Patent Publication Number: US-10317677-B2

Title: Display system

Description:
BACKGROUND 
     Display systems can used to make a desired image visible to a user (viewer). Wearable display systems can be embodied in a wearable headset which is arranged to display an image within a short distance from a human eye. Such wearable headsets are sometimes referred to as head mounted displays, and are provided with a frame which has a central portion fitting over a user&#39;s (wearer&#39;s) nose bridge and left and right support extensions which fit over a user&#39;s ears. Optical components are arranged in the frame so as to display an image within a few centimeters of the user&#39;s eyes. The image can be a computer generated image on a display, such as a micro display. The optical components are arranged to transport light of the desired image which is generated on the display to the user&#39;s eye to make the image visible to the user. The display on which the image is generated can form part of a light engine, such that the image itself generates collimated lights beams which can be guided by the optical component to provide an image visible to the user. 
     Different kinds of optical components have been used to convey the image from the display to the human eye. These can include lenses, mirrors, optical waveguides, holograms and diffraction gratings, for example. In some display systems, the optical components are fabricated using optics that allows the user to see the image but not to see through this optics at the “real world”. Other types of display systems provide a view through this optics so that the generated image which is displayed to the user is overlaid onto a real world view. This is sometimes referred to as augmented reality. 
     Waveguide-based display systems typically transport light from a light engine to the eye via a TIR (Total Internal Reflection) mechanism in a waveguide (light guide). Such systems can incorporate diffraction gratings, which cause effective beam expansion so as to output expanded versions of the beams provided by the light engine. This means the image is visible over a wider area when looking at the waveguide&#39;s output than when looking at the light engine directly: provided the eye is within an area such that it can receive some light from substantially all of the expanded beams, the whole image will be visible to the user. Such an area is referred to as an eye box. 
     To maintain image quality, the structure of the waveguide can be configured in various ways to mitigate distortion of the transported light. 
     SUMMARY 
     According to one aspect of the present disclosure there is provided a display system comprising: an optical waveguide having an incoupling grating, an intermediate grating and an exit grating; an actuator coupled to the optical waveguide arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; and a light engine configured to generate multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction, whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; and wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     According to another aspect of the present disclosure there is provided an optical waveguide for a display system, the optical waveguide coupled to an actuator arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; the optical waveguide having an incoupling grating, an intermediate grating and an exit grating, the incoupling grating arranged to receive multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     According to another aspect of the present disclosure there is provided a wearable headset comprising: a headpiece; an optical waveguide having an incoupling grating, an intermediate grating and an exit grating; an actuator coupled to the optical waveguide arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; and a light engine mounted to the headpiece, the light engine configured to generate multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction, whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; and wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Nor is the claimed subject matter limited to implementations that solve any or all of the disadvantages noted in the background section. 
    
    
     
