, light may be diffracted by a superposition of the first and second diffractive optical elements which has effective grooves that are parallel to the x-axis so that light is coupled directly out of the waveguide306towards a viewer; this is sometimes referred to as the straight-to-eye (STE) order. The superposition of the first and second diffractive optical elements may be considered as a third diffractive optical element having a grating vector that is angled respectively at 60° to the first and second diffractive optical elements; thus, the grating vectors for the first, second and third diffractive optical elements within the output element304may be combined in an equilateral triangle.

In a first optical path light in the waveguide306light is diffracted by the input grating301and coupled into the waveguide306whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element304. In this first optical path light is undiffracted by the output element304and it continues to propagate in the negative y-direction until it encounters the third return grating312. Light is diffracted by the third return grating312so that it returns towards the output element304in the positive y-direction. Light then has another opportunity to be diffracted by the output element304so that it can be coupled out of the waveguide306and towards a viewer. In this exemplary first optical path light the returned light is diffracted by the superposition of the first and second diffractive optical elements having a grating vector that is parallel to the y-axis; in other words, the returned light is a STE order upon interaction with the output element304, following diffraction by the third return grating312.

FIG.10is a schematic diagram showing the grating vectors of the input grating311, the third return grating322and the output element322, where the grating vector of the output element322is a superposition of the grating vectors of the first and second diffractive optical elements which are angled at ±30° to the y-axis and are overlaid on top of one another in the waveguide; the equal and opposite components aligned with the x-axis cancel one another, leaving a resultant vector that is aligned with the y-axis. Light in the first optical path is therefore diffracted by three diffractive optical elements before it is coupled towards a viewer. In this example, the input grating301diffracts light into a +1 order, the return grating312diffracts light into a −1 order and the output element304diffracts light into a +1 order. The grating vectors311,322,314can therefore be added together as shown inFIG.10to produce a resultant vector having substantially zero magnitude. This is achieved because the return grating312has a pitch that is half that of the input grating301and the superposition of the first and second output diffractive optical elements in the output element304.

In a second exemplary optical path in the waveguide306, light is diffracted by the input grating301and subsequently light is diffracted by the first diffractive optical element with grooves angled at −30° to the y-axis. The diffracted light extends in a direction that is oriented at +120° to the y-axis (i.e. in a direction that is towards the second return grating309). Light continues to propagate towards the second return grating309and at each interaction with the output element304light is either diffracted by the second diffractive optical element having grooves oriented at +30° to the y-axis so that it can be coupled out of the waveguide306towards a viewer or else it is undiffracted and continues to propagate towards the second return grating309, in a direction that is oriented at 120° to the y-axis. Some light remains undiffracted by the second diffractive optical element in which case it encounters the second return grating309. The second return grating309diffracts the light so that it is returned towards the output element304in the opposite direction (i.e. in a direction that is oriented at −60° to the y-axis). The returned light has another opportunity to interact with the second diffractive optical element with grooves oriented at +30°. When light is diffracted by the second diffractive optical element it is coupled out of the waveguide306towards a viewer in a direction that is parallel to the z-axis.

FIG.11is a schematic diagram showing grating vectors for the active diffractive interactions along this second exemplary optical path. Thus, light is diffracted sequentially by the input grating301, the first diffractive optical element with grooves angled at −30° to the y-axis, the second return grating309and finally by the second diffractive optical element with grooves angled at +30° to the y-axis. The respective grating vectors311,323,325,327can be added together to produce a resultant vector having zero magnitude. The grating vector311for the input grating is oriented at 60° to the grating vector323for the first diffractive optical element, and these grating vectors311,323have the same magnitude. The grating vector325for the second return grating is angled at 60° to the grating vector323for the first diffractive optical element, but has twice the magnitude. Finally, the grating vector327for the second diffractive optical element is oriented in the same direction as the grating vector325for the second return grating, but has half the magnitude.

A third exemplary optical path is also discussed, which is a mirror image of the second exemplary optical path. Thus, in this third optical path in the waveguide306, light is diffracted by the input grating301and subsequently light is diffracted by the second diffractive optical element with grooves angled at +30° to the y-axis. The diffracted light extends in a direction that is oriented at −120° to the y-axis (i.e. in a direction that is towards the first return grating307). Light continues to propagate towards the first return grating307and at each interaction with the output element304light is either diffracted by the first diffractive optical element having grooves oriented at −30° to the y-axis so that it can be coupled out of the waveguide306towards a viewer or else it is undiffracted and continues to propagate towards the first return grating307, in a direction that is oriented at −120° to the y-axis. Some light remains undiffracted by the first diffractive optical element in which case it encounters the first return grating307. The first return grating307diffracts the light so that it is returned towards the output element304in the opposite direction (i.e. in a direction that is oriented at +60° to the y-axis). The returned light has another opportunity to interact with the first diffractive optical element with grooves oriented at −30° to the y-axis. When light is diffracted by the first diffractive optical element it is coupled out of the waveguide306towards a viewer in a direction that is parallel to the z-axis.

