Interlaced hologram replication

Abstract

Displaying a holographic image, comprising: a holographic pupil expander receiving a first (810) and second (820) holographic wavefront at a waveguide (Fig. 9A; 904), arranged between two partially re

Description

FIELD The present disclosure relates to a hologram replicator, a holographic display and a method of holographic display. More specifically, the present disclosure relates a method of reducing or eliminating crosstalk in a display using a hologram replicator. Some embodiments relate to a holographic projector, picture generating unit or head-up display. BACKGROUND AND INTRODUCTION Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well-known interference techniques to form a holographic recording, or “hologram”, comprising interference fringes. The hologram may be reconstructed by illumination with suitable light to form a two-dimensional or three-dimensional holographic reconstruction, or replay image, representative of the original object. Computer-generated holography may numerically simulate the interference process. A computer-generated hologram may be calculated by a technique based on a mathematical transformation such as a Fresnel or Fourier transform. These types of holograms may be referred to as Fresnel / Fourier transform holograms or simply Fresnel / Fourier holograms. A Fourier hologram may be considered a Fourier domain / plane representation of the object or a frequency domain / plane representation of the object. A computer-generated hologram may also be calculated by coherent ray tracing or a point cloud technique, for example. A computer-generated hologram may be encoded on a spatial light modulator arranged to modulate the amplitude and / or phase of incident light. Light modulation may be achieved using electrically-addressable liquid crystals, optically-addressable liquid crystals or micro-mirrors, for example. A spatial light modulator typically comprises a plurality of individually-addressable pixels which may also be referred to as cells or elements. The light modulation scheme may be binary, multilevel or continuous. Alternatively, the device may be continuous (i.e. is not comprised of pixels) and light modulation may therefore be continuous across the device. The spatial light modulator may be reflective meaning that modulated light is output in reflection. The spatial light modulator may equally be transmissive meaning that modulated light is output in transmission. A holographic projector may be provided using the system described herein. Such projectors have found application in head-up displays, “HUD”. SUMMARY Aspects of the present disclosure are defined in the appended independent claims. There is disclosed herein a holographic display comprising a display system and a waveguide. More generally, the waveguide may be a pupil expander or hologram replicator. The display system is arranged to form a first holographic wavefront (corresponding to a first picture or a first part of a picture) and a second holographic wavefront (corresponding to a second picture or a second part of a picture. The second picture may be different to the first picture or the first part may be different to the second part. The first part and second part may be components or sections of the same picture. The first and second holographic wavefronts encode different image or picture content. The first and second holographic wavefronts may be formed from different holograms - e.g. holograms that have been independently determined or calculated. The first and second holographic wavefronts may correspond to different input images. The waveguide is arranged to receive the first holographic wavefront and second holographic wavefront. The waveguide is further arranged to waveguide the first holographic wavefront and second holographic wavefront between a pair of at least partially reflective surfaces thereof. The display system and waveguide are respectively arranged such that a first plurality of replicas of the first holographic wavefront are emitted from a first plurality of locations on a first surface of the pair of reflective surfaces of the waveguide and a second plurality of replicas of the second holographic wavefront are emitted from a second plurality of locations on the first surface. The display system of the present disclosure defines a physical aperture (for picture-forming light such as a holographic wavefront) which may be a pupil of the holographic system. Conventionally, the display system comprises an array of pixels of a display device, such as a spatial light modulator. The array of pixels may display a hologram of a picture. The waveguide may be said to expand or replicate the pupil defined by the array of pixels and / or replicate the hologram displayed on the array of pixels. In some embodiments, pupil expansion corresponds to expansion of an eye-box of a head-up display. Through extensive simulation and experimental work, it has been found that the size of the array of pixels is critical to the holographic reconstruction process when a plurality of hologram replicas contribute to formation of the image. Specifically, it has been found that a human viewer is particularly sensitive to the physical size of the display device used to display the hologram. In real-world cases, it is found that the display device should have a minimum size relative to the pupil of the human eye (when a hologram replicator is used as described herein). In some embodiments, a dimension of the display device is greater than the