       BRIEF DESCRIPTION OF FIGURES 
         FIG. 1  shows a wearable display system; 
         FIG. 2  shows a plan view of part of the display system; 
         FIGS. 3A and 3B  shows perspective and frontal view of an optical component; 
         FIG. 4A  shows a schematic plan view of an optical component having a surface relief grating formed on its surface; 
         FIG. 4B  shows a schematic illustration of the optical component of  FIG. 4A , shown interacting with incident light and viewed from the side; 
         FIG. 5A  shows a schematic illustration of a straight binary surface relief grating, shown interacting with incident light and viewed from the side; 
         FIG. 5B  shows a schematic illustration of a slanted binary surface relief grating, shown interacting with incident light and viewed from the side; 
         FIG. 5C  shows a schematic illustration of an overhanging triangular surface relief grating, shown interacting with incident light and viewed from the side; 
         FIG. 6  shows a close up view of part of an incoupling zone of an optical component; 
         FIG. 7A  shows a perspective view of a part of a display system; 
         FIG. 7B  shows a plan view of individual pixels of a display; 
         FIGS. 7C and 7D  show plan and frontal views of a beam interacting with an optical component; 
         FIG. 7E  shows a frontal view of an optical component performing beam expansion; 
         FIG. 7F  shows a plan view of an optical component performing beam expansion; 
         FIG. 7G  is a plan view of a curved optical component; 
         FIGS. 8A and 8B  are plan and frontal views of a part of an optical component; 
         FIG. 9A  shows a perspective view of beam reflection within a fold zone of a waveguide; 
         FIG. 9B  illustrates a beam expansion mechanism; 
         FIG. 10  illustrates a banding effect that is observed in a virtual image by a wearer; 
         FIG. 11  shows a portion of the beam expansion mechanism shown in  FIG. 9B ; and 
         FIG. 12  shows an actuator coupled to the optical component. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a perspective view of a head mounted display. The head mounted display comprises a headpiece, which comprises a frame  2  having a central portion  4  intended to fit over the nose bridge of a wearer, and a left and right supporting extension  6 , 8  which are intended to fit over a user&#39;s ears. Although the supporting extensions are shown to be substantially straight, they could terminate with curved parts to more comfortably fit over the ears in the manner of conventional spectacles. 
     The frame  2  supports left and right optical components, labelled  10 L and  10 R, which are waveguides. For ease of reference herein an optical component  10  (optical waveguide  10 ) will be considered to be either a left or right component, because the components are essentially identical apart from being mirror images of each other. Therefore, all description pertaining to the left-hand component also pertains to the right-hand component. The optical components will be described in more detail later with reference to  FIGS. 3A and 3B . The central portion  4  houses a light engine which is not shown in  FIG. 1  but which is shown in  FIG. 2 . 
       FIG. 2  shows a plan view of a section of the top part of the frame of  FIG. 1 . Thus,  FIG. 2  shows the light engine  13  which comprises a micro display  15  and imaging optics  17  in the form of a collimating lens  20 . The light engine also includes a processor which is capable of generating an image for the micro display. The micro display can be any type of image source, such as liquid crystal on silicon (LCOS) displays, transmissive liquid crystal displays (LCD), matrix arrays of LED&#39;s (whether organic or inorganic) or any other suitable display. The display is driven by circuitry which is not visible in  FIG. 2  which activates individual pixels of the display to generate an image. The substantially collimated light, from each pixel, falls on an exit pupil  22  of the light engine  13 . At exit pupil  22 , collimated light beams are coupled into each optical component,  10 L,  10 R into a respective in-coupling zone  12 L,  12 R provided on each component. These in-coupling zones are clearly shown in  FIG. 1 , but are not readily visible in  FIG. 2 . In-coupled light is then guided, through a mechanism that involves diffraction and TIR, laterally of the optical component in a respective intermediate (fold) zone  14 L,  14 R, and also downward into a respective exit zone  16 L,  16 R where it exits the component  10  towards the users&#39; eye. The zones  14 L,  14 R,  16 L and  16 R are shown in  FIG. 1 . These mechanisms are described in detail below.  FIG. 2  shows a user&#39;s eye (right or left) receiving the diffracted light from an exit zone ( 16 L or  16 R). The output beam OB to a user&#39;s eye is parallel with the incident beam IB. See, for example, the incident beam marked IB in  FIG. 2  and two of the parallel output beams marked OB in  FIG. 2 . The optical component  10  is located between the light engine  13  and the eye i.e. the display system configuration is of so-called transmissive type. 
     Other headpieces are also within the scope of the subject matter. For instance, the display optics can equally be attached to the users head using a head band, helmet or other fit system. The purpose of the fit system is to support the display and provide stability to the display and other head borne systems such as tracking systems and cameras. The fit system will also be designed to meet user population in anthropometric range and head morphology and provide comfortable support of the display system. 
     Beams from the same display  15  may be coupled into both components  10 L,  10 R so that an image is perceived by both eyes from a single display, or separate displays may be used to generate different images for each eye e.g. to provide a stereoscopic image. In alternative headsets, light engine(s) may be mounted at one or both of left and right portions of the frame—with the arrangement of the incoupling, fold and exit zones  12 ,  14 ,  16  flipped accordingly. 
     The optical component  10  is substantially transparent such that a user can not only view the image from the light engine  13 , but also can view a real world view through the optical component  10 . 
     The optical component  10  has a refractive index n which is such that total internal reflection takes place guiding the beam from the in-coupling zone  12  along the intermediate expansion zone  14 , and down towards the exit zone  16 . 
       FIGS. 3A and 3B  show an optical component in more detail. 
       FIG. 3A  shows a perspective view of an optical component  10 . The optical component is flat in that the front and rear portions of its surface are substantially flat (front and rear defined from the viewpoint of the wearer, as indicated by the location of the eye in  FIG. 3A ). The front and rear portions of the surface are parallel to one another. The optical component  10  lies substantially in a plane (xy-plane), with the z axis (referred to as the “normal”) directed towards the viewer from the optical component  10 . The incoupling, fold and exit zones  12 ,  14  and  16  are shown, each defined by respective surface modulations  52 ,  46  and  56  on the surface of the optical component, which are on the rear of the waveguide from a viewpoint of the wearer. Each of the surface modulations  52 ,  46 ,  56  forms a respective surface relief grating (SRG), the nature of which will be described shortly. Instead of the SRGs, the holograms could be used providing the same optical function as the SRGs. 
     As shown in the plan view of  FIG. 3B , the fold zone has a horizontal extent W 2  (referred to herein as the “width” of the expansion zone) in the lateral (x) direction and a vertical extent H 2  (referred to herein as the “height” of the expansion zone) in the y direction which increases from the inner edge of the optical component to its outer edge in the lateral direction along its width W 2 . The exit zone has a horizontal extent W 3  (width of the exit zone) and vertical extent H 3  (height of the exit zone) which define the size of the eye box, which size is independent of the imaging optics in the light engine. 
     Principles of the diffraction mechanisms which underlie operation of the head mounted display described herein will now be described with reference to  FIGS. 4A and 4B . 
     The optical components described herein interact with light by way of reflection, refractions and diffraction. Diffraction occurs when a propagating wave interacts with a structure, such as an obstacle or slit. Diffraction can be described as the interference of waves and is most pronounced when that structure is comparable in size to the wavelength of the wave. Optical diffraction of visible light is due to the wave nature of light and can be described as the interference of light waves. Visible light has wavelengths between approximately 390 and 700 nanometers (nm) and diffraction of visible light is most pronounced when propagating light encounters structures of a similar scale e.g. of order 100 or 1000 nm in scale. 