FIG.12is a schematic diagram showing grating vectors for the active diffractive interactions along this third exemplary optical path. Thus, light is diffracted sequentially by the input grating301, the second diffractive optical element with grooves angled at +30° to the y-axis, the first return grating307and finally by the first diffractive optical element with grooves angled at −30° to the y-axis. The respective grating vectors311,327,329,323can be added together to produce a resultant vector having zero magnitude. The grating vector311for the input grating is oriented at 60° to the grating vector327for the second diffractive optical element, and these grating vectors311,327have the same magnitude. The grating vector329for the first return grating is angled at 60° to the grating vector327for the first diffractive optical element, but has twice the magnitude. Finally, the grating vector323for the first diffractive optical element is oriented in the same direction as the grating vector329for the first return grating, but has half the magnitude.

In this way, the first, second and third return gratings307,309,312can return light towards the output element304. This can reduce scatter from waveguide edges, thereby improving the contrast of augmented reality images that are coupled out of the waveguide306and towards the viewer along the z-axis.

FIG.13is a top view of a waveguide406in another embodiment of the invention, which is structurally similar to the waveguide306described above and shown inFIG.9. In the arrangement ofFIG.13, the third return grating includes a first portion412aand a second portion412b. The first portion412aof the third return grating has grooves oriented at −60° to the y-axis. The second portion412bof the third return grating has grooves oriented at +60° to the y-axis. Each return grating407,409,412a,412bcan receive light which has not been coupled towards a viewer by the output element404and return the light towards the output element404.

In a first exemplary optical path in the waveguide406light is diffracted by the input grating401and coupled into the waveguide406whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element404. In this first optical path light is initially undiffracted by the output element304and it continues to propagate in the negative y-direction. At a certain position light is then diffracted by the second diffractive optical element within the output element304, having grooves angled at +30° to the y-axis. The diffracted light extends in a direction that is oriented at −120° to the y-axis (i.e. downwards and leftwards in the top view ofFIG.13). Light continues to propagate in this direction until it encounters the first portion412aof the third return grating. In other words, light is diffracted in the output element404at a position with respect to the y-axis which means that it encounters the first portion412aof the third return grating, rather than the first return grating407. Light is diffracted by the first portion412aof the third return grating so that it returns towards the output element404in the positive y-direction (i.e. parallel to the y-axis). In this exemplary first optical path the returned light is diffracted by the superposition of the first and second diffractive optical elements having a grating vector that is parallel to the y-axis; in other words, the returned light is a STE order upon interaction with the output element404, following diffraction by the first portion412aof the third return grating412.

FIG.14is a schematic diagram showing grating vectors for the active diffractive interactions along this first exemplary optical path. Thus, light is diffracted sequentially by the input grating401, the second diffractive optical element with grooves angled at +30° to the y-axis, the first portion412aof the third return grating, with grooves angled at −60° to the y-axis, and finally by a superposition of the grating vectors of the first and second diffractive optical elements which has a grating vector that is aligned with the y-axis (i.e. effective grooves which are parallel to the x-axis). These four sequential diffractive interactions are depicted by grating vectors411,423,440,414. The input grating401has grooves oriented parallel to the x-axis and with a groove separation ‘d’. Thus, grating vector411(for the input grating401) is parallel to the y-axis. The second diffractive optical element with grooves angled at +30° to the y-axis also has a groove separation ‘d’. The first portion412aof the third return grating has grooves angled at −60° to the y-axis and a groove separation which is d/(2*cos(30°)). Finally, the grating vector414corresponding to the superposition of the grating vectors of the first and second diffractive optical elements has an effective groove separation which is ‘d’. When these grating vectors411,423,440,414are combined they produce a resultant vector which has substantially zero magnitude, which means that this sequence of diffractive interactions can provide outcoupled orders towards a viewer with minimum angular and chromatic aberrations.

A second exemplary optical path can be considered, which is effectively a mirror image of the first exemplary optical path described above, about the y-axis. Thus,406light is diffracted sequentially by the input grating401, the first diffractive optical element within the output element304, having grooves angled at −30° to the y-axis, the second portion412bof the third return grating, and finally by the superposition of the first and second diffractive optical elements having a grating vector that is parallel to the y-axis. These four sequential diffractive interactions are depicted inFIG.16with grating vectors411,427,442,414. The input grating401has grooves oriented parallel to the x-axis and a groove separation ‘d’. Thus, grating vector411(for the input grating401) is parallel to the y-axis. The first diffractive optical element has grooves angled at −30° to the y-axis and also has a groove separation ‘d’. The second portion412bof the third return grating has grooves angled at +60° to the y-axis and a groove separation which is d/(2*cos(30°)). Finally, the grating vector414corresponding to the superposition of the grating vectors of the first and second diffractive optical elements has an effective groove separation which is ‘d’. When these grating vectors411,427,442,414are combined they produce a resultant vector which is substantially zero magnitude, which means that this sequence of diffractive interactions can provide outcoupled orders towards a viewer with minimum angular and chromatic aberrations.