average diameter of a human pupil. If the physical size of the display device is too small, it has been found that a human viewer perceives replication artefacts (that is, artefacts caused by the replication process) that degrade the viewing experience. This can drive a need for a relatively large display device and therefore a relatively large hologram (i.e. relatively high number of hologram pixels). For the avoidance of doubt, using larger pixels to form a larger device is not a viable alternative because of the negative effect this would have on the size of the holographic replay field. The best solution to the pupil size requirement is therefore to increase the number of pixels of the display device - but this adds cost, and is excessive from a holographic perspective. Specifically, the inventor identified that, above a certain threshold, increasing the number of hologram pixels does not benefit image quality. In fact, it was found that the minimum size requirement to eliminate the artefacts associated with the replication process drives a need for an “excess” of hologram pixels. The inventor identified that this is an inefficiency that could be addressed by using the “excess” pixels to form at least one additional holographic wavefront. By way of example only, this could be used to deliver additional image content to the viewer and / or provide optionality for a time-interlaced display scheme. The first plurality of locations and second plurality of locations may be at least partially spatially separated. In some embodiments, the first and second holographic wavefronts follow different optical paths through the waveguide. The replicas of the first holographic wavefront may therefore be spaced apart from the replicas of the second holographic wavefront. That is, each replica of the first holographic wavefront may be displaced relative to the corresponding replica of the second holographic wavefront. This provides design flexibility and optionality. The first plurality of locations and second plurality of locations may be spatially interleaved. The inventor further identified that by using the “excess” pixels to display at least a second hologram (rather than merely increase the number of pixels of a single hologram) an additional technical advancement can be achieved. British patent application, GB2607899A published on 21 December 2022, discloses how a shuttering device may be used to improve image quality in a holographic display using a hologram replicator. Specifically, a light shuttering device may be used to reduce or even eliminate crosstalk between hologram replicas particularly between two eyes of a viewer. In some embodiments, the device and method of the present disclosure are used to provide an alternative solution to the crosstalk problem in which the first and second (light emission) locations (of the first and second holographic wavefront, respectively) are spatially interleaved or interlaced. In fact, in these embodiments, the need for a light shuttering device can be negated as will be understood from the detailed description section that follow below. The first holographic wavefront may correspond to a first hologram of a first part of a picture and / or the second holographic wavefront may correspond to a second hologram of a second part of the picture. In some embodiments, each holographic wavefront is encoded with a different part (or parts) of the picture or field of view. The term “field of view” is used herein to refer to the area of space, in angular space, in which picture content may be display. By way of example only, the first holographic wavefront may correspond to one half of the field of view (e.g. -5 degrees to 0 degrees in the x-direction) and the second holographic wavefront may correspond to the other half of the field of view (e.g. 0 degree to +5 degrees in the x-direction). It may be said that the first holographic wavefront is encoded with one half of the field of view and the second holographic wavefront is encoded with the other half of the field of view. The x-direction may be the horizontal direction so the first hologram may be a hologram of the lefthand side of the picture (as viewed by the viewer) and the second hologram may be a hologram of the righthand side of the picture (as viewed by the viewer). In these embodiments, the first and second portions of the field of view are non-overlapping. The first part and second part of the picture may be substantially non-overlapping. The first part and second part of the picture collectively form the entire picture. In some embodiments, the likelihood of replica crosstalk at the viewer is reduced by ensuring that each section of the field of view is only encoded in one of the plurality of different holograms. The first part may comprise a first plurality of spatially separated sub-areas of the picture (field of view) and / or the second part may comprise a second plurality of spatially separated sub-areas of the picture (field of view). The first part and second part of the picture (field of view) may be immediately adjacent parts of the picture (field of view). In some embodiments, a plurality of different sections of the field of view are encoded in each hologram. This is found to be particularly effective for reducing replica crosstalk for a plurality of different viewer positions particularly when at least one additional optical components (such as an optical combiner e.g. windscreen) having a spatially-variant parameter (such as curvature) is disposed between the waveguide and viewer. In