     One example of a diffractive structure is a periodic (substantially repeating) diffractive structure. Herein, a “diffraction grating” means any (part of) an optical component which has a periodic diffractive structure. Periodic structures can cause diffraction of light, which is typically most pronounced when the periodic structure has a spatial period of similar size to the wavelength of the light. Types of periodic structures include, for instance, surface modulations on the surface of an optical component, refractive index modulations, holograms etc. When propagating light encounters the periodic structure, diffraction causes the light to be split into multiple beams in different directions. These directions depend on the wavelength of the light thus diffractions gratings cause dispersion of polychromatic (e.g. white) light, whereby the polychromatic light is split into different coloured beams travelling in different directions. 
     When the period structure is on the surface of an optical component, it is referred to a surface grating. When the periodic structure is due to modulation of the surface itself, it is referred to as a surface relief grating (SRG). An example of a SRG is uniform straight grooves in a surface of an optical component that are separated by uniform straight groove spacing regions. Groove spacing regions are referred to herein as “lines”, “grating lines” and “filling regions”. The nature of the diffraction by a SRG depends both on the wavelength of light incident on the grating and various optical characteristics of the SRG, such as line spacing, groove depth and groove slant angle. An SRG can be fabricated by way of a suitable microfabrication process, which may involve etching of and/or deposition on a substrate to fabricate a desired periodic microstructure on the substrate. The substrate may be the optical component itself or a production master such as a mould for manufacturing optical components. 
       FIGS. 4A and 4B  show from the top and the side respectively part of a substantially transparent optical component  10  having an outer surface S. At least a portion of the surface S exhibits surface modulations that constitute a SRG  44  (e.g.  52 ,  54 ,  56 ), which is a microstructure. Such a portion is referred to as a “grating area”. 
       FIG. 4B  shows the optical component  10 , and in particular the SRG  44 , interacting with an incoming illuminating light beam I that is inwardly incident on the SRG  44 . The light I is white light in this example, and thus has multiple colour components. The light I interacts with the SRG  44  which splits the light into several beams directed inwardly into the optical component  10 . Some of the light I may also be reflected back from the surface S as a reflected beam RO. A zero-order mode inward beam T 0  and any reflection RO are created in accordance with the normal principles of diffraction as well as other non-zero-order (±n-order) modes (which can be explained as wave interference).  FIG. 4B  shows first-order inward beams T 1 , T−1; it will be appreciated that higher-order beams may or may not also be created depending on the configuration of the optical component  10 . Because the nature of the diffraction is dependent on wavelength, for higher-order modes, different colour components (i.e. wavelength components) of the incident light I are, when present, split into beams of different colours at different angles of propagation relative to one another as illustrated in  FIG. 4B . 
       FIGS. 5A-5C  are close-up schematic cross sectional views of different exemplary SRGs  44   a - 44   c  (collectively referenced as  44  herein) that may formed by modulation of the surface S of the optical component  10  (which is viewed from the side in these figures). Light beams are denoted as arrows whose thicknesses denote approximate relative intensity (with higher intensity beams shown as thicker arrows). 
       FIG. 5A  shows an example of a straight binary SRG  44   a . The straight binary SRG  44   a  is formed of a series of grooves  7   a  in the surface S separated by protruding groove spacing regions  9   a  which are also referred to herein as “filling regions”, “grating lines” or simply “lines”. The SRG  44   a  has a spatial period of d (referred to as the “grating period”), which is the distance over which the modulations&#39; shape repeats and which is thus the distance between adjacent lines/grooves. The grooves  7   a  have a depth hand have substantially straight walls and substantially flat bases. The filling regions have a height h and a width that is substantially uniform over the height h of the filling regions, labelled “w” in  FIG. 2  (with w being some fraction f of the period: w=f*d). 
     For a straight binary SRG, the walls are substantially perpendicular to the surface S. For this reason, the SRG  44   a  causes symmetric diffraction of incident light I that is entering perpendicularly to the surface, in that each +n-order mode beam (e.g. T 1 ) created by the SRG  4   a  has substantially the same intensity as the corresponding −n-order mode beam (e.g. T−1), typically less than about one fifth (0.2) of the intensity of the incident beam I. 
       FIG. 5B  shows an example of a slanted binary SRG  44   b . The slanted binary SRG  44   b  is also formed of grooves, labelled  7   b , in the surface S having substantially straight walls and substantially flat bases separated by lines  9   b  of width w. However, in contrast to the straight SRG  44   a , the walls are slanted by an amount relative to the normal, denoted by the angle α in  FIG. 5B . The grooves  7   b  have a depth h as measured along the normal. Due to the asymmetry introduced by the non-zero slant, ±n-order mode inward beams travelling away from the slant direction have greater intensity that their ∓n-order mode counterparts (e.g. in the example of  FIG. 5B , the T 1  beam is directed away from the direction of slant and has usually greater intensity than the T−1 beam, though this depends on e.g. the grating period d); by increasing the slant by a sufficient amount, those ∓n counterparts can be substantially eliminated (i.e. to have substantially zero intensity). The intensity of the T 0  beam is typically also very much reduced by a slanted binary SRG such that, in the example of  FIG. 5B , the first-order beam T 1  typically has an intensity of at most about four fifths (0.8) the intensity of the incident beam I. 
     The binary SRGs  44   a  and  44   b  can be viewed as spatial waveforms embedded in the surface S that have a substantially square wave shape (with period d). In the case of the SRG  44   b , the shape is a skewed square wave shape skewed by α. 
       FIG. 5C  shows an example of an overhanging triangular SRG  44   c  which is a special case of an overhanging trapezoidal SRG. The triangular SRG  44   c  is formed of grooves  7   c  in the surface S that are triangular in shape (and which thus have discernible tips) and which have a depth h as measured along the normal. Filling regions  9   c  take the form of triangular, tooth-like protrusions (teeth), having medians that make an angle α with the normal (α being the slant angle of the SRG  44   c ). The teeth have tips that are separated by d (which is the grating period of the SRG  44   c ), a width that is w at the base of the teeth and which narrows to substantially zero at the tips of the teeth. For the SRG of  FIG. 5C , w≈d, but generally can be w&lt;d. The SRG is overhanging in that the tips of the teeth extend over the tips of the grooves. It is possible to construct overhanging triangular SRGs that substantially eliminate both the transmission-mode T 0  beam and the ∓n-mode beams, leaving only ±n-order mode beams (e.g. only T 1 ). The grooves have walls which are at an angle γ to the median (wall angle). 
     The SRG  44   c  can be viewed as a spatial waveform embedded in S that has a substantially triangular wave shape, which is skewed by α. 
     Other SRGs are also possible, for example other types of trapezoidal SRGs (which may not narrow in width all the way to zero), sinusoidal SRGs etc. Such other SRGs also exhibit depth h, linewidth w, slant angle α and wall angles γ which can be defined in a similar manner to  FIG. 5A-C . 
     In the present display system, d is typically between about 250 and 500 nm, and h between about 30 and 400 nm. The slant angle α is typically between about 0 and 45 degrees (such that slant direction is typically elevated above the surface S by an amount between about 45 and 90 degrees). 
     An SRG has a diffraction efficiency defined in terms of the intensity of desired diffracted beam(s) (e.g. T 1 ) relative to the intensity of the illuminating beam I, and can be expressed as a ratio η of those intensities. As will be apparent from the above, slanted binary SRGs can achieve higher efficiency (e.g.  4   b —up to η≈0.8 if T 1  is the desired beam) than non-slanted SRGs (e.g.  44   a —only up to about η≈0.2 if T 1  is the desired beam). With overhanging triangular SRGs, it is possible to achieve near-optimal efficiencies of η≈1. 
     Returning to  FIGS. 3A and 3B , it can be seen that the incoupling, fold and exit zones  12 ,  14 ,  16  are diffraction gratings whose periodic structure arises due to the modulations  52 ,  54 ,  56  of the optical component&#39;s surface that form the incoupling, fold and exit SRGs respectively, and which cover the incoupling, fold and exit zones  12 ,  14 ,  16  respectively. 
       FIG. 6  shows the incoupling SRG  52  with greater clarity, including an expanded version showing how the light beam interacts with it.  FIG. 6  shows a plan view of the optical component  10 . The light engine  13  provides beams of collimated light, one of which is shown (corresponding to a display pixel). That beam falls on the incoupling SRG  52  and thus causes total internal reflection of the beam in the component  10 . The intermediate grating  14  directs versions of the beams down to the exit grating  16 , which causes diffraction of the image onto the user&#39;s eye. The operation of the grating  12  is shown in more detail in the expanded portion which shows rays of the incoming light beam coming in from the left and denoted I and those rays being diffracted so as to undergo TIR in the optical component  10 . The grating in  FIG. 6  is of the type shown in  FIG. 5B  but could also be of the type shown in  FIG. 5C  or some other slanted grating shape. 