In a third exemplary optical path, in the waveguide406light is diffracted by the input grating401and coupled into the waveguide406whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element404. In this third optical path light is undiffracted by the output element304and it continues to propagate in the negative y-direction towards the third return grating whereupon it is diffracted by the first portion412aof the third return grating. The diffracted light extends back towards the output element404whereupon it is diffracted by the first diffractive optical element within the output element404, having grooves angled at +30° to the y-axis, and coupled out of the waveguide406towards a viewer in a direction that is parallel with the z-axis. These three sequential diffractive interactions are depicted inFIG.15with grating vectors411,440,427which are added together to produce a resultant vector with substantially zero magnitude.

A fourth exemplary optical path is effectively a mirror opposite of the third exemplary optical path, about the y-axis. Thus, light is diffracted by the input grating401and coupled into the waveguide406whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element404. Light is undiffracted by the output element304and it continues to propagate in the negative y-direction towards the third return grating whereupon it is diffracted by the second portion412bof the third return grating. The diffracted light extends back towards the output element404whereupon it is diffracted by the second diffractive optical element within the output element404, having grooves angled at −30° to the y-axis, and coupled out of the waveguide406towards a viewer in a direction that is parallel with the z-axis. These three sequential diffractive interactions are depicted inFIG.17with grating vectors411,442,423which are added together to produce a resultant vector with substantially zero magnitude.

In this way, the first and second portions412a,412bof the third return grating inFIG.13allow light to be returned to the output element both when rays are received undiffracted from the output element404and when a single turning diffractive interaction has taken place.

FIG.18is a top view of another waveguide506in an embodiment of the invention, which is structurally similar to the waveguide306described above and shown inFIG.9. In the arrangement ofFIG.18, however, the first return grating507, situated to the left of the output element504, has grooves oriented parallel to the y-axis. The second return grating509, situated to the right of the output element504also has grooves oriented parallel to the y-axis. For the sake of simplicity, no third return grating is shown, although it would be possible to include a third return grating in a similar way to that shown inFIG.9or13.

In a first exemplary optical path in the waveguide506light is diffracted by the input grating501and coupled into the waveguide506whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element504. In this first optical path light is diffracted by the second diffractive optical element within the output element504, having grooves angled at +30° to the y-axis. The diffracted light extends in a direction that is oriented at −120° to the y-axis (i.e. downwards and leftwards in the top view ofFIG.18) until it encounters the first return grating507, whereupon light is diffracted back towards the output element504. Light is then diffracted again by the second diffracted optical element, having grooves angled at +30° to the y-axis, so that it is coupled out of the waveguide506along the z-axis towards a viewer. The grating pitches are selected so that the respective grating vectors can be combined to produce a resultant vector having substantially zero magnitude.FIG.19is a schematic diagram showing grating vectors for the active diffractive interactions along this first exemplary optical path. Thus, light is diffracted sequentially by the input grating401, the second diffractive optical element with grooves angled at +30° to the y-axis, the first return grating507, and finally, once more by the second diffractive optical element with grooves angled at +30° to the y-axis. These four sequential diffractive interactions are depicted by grating vectors511,523,515,523. The input grating401has grooves oriented parallel to the x-axis and with a separation ‘d’. Thus, grating vector411(for the input grating401) is parallel to the y-axis. The second diffractive optical element with grooves angled at +30° to the y-axis also has a groove separation ‘d’. The first return grating507has grooves angled parallel to the y-axis and a groove separation which is d/(2*sin(60°)). Finally, the second diffractive optical element with grooves angled at +30° to the y-axis also has a groove separation ‘d’.

A second exemplary optical path is effectively a mirror image of the first optical path described above, about the y-axis. In this second optical path, light is diffracted by the input grating501and coupled into the waveguide506whereupon it undergoes total internal reflection extending in the negative y-direction towards the output element504. Light is then diffracted by the first diffractive optical element within the output element504, having grooves angled at −30° to the y-axis. The diffracted light extends in a direction that is oriented at +120° to the y-axis (i.e. downwards and rightwards in the top view ofFIG.18) until it encounters the second return grating509, whereupon light is diffracted back towards the output element504. Light is then diffracted again by the first diffractive optical element, having grooves angled at −30° to the y-axis, so that it is coupled out of the waveguide506along the z-axis towards a viewer. The grating pitches are selected so that the respective grating vectors can be combined to produce a resultant vector having substantially zero magnitude.FIG.20is a schematic diagram showing grating vectors for the active diffractive interactions along this second exemplary optical path. Thus, light is diffracted sequentially by the input grating501, the first diffractive optical element with grooves angled at −30° to the y-axis, the second return grating509, and finally, once more by the first diffractive optical element with grooves angled at −30° to the y-axis. These four sequential diffractive interactions are depicted by grating vectors511,527,529,527. The second return grating509has grooves angled parallel to the y-axis and a groove separation which is d/(2*sin(60°)). Thus, the four gratings can be combined additively to produce a resultant vector having substantially zero magnitude. This provides a return grating arrangement that can effectively return light towards the output element504, thereby improving image contrast within the output element504by reducing scatter from waveguide edges.

The above description refers to surface relief gratings. However, the person skilled in the art will recognise that the concepts can be extended to all types of grating, including volume gratings.