some embodiments, by dividing the field of view into a plurality of different sections for each hologram, it has been found that replica crosstalk can be substantially eliminated over a range of permitted viewing positions (e.g. eyebox). Each hologram may be arranged to divide the spatial content of the picture, or respective part of the picture, by angle. Therefore, each diffraction angle within the holographic wavefront formed by the hologram corresponds to a spatial coordinate of the picture. It is described in the detailed description of embodiments that follow how each hologram of the present disclosure may be a hologram arranged to divide the spatial content of the field of view (in at least one-dimension) by angle in the holographic wavefront. For example, each hologram may divide the horizontal content of the field of view in the spatial domain by angle in the horizontal direction in the hologram domain. For example, each x-coordinate of the field of view (i.e. line of pixel values of the field of view defined by an x-coordinate) may correspond to a unique angle on the x-z plane (horizontal plane) with respect to the surface normal of the hologram / array of pixels. The holographic display may further comprise a controller. The controller may be arranged to determine the first part and second part of the picture such that a viewer downstream of the waveguide only receives each diffraction angle once within an integration time of the viewer. Alternatively, the controller may be arranged to determine the first part and second part of the picture such that a viewer downstream of the waveguide only receives each diffraction angle from one location of the first and / or second plurality of locations on the first surface of the pair of reflective surfaces of the waveguide. In these embodiments, each diffraction angle I angle within the holographic wavefront corresponds to a different spatial section (e.g. slice) of the field of view and the controller is arranged to divide the field of view such that, from each viewing position, each angle is only received from one replica. This is found to minimize replica crosstalk. By way of example only, the controller may be able to make this division of the field of view by retrieving data stored in memory. The stored data may define how the field of view should be optimally divided for each of a plurality of different viewing positions. By way of example only, this data may be obtained by experiment or simulation using ray tracing within the abilities of the person skilled in the art. The holographic display may further comprise a viewer tracking system such as an eye-tracking and / or gaze direction tracking system. The viewer tracking system may determine a viewing position of the viewer within a viewing area. The determined viewing position may be input to the controller in order to determine the first part and second part of the picture. In notable embodiments, the holographic display further comprises an optical combiner between the waveguide and viewing area. The optical combiner may have curvature such as spatially variant curvature. The optical combiner may be a windscreen of a vehicle. In these embodiments, the complex curvature of the optical combiner effectively redirects the different hologram replicas onto different optical paths. This effectively jumbles up the replicas before they reach the viewing window e.g. eye-box. However, the device and method of the present disclosure can account for the complex curvature of the optical combiner through the software-based division of the field of view between the two holograms. The present disclosure can therefore minimize the effect of replica crosstalk through an irregular or uneven division of the field of view. The display system may comprise a spatial light modulator having a first group of pixels arranged to display the first hologram and a second group of pixels arranged to display the second hologram. Alternatively, the display system may comprise a first spatial light modulator arranged to display the first hologram and a second spatial light modulator arranged to display the second hologram. There is also disclosed herein a method of holographic display comprising a first step and second step. The first step comprises a pupil expander (or hologram replicator) receiving a first holographic wavefront and a second holographic wavefront. The second step comprises forming a first plurality of replicas of the first holographic wavefront at a first plurality of locations on a first surface of the pupil expander. The second step further comprises forming a second plurality of replicas of the second holographic wavefront at a second plurality of locations on the first surface. The first step may be performed at a first time. The second step may be performed at a second time. The second time may be different to the first time. The second step may be performed after the first step. In the present disclosure, the term “replica” is merely used to reflect that spatially modulated light is divided such that a complex light field is directed along a plurality of different optical paths. The word “replica” is used to refer to each occurrence or instance of the complex light field after a replication event - such as a partial reflection-transmission by a pupil expander. Each replica travels along a different optical path. Some embodiments of the present disclosure relate to propagation of light that is encoded with a hologram, not an image - i.e., light that is spatially modulated with a hologram