     Optical principles underlying certain embodiments will now be described with reference to  FIGS. 7A-9B . 
       FIG. 7 a    shows a perspective view of the display  15 , imaging optics  17  and incoupling SRG  52 . Different geometric points on the region of the display  15  on which an image is displayed are referred to herein as image points, which may be active (currently emitting light) or inactive (not currently emitting light). In practice, individual pixels can be approximated as image points. 
     The imaging optics  17  can typically be approximated as a principal plane (thin lens approximation) or, in some cases, more accurately as a pair of principal planes (thick lens approximation) the location(s) of which are determined by the nature and arrangement of its constituent lenses  24 ,  20  (not shown individually in  FIG. 7 a   ). In these approximations, any refraction caused by the imaging optics  17  is approximated as occurring at the principal plane(s). To avoid unnecessary complication, principles of various embodiments will be described in relation to a thin lens approximation of the imaging optics  17 , and thus in relation to a single principal plane labelled  31  in  FIG. 7 a   , but it will be apparent that more complex imaging optics that do not fit this approximation still can be utilized to achieve the desired effects. 
     The imaging optics  17  has an optical axis  30  and a front focal point, and is positioned relative to the optical component  10  so that the optical axis  30  intersects the incoupling SRG  52  at or near the geometric centre of the incoupling SRG  52  with the front focal point lying substantially at an image point X 0  on the display (that is, lying in the same plane as the front of the display). Another arbitrary image point X on the display is shown, and principles underlying various embodiments will now be described in relation to X without loss of generality. In the following, the terminology “for each X” or similar is used as a convenient shorthand to mean “for each image point (including X)” or similar, as will be apparent in context. 
     When active, image points—including the image point labelled X and X 0 —act as individual illumination point sources from which light propagates in a substantially isotropic manner through the half-space forward of the display  15 . Image points in areas of the image perceived as lighter emit light of higher intensity relative to areas of the image perceived as darker. Image points in areas perceived as black emit no or only very low intensity light (inactive image points). The intensity of the light emitted by a particular image point may change as the image changes, for instance when a video is displayed on the display  15 . 
     Each active image point provides substantially uniform illumination of a collimating area A of the imaging optics  17 , which is substantially circular and has a diameter D that depends on factors such as the diameters of the constituent lenses (D may be of order 1-10 mm, but this is just an example). This is illustrated for the image point X in  FIG. 7 a   , which shows how any propagating light within a cone  32 (X) from X is incident on the collimating area A. The imaging optics collimates any light  32 (X) incident on the collimating area A to form a collimated beam  34 (X) of diameter D (input beam), which is directed towards the incoupling grating  52  of the optical component  10 . The beam  34 (X) is thus incident on the incoupling grating  52 . A shielding component (not shown) may be arranged to prevent any un-collimated light from outside of the cone  32 (X) that is emitted from X from reaching the optical component  10 . 
     The beam  34 (X) corresponding to the image point X is directed in an inward propagation direction towards the incoupling SRG  52 , which can be described by a propagation vector {circumflex over (k)} in (X) (herein, bold typeface is used to denote 3-dimensional vectors, with hats on such vectors indicating denoting a unit vector). The inward propagation direction depends on the location of X in the image and, moreover, is unique to X. That unique propagation direction can be parameterized in terms of an azimuthal angle ϕ in (X) (which is the angle between the x-axis and the projection of {circumflex over (k)} in (X) in the xy-plane) and a polar angle θ in (X)(which is the angle between the z-axis and {circumflex over (k)} in (P) as measured in the plane in which both the z-axis and {circumflex over (k)} in (X) lie—note this is not the xz-plane in general). The notation ϕ in (X), θ in (X) is adopted to denote the aforementioned dependence on X; as indicated ϕ in (X), θ in (X) are unique to that X. Note that, herein, both such unit vectors and such polar/azimuthal angle pairs parameterizing such vectors are sometimes referred herein to as “directions” (as the latter represent complete parameterizations thereof), and that sometimes azimuthal angles are referred to in isolation as xy-directions for the same reason. Note further that “inward” is used herein to refer to propagation that is towards the waveguide (having a positive z-component when propagation is towards the rear of the waveguide as perceived by the viewer and a negative z-component when propagation is towards the front of the waveguide). 
     The imaging optics has a principle point P, which is the point at which the optical axis  30  intersects the principal plane  31  and which typically lies at or near the centre of the collimation area A. The inward direction {circumflex over (k)} in (X) and the optical axis  30  have an angular separation β(X) equal to the angle subtended by X and X 0  from P. β(X)=θ in (X) if the optical axis is parallel to the z-axis (which is not necessarily the case). 
     As will be apparent, the above applies for each active image point and the imaging optics is thus arranged to substantially collimate the image which is currently on the display  15  into multiple input beams, each corresponding to and propagating in a unique direction determined by the location of a respective active image point (active pixel in practice). That is, the imaging optics  17  effectively converts each active point source X into a collimated beam in a unique inward direction {circumflex over (k)} in (X). As will be apparent, this can be equivalently stated as the various input beams for all the active image points forming a virtual image at infinity that corresponds to the real image that is currently on the display  17 . A virtual image of this nature is sometimes referred to herein as a virtual version of the image (or similar). 
     The input beam corresponding to the image point X 0  (not shown) would propagate parallel to the optical axis  30 , towards or near the geometric centre of the incoupling SRG  52 . 
     As mentioned, in practice, individual pixels of the display  15  can be approximated as single image points. This is illustrated in  FIG. 7B  which is a schematic plan view showing the principal plane  31  and two adjacent pixels Xa, Xb of the display  15 , whose centres subtend an angle Δβ from the principal point P. Light emitted the pixels Xa, Xb when active is effectively converted into collimated beams  34 (Xa),  34 (Xb) having an angular separation equal to Δβ. As will be apparent, the scale of the pixels Xa, Xb has been greatly enlarged for the purposes of illustration. 
     The beams are highly collimated and are highly parallel to one another, exhibiting overall angular variation no greater (and potentially significantly less) than the angle subtended by an individual pixel from P (˜Δβ) e.g. typically having an angular range no more than about ½ milliradian. As will become apparent in view of the following, this increases the image quality of the final image as perceived by the wearer. 
       FIGS. 7C and 7D  show schematic plan (xz) and frontal (yz) views of part of the optical component respectively. As indicated in these figures, the incoupling grating  52  causes diffraction of the beam  34 (X) thereby causing a first (±1) order mode beam to propagate within the optical component  10  in a new direction {circumflex over (k)}(X) that is generally towards the fold SRG  54  (i.e. that has a positive x-component). The new direction {circumflex over (k)}(X) can be parameterized by azimuthal and polar angles ϕ(X)—where |ϕ(X)|≤|ϕ in (X)| and θ(X)—where |θ(X)|&gt;|θ in (X)|—which are also determined by the location of and unique to the image point X. The grating  52  is configured so that the first order mode is the only significant diffraction mode, with the intensity of this new beam thus substantially matching that of the input beam. As mentioned above, a slanted grating can be used to achieve this desired effect (the beam as directed away from the incoupling SRG  52  would correspond, for instance, to beam T 1  as shown in  FIG. 4B or 4C ). In this manner, the beam  34 (X) is coupled into the incoupling zone  12  of the optical component  10  in the new direction {circumflex over (k)}(X). 
     The optical component has a refractive index n and is configured such that the polar angle θ(X) satisfies total internal reflection criteria given by:
 