of an image, not the image itself. It may therefore be said that a plurality of replicas of the hologram are formed. The person skilled in the art of holography will appreciate that the complex light field associated with propagation of light encoded with a hologram will change with propagation distance. Use herein of the term “replica” is independent of propagation distance and so the two branches or paths of light associated with a replication event are still referred to as “replicas” of each other even if the branches are a different length, such that the complex light field has evolved differently along each path. That is, two complex light fields are still considered “replicas” in accordance with this disclosure even if they are associated with different propagation distances - providing they have arisen from the same replication event or series of replication events. A “diffracted light field” or “diffractive light field” in accordance with this disclosure is a light field formed by diffraction. A diffracted light field may be formed by illuminating a corresponding diffractive pattern. In accordance with this disclosure, an example of a diffractive pattern is a hologram and an example of a diffracted light field is a holographic light field or a light field forming a holographic reconstruction of an image. The holographic light field forms a (holographic) reconstruction of an image on a replay plane. The holographic light field that propagates from the hologram to the replay plane may be said to comprise light encoded with the hologram or light in the hologram domain. A diffracted light field is characterized by a diffraction angle determined by the smallest feature size of the diffractive structure and the wavelength of the light (of the diffracted light field). In accordance with this disclosure, it may also be said that a “diffracted light field” is a light field that forms a reconstruction on a plane spatially separated from the corresponding diffractive structure. An optical system is disclosed herein for propagating a diffracted light field from a diffractive structure to a viewer. The diffracted light field may form an image. The term “hologram” is used to refer to the recording which contains amplitude information or phase information, or some combination thereof, regarding the object. The term “holographic reconstruction” is used to refer to the optical reconstruction of the object which is formed by illuminating the hologram. The system disclosed herein is described as a “holographic projector” because the holographic reconstruction is a real image and spatially-separated from the hologram. The term “replay field” is used to refer to the 2D area within which the holographic reconstruction is formed and fully focused. If the hologram is displayed on a spatial light modulator comprising pixels, the replay field will be repeated in the form of a plurality diffracted orders wherein each diffracted order is a replica of the zeroth-order replay field. The zeroth-order replay field generally corresponds to the preferred or primary replay field because it is the brightest replay field. Unless explicitly stated otherwise, the term “replay field” should be taken as referring to the zeroth-order replay field. The term “replay plane” is used to refer to the plane in space containing all the replay fields. The terms “image”, “replay image” and “image region” refer to areas of the replay field illuminated by light of the holographic reconstruction. In some embodiments, the “image” may comprise discrete spots which may be referred to as “image spots” or, for convenience only, “image pixels”. The terms “encoding”, “writing” or “addressing” are used to describe the process of providing the plurality of pixels of the SLM with a respective plurality of control values which respectively determine the modulation level of each pixel. It may be said that the pixels of the SLM are configured to “display” a light modulation distribution in response to receiving the plurality of control values. Thus, the SLM may be said to “display” a hologram and the hologram may be considered an array of light modulation values or levels. It has been found that a holographic reconstruction of acceptable quality can be formed from a “hologram” containing only phase information related to the Fourier transform of the original object. Such a holographic recording may be referred to as a phase-only hologram. Embodiments relate to a phase-only hologram but the present disclosure is equally applicable to amplitude-only holography. The present disclosure is also equally applicable to forming a holographic reconstruction using amplitude and phase information related to the Fourier transform of the original object. In some embodiments, this is achieved by complex modulation using a so-called fully complex hologram which contains both amplitude and phase information related to the original object. Such a hologram may be referred to as a fully-complex hologram because the value (grey level) assigned to each pixel of the hologram has an amplitude and phase component. The value (grey level) assigned to each pixel may be represented as a complex number having both amplitude and phase components. In some embodiments, a fully-complex computer-generated hologram is calculated. Reference may be made to the phase value, phase component, phase information or, simply, phase of pixels of the computer-generated hologram or the spatial light modulator as shorthand for “phase-delay”. That is, any phase value described is, in