sin θ( X )&gt;1/ n  for each  X.   (1):
 
As will be apparent, each beam input from the imaging optics  17  thus propagates through the optical component  10  by way of total internal reflection (TIR) in a generally horizontal (+x) direction (offset from the x-axis by ϕ(X)&lt;ϕ in (X)). In this manner, the beam  34 (X) is coupled from the incoupling zone  12  into the fold zone  14 , in which it propagates along the width of the fold zone  14 .
 
       FIG. 7E  shows  10  a frontal (xy) view of the whole of the optical component  10 , from a viewpoint similar to that of the wearer. As explained in more detail below, a combination of diffractive beam splitting and total internal reflection within the optical component  10  results in multiple versions of each input beam  34 (X) being outwardly diffracted from the exit SRG along both the width and the height of the exit zone  16  as output beams  38 (X) in respective outward directions (that is, away from the optical component  10 ) that substantially match the respective inward direction {circumflex over (k)} in (X) of the corresponding input beam  34 (X). 
     In  FIG. 7E , beams external to the optical component  10  are represented using shading and dotted lines are used to represent beams within the optical component  10 . Perspective is used to indicate propagation in the z-direction, with widening (resp. narrowing) of the beams in  FIG. 7E  representing propagation in the positive (resp. negative) z direction; that is towards (resp. away from) the wearer. Thus, diverging dotted lines represent beams within the optical component  10  propagating towards the front wall of the optical component  10 ; the widest parts represent those beams striking the front wall of the optical component  10 , from which they are totally internally reflected back towards the rear wall (on which the various SRGs are formed), which is represented by the dotted lines converging from the widest points to the narrowest points at which they are incident on the rear wall. Regions where the various beams are incident on the fold and exit SRGs are labelled S and E and termed splitting and exit regions respectively for reasons that will become apparent. 
     As illustrated, the input beam  34 (X) is coupled into the waveguide by way of the aforementioned diffraction by the incoupling SRG  52 , and propagates along the width of the incoupling zone  12  by way of TIR in the direction ϕ(X), ±θ(X) (the sign but not the magnitude of the polar angle changing whenever the beam is reflected). As will be apparent, this results in the beam  34 (X) eventually striking the fold SRG at the left-most splitting region S. 
     When the beam  34 (X) is incident at a splitting region S, that incident beam  34 (X) is effectively split in two by way of diffraction to create a new version of that beam  42 (X) (specifically a −1 reflection mode beam) which directed in a specific and generally downwards (−y) direction ϕ′(X), ±θ′(X) towards the exit zone  16  due to the fold SRG  54  having a particular configuration which will be described in due course, in addition to a zero order reflection mode beam (specular reflection beam), which continues to propagate along the width of the beam in the same direction ϕ(X), ±θ(X) just as the beam  34 (X) would in the absence of the fold SRG (albeit at a reduced intensity). Thus, the beam  34 (X) effectively continues propagates along substantially the whole width of the fold zone  14 , striking the fold SRG at various splitting regions S, with another new version of the beam (in the same specific downward direction ϕ′(X), ±θ′(X)) created at each splitting region S. As shown in  FIG. 7E , this results in multiple versions of the beam  34 (X) being coupled into the exit zone  16 , which are horizontally separated so as to collectively span substantially the width of the exit zone  16 . 
     As also shown in  FIG. 7E , a new version  42 (X) of the beam as created at a splitting region S may itself strike the fold SRG during its downward propagation. This will result in a zero order mode being created which continues to propagate generally downwards in the direction ϕ′(X), ±θ′(X) and which can be viewed as continued propagation of that beam, but may also result in a non-zero order mode beam  40 (X) (further new version) being created by way of diffraction. However, any such beam  40 (X) created by way of such double diffraction at the same SRG will propagate in substantially the same direction ϕ(X), ±θ(X) along the width of the fold zone  14  as the original beam  34 (X) as coupled into the optical component  10  (see below). Thus, notwithstanding the possibility of multiple diffractions by the fold SRG, propagation of the various versions of the beam  34 (X) (corresponding to image point X) within the optical component  10  is effectively limited to two xy-directions: the generally horizontal direction (ϕ(X), ±θ(X)), and the specific and generally downward direction (ϕ′(X), ±θ′(X)) that will be discussed shortly. 
     Propagation within the fold zone  14  is thus highly regular, with all beam versions corresponding to a particular image point X substantially constrained to a lattice like structure in the manner illustrated. 
     The exit zone  16  is located below the fold zone  14  and thus the downward-propagating versions of the beam  42 (X) are coupled into the exit zone  16 , in which they are guided onto the various exit regions E of the output SRG. The exit SRG  56  is configured so as, when a version of the beam strikes the output SRG, that beam is diffracted to create a first order mode beam directed outwardly from the exit SRG  56  in an outward direction that substantially matches the unique inward direction in which the original beam  34 (X) corresponding to image point X was inputted. Because there are multiple versions of the beam propagating downwards that are substantially span the width of the exit zone  16 , multiple output beams are generated across the width of the exit zone  16  (as shown in  FIG. 7E ) to provide effective horizontal beam expansion. 
     Moreover, the exit SRG  56  is configured so that, in addition to the outwardly diffracted beams  38 (X) being created at the various exit regions E from an incident beam, a zero order diffraction mode beam continuous to propagate downwards in the same specific direction as that incident beam. This, in turn, strikes the exit SRG at a lower exit zone  16   s  in the manner illustrated in  FIG. 7E , resulting in both continuing zero-order and outward first order beams. Thus, multiple output beams  38 (X) are also generated across substantially the height of the exit zone  16  to provide effective vertical beam expansion. 
     The output beams  38 (X) are directed outwardly in outward directions that substantially match the unique input direction in which the original beam  34 (X) is inputted. In this context, substantially matching means that the outward direction is related to the input direction in a manner that enables the wearer&#39;s eye to focus any combination of the output beams  38 (X) to a single point on the retina, thus reconstructing the image point X (see below). 
     For a flat optical component (that is, whose front and rear surfaces lie substantially parallel to the xy-plane in their entirety), the output beams are substantially parallel to one another (to at least within the angle Δβ subtended by two adjacent display pixels) and propagate outwardly in an output propagation direction {circumflex over (k)} out (X) that is parallel to the unique inward direction {circumflex over (k)} in (X) in which the corresponding input beam  34 (X) was directed to the incoupling SRG  52 . That is, directing the beam  34 (X) corresponding to the image point X to the incoupling SRG  52  in the inward direction {circumflex over (k)} in (X) causes corresponding output beams  38 (X) to be diffracted outwardly and in parallel from the exit zone  16 , each in an outward propagation direction {circumflex over (k)} out (X)={circumflex over (k)} in (X) due to the configuration of the various SRGs (see below). 
     As will now be described with reference to  FIG. 7F , this enables a viewer&#39;s eye to reconstruct the image when looking at the exit zone  16 .  FIG. 7F  shows a plan (xz) view of the optical component  10 . The input beam  34 (X) is in coupled to the optical component  10  resulting in multiple parallel output beams  38 (X) being created at the various exit regions E in the manner discussed above. This can be equivalently expressed at the various output beams corresponding to all the image points forming the same virtual image (at infinity) as the corresponding input beams. 
     Because the beams  38 (X) corresponding to the image point X are all substantially parallel, any light of one or more of the beam(s)  38 (X) which is received by the eye  37  is focussed as if the eye  37  were perceiving an image at infinity (i.e. a distant image). The eye  37  thus focuses such received light onto a single retina point, just as if the light were being received from the imaging optics  17  directly, thus reconstructing the image point X (e.g. pixel) ion the retina. As will be apparent, the same is true of each active image point (e.g. pixel) so that the eye  37  reconstructs the whole image that is currently on the display  15 . 
     However, in contrast to receiving the image directly from the optics  17 —from which only a respective single beam  34 (X) of diameter D is emitted for each X—the output beams  39 (X) are emitted over a significantly wider area i.e. substantially that of the exit zone  16 , which is substantially larger than the area of the inputted beam (˜D 2 ). It does not matter which (parts) of the beam(s)  38 (X) the eye receives as all are focused to the same retina point—e.g., were the eye  37  to be moved horizontally (±x) in  FIG. 7F , it is apparent that the image will still be perceived. Thus, no adaptation of the display system is required for, say, viewers with different pupillary distances beyond making the exit zone  16  wide enough to anticipate a reasonable range of pupillary distances: whilst viewers whose eyes are closer together will generally receive light from the side of the exit zone  16  nearer the incoupling zone  12  as compared with viewers whose eyes are further apart, both will nonetheless perceive the same image. Moreover, as the eye  27  rotates, different parts of the image are brought towards the centre of the viewer&#39;s field of vision (as the angle of the beams relative to the optical axis of the eye changes) with the image still remaining visible, thereby allowing the viewer to focus their attention on different parts of the image as desired. 
     The same relative angular separation Δβ exhibited the input beams corresponding any two adjacent pixels Xa, Xb is also exhibited by the corresponding sets of output beams  38 (Xa),  38 (Xb)—thus adjacent pixels are focused to adjacent retina points by the eye  37 . All the various versions of the beam remain highly collimated as they propagate through the optical component  10 , preventing significant overlap of pixel images as focused on the retina, thereby preserving image sharpness. 
     It should be noted that  FIGS. 7A-7G  are not to scale and that in particular beams diameters are, for the sake of clarity, generally reduced relative to components such as the display  15  than would typically be expected in practice. 
     The configuration of the incoupling SRG  52  will now be described with reference to  FIGS. 8A and 8B , which show schematic plan and frontal views of part of the fold grating  52 . Note, in  FIGS. 8A and 8B , beams are represented by arrows (that is, their area is not represented) for the sake of clarity. 
       FIG. 8A  shows two image points XL, XR located at the far left and far right of the display  15  respectively, from which light is collimated by the optics  17  to generate respective input beams  34 (XL),  34 (XR) in inward directions (θ in (XL), ϕ in (XL)), (θ in (XR), ϕ in (XR)). These beams are coupled into the optical component  10  by the incoupling SRG  52  as shown—the incoupled beams shown created at the incoupling SRG  52  are first order (+1) mode beams created by way of diffraction of the beams incident on the SRG  52 . The beams  34 (XL),  34 (XR) as coupled into the waveguide propagate in directions defined by the polar angles θ(XL), θ(XR). 
       FIG. 8B  shows two image points XR 1  and XR 2  at the far top-right and far bottom-right of the display  15 . Note in this figure dashed-dotted lines denote aspects which are behind the optical component  10  (−z). Corresponding beams  34 (XL),  34 (XR) in directions within the optical component  10  with polar angles ϕ(XL), ϕ(XR). 
     Such angles θ(X), ϕ(X) are given by the (transmissive) grating equations: 
                     n   ⁢           ⁢   sin   ⁢           ⁢     θ   ⁡     (   X   )       ⁢           ⁢   sin   ⁢           ⁢     ϕ   ⁡     (   X   )         =     sin   ⁢           ⁢       θ   in     ⁡     (   X   )       ⁢           ⁢   sin   ⁢           ⁢       ϕ   in     ⁡     (   X   )                 (   2   )                 n   ⁢           ⁢   sin   ⁢           ⁢     θ   ⁡     (   X   )       ⁢           ⁢   cos   ⁢           ⁢     ϕ   ⁡     (   X   )         =       sin   ⁢           ⁢       θ   in     ⁡     (   X   )       ⁢           ⁢   cos   ⁢           ⁢       ϕ   in     ⁡     (   X   )         +     λ     d   1                 (   3   )               
with the SRG  52  having a grating period d 1 , the beam light having a wavelength λ, and n the refractive index of the optical component.
 