fact, a number (e.g. in the range 0 to 2tt) which represents the amount of phase retardation provided by that pixel. For example, a pixel of the spatial light modulator described as having a phase value of tt / 2 will retard the phase of received light by tt / 2 radians. In some embodiments, each pixel of the spatial light modulator is operable in one of a plurality of possible modulation values (e.g. phase delay values). The term “grey level” may be used to refer to the plurality of available modulation levels. For example, the term “grey level” may be used for convenience to refer to the plurality of available phase levels in a phase-only modulator even though different phase levels do not provide different shades of grey. The term “grey level” may also be used for convenience to refer to the plurality of available complex modulation levels in a complex modulator. The hologram therefore comprises an array of grey levels - that is, an array of light modulation values such as an array of phase-delay values or complex modulation values. The hologram is also considered a diffractive pattern because it is a pattern that causes diffraction when displayed on a spatial light modulator and illuminated with light having a wavelength comparable to, generally less than, the pixel pitch of the spatial light modulator. Reference is made herein to combining the hologram with other diffractive patterns such as diffractive patterns functioning as a lens or grating. For example, a diffractive pattern functioning as a grating may be combined with a hologram to translate the replay field on the replay plane or a diffractive pattern functioning as a lens may be combined with a hologram to focus the holographic reconstruction on a replay plane in the near field. Although different embodiments and groups of embodiments may be disclosed separately in the detailed description which follows, any feature of any embodiment or group of embodiments may be combined with any other feature or combination of features of any embodiment or group of embodiments. That is, all possible combinations and permutations of features disclosed in the present disclosure are envisaged. BRIEF DESCRIPTION OF THE DRAWINGS Specific embodiments are described by way of example only with reference to the following figures: Figure 1 is a schematic showing a reflective SLM producing a holographic reconstruction on a screen; Figure 2 shows an image for projection comprising eight image areas / components, V1 to V8, and cross-sections of the corresponding hologram channels, H1-H8; Figure 3 shows a hologram displayed on an LCOS that directs light into a plurality of discrete areas; Figure 4 shows a system, including a display device that displays a hologram that has been calculated as illustrated in Figures 2 and 3; Figure 5A shows a perspective view of a first example two-dimensional pupil expander comprising two replicators each comprising pairs of stacked surfaces; Figure 5B shows a perspective view of a first example two-dimensional pupil expander comprising two replicators each in the form of a solid waveguide; Figure 6A to 6J show the functionality of a light shuttering device in accordance with the prior art; Figure 7A shows the replication of a holographic wavefront; Figure 7B shows a field of view or image encoded in the holographic wavefront of Figure 7A; Figure 8A shows the interleaving of three different holographic wavefronts from three different holograms; Figures 8B to 8D show the input image used for each of the three different holograms; Figure 9A shows the effect of a nonlinear optical combiner of the replication process; and Figures 9B to 9D show how an irregular division of the field of view may be used to counteract the nonlinear optical combiner. The same reference numbers will be used throughout the drawings to refer to the same or like parts. DETAILED DESCRIPTION OF EMBODIMENTS The present invention is not restricted to the embodiments described in the following but extends to the full scope of the appended claims. That is, the present invention may be embodied in different forms and should not be construed as limited to the described embodiments, which are set out for the purpose of illustration. Terms of a singular form may include plural forms unless specified otherwise. A structure described as being formed at an upper portion / lower portion of another structure or on / under the other structure should be construed as including a case where the structures contact each other and, moreover, a case where a third structure is disposed there between. In describing a time relationship - for example, when the temporal order of events is described as “after”, “subsequent”, “next”, “before” or suchlike - the present disclosure should be taken to include continuous and non-continuous events unless otherwise specified. For example, the description should be taken to include a case which is not continuous unless wording such as “just”, “immediate” or “direct” is used. Although the terms “first”, “second”, etc. may be used herein to describe various elements, these elements are not to be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the appended claims. Features of different embodiments may be partially or overall coupled to or combined with each other, and may be variously inter-operated with each other. Some embodiments may be carried out independently from each other, or may be carried out together in co-dependent relationship. In the present disclosure, the term “substantially” when applied to a structural units of