     It is straightforward to show from (2), (3) that θ(XL)=θ max  and θ(XR)=θ min  i.e. that any beam as coupled into the component  10  propagates with an initial polar angle in the range [θ(XR), θ(XL)]; and that ϕ(XR 2 )=ϕ max  and ϕ(XR 1 )=ϕ min  (≈−ϕ max  in this example) i.e. that any beam as coupled into the component initially propagates with an azimuthal angle in the range [ϕ(XR 1 ), ϕ(XR 2 )](≈[−ϕ(XR 2 ), ϕ(XR 2 )]). 
     The configuration of the fold SRG  54  will now be described with references to  FIGS. 9A-9B . Note, in  FIGS. 9A and 9B , beams are again represented by arrows, without any representation of their areas, for the sake of clarity. In these figures, dotted lines denote orientations perpendicular to the fold SRG grating lines, dashed lines denote orientations perpendicular to the incoupling SRG grating lines, and dash-dotted lines denote orientations perpendicular to the exit SRG grating lines. 
       FIG. 9A  shows a perspective view of the beam  34 (X) as coupled into the fold zone  14  of the optical component  10 , having been reflected from the front wall of the optical component  10  and thus travelling in the direction (ϕ(X), −θ(X)) towards the fold SRG  54 . A dotted line (which lies perpendicular to the fold SRG grating lines) is shown to represent the orientation of the fold SRG. 
     The fold SRG  54  and incoupling SRG  52  have a relative orientation angle A (which is the angle between their respective grating lines). The beam thus makes an angle A+ϕ(X) (see  FIG. 9B ) with the fold SRG grating lines as measured in the xy-plane. The beam  34  is incident on the fold SRG  54 , which diffracts the beam  34  into different components. A zero order reflection mode (specular reflection) beam is created which continues to propagate in the direction (ϕ(X), +θ(X)) just as the beam  34 (X) would due to reflection in the absence of the fold SRG  54  (albeit at a reduced intensity). This specular reflection beam can be viewed as effectively a continuation of the beam  34 (X) and for this reason is also labelled  34 (X). A first order (−1) reflection mode beam  42 (X) is also created which can be effectively considered a new version of the beam. 
     As indicated, the new version of the beam  42 (X) propagates in a specific direction (ϕ′(X), θ′(X)) which is given by the known (reflective) grating equations: 
                     n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     sin   ⁡     (     A   +       ϕ   ′     ⁡     (   X   )         )         =     n   ⁢           ⁢   sin   ⁢           ⁢     θ   ⁡     (   X   )       ⁢           ⁢   sin   ⁢           ⁢     (     A   +     ϕ   ⁡     (   X   )         )               (   4   )                 n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (     A   +       ϕ   ′     ⁡     (   X   )         )         =       n   ⁢           ⁢   sin   ⁢           ⁢     θ   ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (     A   +     ϕ   ⁡     (   X   )         )         -     λ     d   2                 (   5   )               
where the fold SRG has a grating period d 2 , the beam light has a wavelength Δ and n is the refractive index of the optical component  10 .
 
     As shown in  FIG. 9B , which shows a schematic frontal view of the optical component  10 , the beam  34 (X) is coupled into the incoupling zone  12  with azimuthal angle ϕ(X) and thus makes an xy-angle ϕ(X)+A the fold SRG  54 . 
     A first new version  42   a (X) (−1 mode) of the beam  34 (X) is created when it is first diffracted by the fold SRG  54  and a second new version  42   b (X) (−1 mode) when it is next diffracted by the fold SRG  54  (and so on), which both propagate in xy-direction ϕ′(X). In this manner, the beam  34 (X) is effectively split into multiple versions, which are horizontally separated (across the width of the fold zone  14 ). These are directed down towards the exit zone  16  and thus coupled into the exit zone  16  (across substantially the width of the exit zone  16  due to the horizontal separation). As can be see, the multiple versions are thus incident on the various exit regions (labelled E) of the exit SRG  56 , which lie along the width of the exit zone  16 . 
     These new, downward-propagating versions (in the ϕ′(X) direction) may themselves meet the fold SRG once again, as illustrated. However, it can be shown from (4), (5) that any first order reflection mode beam (e.g.  40   a (X), +1 mode) created by diffraction at an SRG of an incident beam (e.g.  42   a (X), −1 mode) which is itself a first order reflection mode beam created by an earlier diffraction of an original beam (e.g.  34 (X)) at the same SRG will revert to the direction of the original beam (e.g. ϕ(X), ±θ(X), which is the direction of propagation of  40   a (X)). Thus, propagation within the fold zone  14  is restricted to a diamond-like lattice, as can be seen from the geometry of  FIG. 9B . The beam labelled  42   ab (X) is a superposition of a specular reflection beam created when  42   b (X) meets the fold SRG  54  and a −1 mode beam created when  40   a (X) meets the fold SRG at substantially the same location; the beam labelled  42   ab (X) is a superposition of a specular reflection beam created when  40   a (X) meets the fold SRG  54  and a +1 mode beam created when  42   b (X) meets the fold SRG at substantially the same location (and so on). 
     The exit SRG and incoupling SRG  52 ,  56  are oriented with a relative orientation angle A′ (which is the angle between their respective grating lines). At each of the exit regions, the version meeting that region is diffracted so that, in addition to a zero order reflection mode beam propagating downwards in the direction ϕ′(X), ±θ′(X), a first order (+1) transmission mode beam  38 (X) which propagates away from the optical component  10  in an outward direction ϕ out (X), θ out (X) given by: 
                     sin   ⁢           ⁢       θ   out     ⁡     (   X   )       ⁢           ⁢     sin   ⁡     (       A   ′     +       ϕ   out     ⁡     (   X   )         )         =     n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     sin   ⁡     (       A   ′     +       ϕ   ′     ⁡     (   X   )         )                 (   6   )                 sin   ⁢           ⁢       θ   out     ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (       A   ′     +       ϕ   out     ⁡     (   X   )         )         =       n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (       A   ′     +       ϕ   ′     ⁡     (   X   )         )         +     λ     d   3                 (   7   )               
The output direction θ out (X), ϕ out (X) is that of the output beams outside of the waveguide (propagating in air). For a flat waveguide, equations (6), (7) hold both when the exit grating is on the front of the waveguide—in which case the output beams are first order transmission mode beams (as can be seen, equations (6), (7) correspond to the known transmission grating equations)—but also when the exit grating is on the rear of the waveguide (as in  FIG. 7F )—in which case the output beams correspond to first order reflection mode beams which, upon initial reflection from the rear exit grating propagate in a direction θ out ′(X), ϕ′ out (X) within the optical component  10  given by:
 
                     n   ⁢           ⁢   sin   ⁢           ⁢       θ   out   ′     ⁡     (   X   )       ⁢           ⁢     sin   ⁡     (       A   ′     +       ϕ   out   ′     ⁡     (   X   )         )         =     n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     sin   ⁡     (       A   ′     +       ϕ   ′     ⁡     (   X   )         )                 (     6   ′     )                   n   ⁢           ⁢   sin   ⁢           ⁢       θ   out   ′     ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (       A   ′     +       ϕ   out   ′     ⁡     (   X   )         )         =       n   ⁢           ⁢   sin   ⁢           ⁢       θ   ′     ⁡     (   X   )       ⁢           ⁢     cos   ⁡     (       A   ′     +       ϕ   ′     ⁡     (   X   )         )         +     λ     d   3           ;           (     7   ′     )               
these beams are then refracted at the front surface of the optical component, and thus exit the optical component in a direction ω in (X), ϕ in (X) given by Snell&#39;s law:
 
sin θ out ( X )= n  sin θ′ out ( X )  (8)
 
ϕ′ out ( X )=ϕ out ( X )  (9)
 
As will be apparent, the conditions of equations (6), (7) follow straight forwardly from (6′), (7′), (8) and (9). Note that such refraction at the front surface, whilst not readily visible in  FIG. 7F , will nonetheless occur in the arrangement of  FIG. 7F .
 
It can be shown from the equations (2-7) that, when
 
 d=d   1   =d   3   (10)
 
(that is, when the periods of the incoupling and exit SRGs  52 ,  56  substantially match);
 
 d   2   =d /(2 cos  A );  (11)
 
and
 
 A′= 2 A;   (12)
 
then (θ out (X), ϕ out (X))=(θ in (X), ϕ in (X)).
 
Moreover, when the condition
 
                       (     1   +     8   ⁢           ⁢     cos   2     ⁢           ⁢   A       )       &gt;     nd   λ             (   13   )               
is met, no modes besides the above-mentioned first order and zero order reflection modes are created by diffraction at the fold SRG  54 . That is, no additional undesired beams are created in the fold zone when this criteria is met. The condition (13) is met for a large range of A, from about 0 to 70 degrees.
 