an apparatus may be interpreted as the technical feature of the structural units being produced within the technical tolerance of the method used to manufacture it. Conventional optical configuration for holographic projection Figure 1 shows an embodiment in which a computer-generated hologram is encoded on a single spatial light modulator. The computer-generated hologram is a Fourier transform of the object for reconstruction. It may therefore be said that the hologram is a Fourier domain or frequency domain or spectral domain representation of the object. In this embodiment, the spatial light modulator is a reflective liquid crystal on silicon, “LCOS”, device. The hologram is encoded on the spatial light modulator and a holographic reconstruction is formed at a replay field, for example, a light receiving surface such as a screen or diffuser. A light source 110, for example a laser or laser diode, is disposed to illuminate the SLM 140 via a collimating lens 111. The collimating lens causes a generally planar wavefront of light to be incident on the SLM. In Figure 1, the direction of the wavefront is off-normal (e.g. two or three degrees away from being truly orthogonal to the plane of the transparent layer). However, in other embodiments, the generally planar wavefront is provided at normal incidence and a beam splitter arrangement is used to separate the input and output optical paths. In the embodiment shown in Figure 1, the arrangement is such that light from the light source is reflected off a mirrored rear surface of the SLM and interacts with a light-modulating layer to form an exit wavefront 112. The exit wavefront 112 is applied to optics including a Fourier transform lens 120, having its focus at a screen 125. More specifically, the Fourier transform lens 120 receives a beam of modulated light from the SLM 140 and performs a frequency-space transformation to produce a holographic reconstruction at the screen 125. Notably, in this type of holography, each pixel of the hologram contributes to the whole reconstruction. There is not a one-to-one correlation between specific points (or image pixels) on the replay field and specific light-modulating elements (or hologram pixels). In other words, modulated light exiting the light-modulating layer is distributed across the replay field. In these embodiments, the position of the holographic reconstruction in space is determined by the dioptric (focusing) power of the Fourier transform lens. In the embodiment shown in Figure 1, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens and the Fourier transform is performed optically. Any lens can act as a Fourier transform lens but the performance of the lens will limit the accuracy of the Fourier transform it performs. The skilled person understands how to use a lens to perform an optical Fourier transform In some embodiments of the present disclosure, the lens of the viewer’s eye performs the hologram to image transformation. Hologram calculation In some embodiments, the computer-generated hologram is a Fourier transform hologram, or simply a Fourier hologram or Fourier-based hologram, in which an image is reconstructed in the far field by utilising the Fourier transforming properties of a positive lens. The Fourier hologram is calculated by Fourier transforming the desired light field in the replay plane back to the lens plane. Computer-generated Fourier holograms may be calculated using Fourier transforms. Embodiments relate to Fourier holography and Gerchberg-Saxton type algorithms by way of example only. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms which may be calculated by a similar method. In some embodiments, the hologram is a phase or phase-only hologram. However, the present disclosure is also applicable to holograms calculated by other techniques such as those based on point cloud methods. In some embodiments, the hologram engine is arranged to exclude from the hologram calculation the contribution of light blocked by a limiting aperture of the display system. British patent application 2101666.2, filed 5 February 2021 and incorporated herein by reference, discloses a first hologram calculation method in which eye-tracking and ray tracing are used to identify a sub-area of the display device for calculation of a point cloud hologram which eliminates ghost images. The sub-area of the display device corresponds with the aperture, of the present disclosure, and is used exclude light paths from the hologram calculation. British patent application 2112213.0, filed 26 August 2021 and incorporated herein by reference, discloses a second method based on a modified Gerchberg-Saxton type algorithm which includes steps of light field cropping in accordance with pupils of the optical system during hologram calculation. The cropping of the light field corresponds with the determination of a limiting aperture of the present disclosure. British patent application 2118911.3, filed 23 December 2021 and also incorporated herein by reference, discloses a third method of calculating a hologram which includes a step of determining a region of a so-called extended modulator formed by a hologram replicator. The region of the extended modulator is also an aperture in accordance with this disclosure. In some embodiments, there is provided a real-time engine arranged to receive image data and calculate holograms in real-time using the algorithm. In some embodiments, the image data is a video comprising a sequence of image frames. In other embodiments, the holograms are pre calculated, stored in computer memory and recalled as needed for display on a SLM. That is, in some embodiments, there is provided a repository of predetermined holograms. Large field of view using small display device Broadly, the present disclosure relates to image projection. It relates to a method of image projection and an image projector which comprises a display device. The present disclosure also relates to a projection system comprising the image projector and a viewing system, in which the image projector projects or relays light from the display device to the viewing system. The present disclosure is equally applicable to a monocular and binocular viewing system. The viewing system may comprise a viewer’s eye or eyes. The viewing system comprises an optical element having optical power (e.g., lens / es of the human eye) and a viewing plane (e.g., retina of the human eye / s). The projector may be referred to as a ‘light engine’. The display device and the image formed (or perceived) using the display device are spatially separated from one another. The image is formed, or perceived by a viewer, on a display plane. In some embodiments, the image is a virtual image and the display plane may be referred to as a virtual image plane. In other examples, the image is a real image formed by holographic reconstruction and the image is projected or relayed to the viewing plane. In these other examples, spatially modulated light of an intermediate holographic reconstruction formed either in free space or on a screen or other light receiving surface between the display device and the viewer, is propagated to the viewer. In both cases, an image is formed by illuminating a diffractive pattern (e.g., hologram or kinoform) displayed on the display device. The display device comprises pixels. The pixels of the display may display a diffractive pattern or structure that diffracts light. The diffracted light may form an image at a plane spatially separated from the display device. In accordance with well-understood optics, the magnitude of the maximum diffraction angle is determined by the size of the pixels and other factors such as the wavelength of the light. In embodiments, the display device is a spatial light modulator such as liquid crystal on silicon (“LCOS”) spatial light modulator (SLM). Light propagates over a range of diffraction angles (for example, from zero to the maximum diffractive angle) from the LCOS, towards a viewing entity / system such as a camera or an eye. In some embodiments, magnification techniques may be used to increase the range of available diffraction angles beyond the conventional maximum diffraction angle of an LCOS. In some embodiments, the (light of a) hologram itself is propagated to the eyes. For example, spatially modulated light of the hologram (that has not yet been fully transformed to a holographic reconstruction, i.e. image) - that may be informally said to be “encoded” with / by the hologram - is propagated directly to the viewer’s eyes. A real or virtual image may be perceived by the viewer. In these embodiments, there is no intermediate holographic reconstruction I image formed between the display device and the viewer. It is sometimes said that, in these embodiments, the lens of the eye performs a hologram-to-image conversion or transform. The projection system, or light engine, may be configured so that the viewer effectively looks directly at the display device. Reference is made herein to a “light field” which is a “complex light field”. The term “light field” merely indicates a pattern of light having a finite size in at least two orthogonal spatial directions, e.g. x and y. The word “complex” is used herein merely to indicate that the light at each point in the light field may be defined by an amplitude value and a phase value, and may therefore be represented by a complex number or a pair of values. For the purpose of hologram calculation, the complex light field may be a two-dimensional array of complex numbers, wherein the complex numbers define the light intensity and phase at a plurality of discrete locations within the light field. In accordance with the principles of well-understood optics, the range of angles of light propagating from a display device that can be viewed, by an eye or other viewing entity / system, varies with the distance between the display device and the viewing entity. At a 1 metre viewing distance, for example, only a small range of angles from an LCOS can propagate through an eye’s pupil to form an image at the retina for a given eye position. The range of angles of light rays that are propagated from the display device, which can successfully propagate through an eye’s pupil to form an image at the retina for a given eye position, determines the portion of the image that is ‘visible’ to the viewer. In other words, not all parts of the image are visible from any one point on the viewing plane (e.g., any one eye position within a viewing window such as eyebox.) In some embodiments, the image perceived by a viewer is a virtual image that appears upstream of the display device - that is, the viewer perceives the image as being further away from them than the display device. Conceptually, it may therefore be considered that the viewer is looking at a virtual image through an ‘display device-sized window’, which may be very small, for example 1cm in diameter, at a relatively large distance, e.g., 1 metre. And the user will be viewing the display device-sized window via the pupil(s) of their eye(s), which can also be very