     In other words, when these criteria are met, the exit SRG  56  effectively acts as an inverse to the incoupling SRG  52 , reversing the effect of the incoupling SRG diffraction for each version of the beam with which it interacts, thereby outputting what is effectively a two-dimensionally expanded version of that beam  34 (X) having an area substantially that of the exit SRG  56  (&gt;&gt;D 2  and which, as noted, is independent of the imaging optics  17 ) in the same direction as the original beam was inputted to the component  10  so that the outwardly diffracted beams form substantially the same virtual image as the inwardly inputted beams but which is perceivable over a much larger area. 
     In the example of  FIG. 9B , A≈45° i.e. so that the fold SRG and exit SRGs  54 ,  56  are oriented at substantially 45 and 90 degrees to the incoupling SRG  52  respectively, with the grating period of the fold region d 2 =d/√{square root over (2)}. However, this is only an example and, in fact, the overall efficiency of the display system is typically increased when A≥50°. 
     The above considers flat optical components, but a suitably curved optical component (that is, having a radius of curvature extending substantially along the z direction) can be configured to function as an effective lens such that the output beams  30 (X) are and are no longer as highly collimated and are not parallel, but have specific relative direction and angular separations such that each traces back to a common point of convergence—this is illustrated in  FIG. 7G , in which the common point of convergence is labelled Q. Moreover, when every image point is considered, the various points of convergence for all the different active image points lie in substantially the same plane, labelled  50 , located a distance L from the eye  37  so that the eye  37  can focus accordingly to perceive the whole image as if it were the distance L away. This can be equivalently stated as the various output beams forming substantially the same virtual version of the current display image as the corresponding input beams, but at the distance L from the eye  37  rather than at infinity. Curved optical components may be particularly suitable for short-sighted eyes unable to properly focus distant images. 
     Note, in general the “width” of the fold and exit zones does not have to be their horizontal extent—in general, the width of a fold or exit zone  14 ,  16  is that zone&#39;s extent in the general direction in which light is coupled into the fold zone  14  from the incoupling zone  12  (which is horizontal in the above examples, but more generally is a direction substantially perpendicular to the grating lines of the incoupling zone  12 ). 
     Note that the above arrangement of the light engine  13  is just an example. For example, an alternative light engine based on so-called scanning can provide a single beam, the orientation of which is fast modulated whilst simultaneously modulating its intensity and/or colour. As will be apparent, a virtual image can be simulated in this manner that is equivalent to a virtual image that would be created by collimating light of a (real) image on a display with collimating optics. 
     As is well known to persons skilled in the art, the modular transfer function (MTF) is a measure of the ability of an optical system to transfer various levels of detail from object to image. An MTF of 1.0 (or 100%) represents perfect contrast preservation, whereas values less than this mean that more and more contrast is being lost—until an MTF of 0 (or 0%), where line pairs (a line pair is a sequence of one black line and one white line) can no longer be distinguished at all. 
     The optical components described herein achieve high MTF performance due to the highly regular diffractive surfaces which produce the highly collimated output beams which are highly parallel to each other, exhibiting overall angular variation no greater (an potentially significantly less) than the angle subtended by an individual pixel from P (˜Δβ) e.g. exhibiting an overall angular variation of less than or equal to 0.5 milliradian, thus increasing the image quality of the final image as perceived by the wearer. 
     The inventors have noticed a surprising effect that has arisen due to the increased performance of the optical components described herein. That is, a banding effect is observed in the final image by the wearer.  FIG. 10  illustrates the banding effect that is observed in the final image by the wearer. The intensity over observer&#39;s position in the eye box, rather than remaining substantially constant, varies almost from zero to maximum value due to loop interference (described in more detail below). Therefore, depending on the position of the observer, the intensity varies heavily. The banding appears as vertical black and/or white stripes in the eye box. The dark and bright bands in the observed banding depend heavily on very small variations in the surface and grating line characteristics. Even some tens of nanometers changes in the surface level can create almost 100% changes in the local brightness. 
     The inventors have identified that this observed banding effect is caused by different optical paths taken by incoherent light propagating through the fold zone  14  having equal (or very close to equal) path lengths. 
       FIG. 11  illustrates a portion of the diamond-like lattice of  FIG. 9B  to explain the cause of the banding effect. A beam that is guided onto point A otherwise referred to herein as a first splitting region of the fold SRG  54  is split into two versions of that beam. Both of these versions take respective optical paths between point A before being incident on the exit grating  16 . The footprints of the two versions on the exit grating  16  substantially overlap. That is, the two versions are incident on the exit grating  16  at respective angles (having an angular variation less than or equal to 0.5 miliradian). 
     Along a first optical path, a first version (of the two versions) propagates from point A (where beam  34 (X) is first diffracted by the fold SRG  54 ) in beam  42   a (X) by way of TIR to point B otherwise referred to herein as a second splitting region of the fold SRG  54  (where beam  42   a (X) is diffracted by the fold SRG  54 ) and propagates in first order reflection beam  40   a (X) to a third splitting region of the fold SRG  54  by way of TIR. 
     Along a second optical path, a second version (of the two versions) propagates from point A in beam  34 (X) by way of TIR to point C otherwise referred to herein as a fourth splitting region of the fold SRG  54  (where beam  34 (X) is diffracted by the fold SRG  54 ) and propagates in beam  42   b (X) to a fifth splitting region of the fold SRG  54  by way of TIR. The third and fifth splitting regions of the fold SRG  54  partially overlap which is shown collectively in  FIG. 11  as point D. 
     It has been observed by the inventors that banding occurs at very high MTF, which suggests that as the difference in path lengths between path A→B→D and path A→C→D is surprisingly very small (e.g. less than 50 nanometers) due to the highly regular diffractive surfaces of the fold zone  14 , this causes destructive and constructive interference (referred to herein as loop interference) and thus dark and bright areas in the final image perceived by the wearer. 
     The inventors have recognised that, rather than attempting to eliminate the banding effect that is observed in the final image by the wearer, if the bands are shifted at a high enough rate spatially then the banding effect will not be perceivable by the wearer. 
     In embodiments, an actuator is used to introduce acoustic waves into the optical component  10 .  FIG. 12 a    illustrates an actuator  120  coupled to the rear surface of the optical component  10 . The position of the actuator  120  on the rear surface of the optical component  10  shown in  FIG. 12 a    is merely an example, and the actuator  120  may be positioned anywhere on the rear surface of the optical component  10 . By positioning the actuator  120  towards an edge of the rear surface of the optical component  10 , the viewer is advantageously not distracted by its presence. 
     The actuator  120  that is coupled to the optical component  10  is operable to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical component  10 . 
     The actuator comprises a piezo-electric element that is configured to generate the acoustic waves and transmit the generated acoustic waves into the optical component  10  in response to a voltage being applied to the piezo-electric element. The generated acoustic waves are ultrasound waves, thus the actuator  120  acts as an ultrasonic transducer. 
     The piezo-electric element may be a block of ceramic material that creates ultrasonic vibrations in response to an applied voltage. The piezo-electric element may alternatively be made of other materials well known to persons skilled in the art. The acoustic waves generated by the actuator  120  may be longitudinal, transversal or surface acoustic waves. 
     The ultrasonic vibrations propagate in the waveguide and locally change the refractive index n of the optical component  10  slightly, due to density variations (as sound does). These refractive index changes change the optical path lengths and therefore the interference in the loop. Thus, due to the acoustic waves propagating through the structure of the optical component  10 , the fringes of the bands are shifted at such a rate that the banding effect in the final image is not perceived by the wearer. 
     The frequency of the acoustic waves controls the rate at which the fringes of the bands are shifted. Thus, the frequency of the acoustic waves that are needed here have a frequency of the order of MHz, thus exceeding the limit of human visual perception of motion. 
     Whilst  FIG. 12  shows the actuator  120  being coupled to the rear surface of the optical component  10 , in alternative embodiments the actuator  120  is coupled to the front surface of the optical component  10 . In further alternative embodiments, the actuator  120  is coupled to an edge surface of the optical component  10  that adjoins the front surface of the optical component  10  with the rear surface of the optical component  10 . In other embodiments a first actuator corresponding to the actuator  120  is coupled to the rear surface of the optical component  10  and a second actuator corresponding to the actuator  120  is coupled to the front surface of the optical component  10 . 
     In one aspect of the present disclosure there is provided a display system comprising: an optical waveguide having an incoupling grating, an intermediate grating and an exit grating; an actuator coupled to the optical waveguide arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; and a light engine configured to generate multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction, whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; and wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     The actuator may comprise a piezo-electric element that is configured to generate the acoustic waves and transmit the generated acoustic waves into the optical waveguide in response to a voltage being applied to the piezo-electric element. 
     The piezo-electric element may be made of a ceramic material. 
     The generated acoustic waves may be one of: (i) longitudinal acoustic waves, (ii) transversal acoustic waves, and (iii) surface acoustic waves. 
     The generated acoustic waves may be ultrasound waves. 
     The optical waveguide may be substantially flat so as to outwardly diffract the multiple versions of each beam substantially in parallel to one another and in an outward direction which substantially matches the unique inward direction in which that beam was incoupled. Alternatively, the optical waveguide is curved so as to form the version of the virtual image a finite distance from the waveguide. 
     The multiple splitting regions may be on a first surface of the optical waveguide. 
     The actuator may be coupled to said first surface of the optical waveguide. 
     The optical waveguide may comprise a second surface opposing the first surface, and the actuator is coupled to said second surface of the optical waveguide. 
     The intermediate grating may have a height that increases in a direction along its width and away from the incoupling grating. 
     The display system may be wearable by a user. 
     The display system may be embodied in a wearable headpiece, the exit grating positioned forward of an eye of the user when worn to make the image visible to the user. 
     The display system may comprise two such optical waveguides, each of which provides image light to a different eye of the user. 
     In another aspect of the present disclosure there is provided an optical waveguide for a display system, the optical waveguide coupled to an actuator arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; the optical waveguide having an incoupling grating, an intermediate grating and an exit grating, the incoupling grating arranged to receive multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     In another aspect of the present disclosure there is provided a wearable headset comprising: a headpiece; an optical waveguide having an incoupling grating, an intermediate grating and an exit grating; an actuator coupled to the optical waveguide arranged to generate acoustic waves, wherein the generated acoustic waves are incident on, and propagate through, the optical waveguide; and a light engine mounted to the headpiece, the light engine configured to generate multiple input beams, each beam being substantially collimated and directed to the incoupling grating in a unique inward direction, whereby the multiple input beams form a virtual image; wherein the intermediate and exit grating have widths substantially larger than the beams&#39; diameters; wherein the incoupling grating is arranged to couple each beam into the intermediate grating, in which that beam is guided onto multiple splitting regions of the intermediate grating in a direction along the width of the intermediate grating; wherein the intermediate grating is arranged to split that beam at the splitting regions to provide multiple substantially parallel versions of that beam which are coupled into the exit grating, in which the multiple versions are guided onto multiple exit regions of the exit grating, the exit regions lying in a direction along the width of the exit grating; and wherein the exit grating is arranged to diffract the multiple versions of that beam outwardly, the multiple input beams thus causing multiple exit beams to exit the waveguide which form a version of the virtual image. 
     The actuator may comprise a piezo-electric element that is configured to generate the acoustic waves and transmit the generated acoustic waves into the optical waveguide in response to a voltage being applied to the piezo-electric element. 
     The piezo-electric element may be made of a ceramic material. The generated acoustic waves may be one of: (i) longitudinal acoustic waves, (ii) transversal acoustic waves, and (iii) surface acoustic waves. 
     The generated acoustic waves may be ultrasound waves. 
     Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.