small. Accordingly, the field of view becomes small and the specific angular range that can be seen depends heavily on the eye position, at any given time. A pupil expander addresses the problem of how to increase the range of angles of light rays that are propagated from the display device that can successfully propagate through an eye’s pupil to form an image. The display device is generally (in relative terms) small and the projection distance is (in relative terms) large. In some embodiments, the projection distance is at least one - such as, at least two - orders of magnitude greater than the diameter, or width, of the entrance pupil and / or aperture of the display device (i.e., size of the array of pixels). Use of a pupil expander increases the viewing area (i.e., user’s eye-box) laterally, thus enabling some movement of the eye / s to occur, whilst still enabling the user to see the image. As the skilled person will appreciate, in an imaging system, the viewing area (user’s eye box) is the area in which a viewer’s eyes can perceive the image. The present disclosure encompasses noninfinite virtual image distances - that is, near-field virtual images. Conventionally, a two-dimensional pupil expander comprises one or more one-dimensional optical waveguides each formed using a pair of opposing reflective surfaces, in which the output light from a surface forms a viewing window or eye-box. Light received from the display device (e.g., spatially modulated light from a LCOS) is replicated by the or each waveguide so as to increase the field of view (or viewing area) in at least one dimension. In particular, the waveguide enlarges the viewing window due to the generation of extra rays or “replicas” by division of amplitude of the incident wavefront. The display device may have an active or display area having a first dimension that may be less than 10 cms such as less than 5 cms or less than 2 cms. The propagation distance between the display device and viewing system may be greater than 1 m such as greater than 1.5 m or greater than 2 m. The optical propagation distance within the waveguide may be up to 2 m such as up to 1.5 m or up to 1 m. The method may be capable of receiving an image and determining a corresponding hologram of sufficient quality in less than 20 ms such as less than 15 ms or less than 10 ms. In some embodiments - described only by way of example of a diffracted or holographic light field in accordance with this disclosure - a hologram is configured to route light into a plurality of channels, each channel corresponding to a different part (i.e. sub-area) of an image. The channels formed by the diffractive structure are referred to herein as “hologram channels” merely to reflect that they are channels of light encoded by the hologram with image information. It may be said that the light of each channel is in the hologram domain rather than the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram and the hologram domain is therefore the Fourier or frequency domain. The hologram may equally be a Fresnel or Fresnel transform hologram. The hologram may also be a point cloud hologram. The hologram is described herein as routing light into a plurality of hologram channels to reflect that the image that can be reconstructed from the hologram has a finite size and can be arbitrarily divided into a plurality of image sub-areas, wherein each hologram channel would correspond to each image sub-area. Importantly, the hologram of this example is characterised by how it distributes the image content when illuminated. Specifically and uniquely, the hologram divides the image content by angle. That is, each point on the image is associated with a unique light ray angle in the spatially modulated light formed by the hologram when illuminated - at least, a unique pair of angles because the hologram is two-dimensional. For the avoidance of doubt, this hologram behaviour is not conventional. The spatially modulated light formed by this special type of hologram, when illuminated, may be divided into a plurality of hologram channels, wherein each hologram channel is defined by a range of light ray angles (in two-dimensions). It will be understood from the foregoing that any hologram channel (i.e. sub-range of light ray angles) that may be considered in the spatially modulated light will be associated with a respective part or sub-area of the image. That is, all the information needed to reconstruct that part or sub-area of the image is contained within a sub-range of angles of the spatially modulated light formed from the hologram of the image. When the spatially modulated light is observed as a whole, there is not necessarily any evidence of a plurality of discrete light channels. Nevertheless, the hologram may still be identified. For example, if only a continuous part or subarea of the spatially modulated light formed by the hologram is reconstructed, only a sub-area of the image should be visible. If a different, continuous part or sub-area of the spatially modulated light is reconstructed, a different sub-area of the image should be visible. A further identifying feature of this type of hologram is that the shape of the cross-sectional area of any hologram channel substantially corresponds to (i.e. is substantially the same as) the shape of the entrance pupil although the size may be different - at least, at the correct plane for which the hologram was calculated. Each light I hologram channel propagates from the hologram at a different angle or range of angles. Whilst these are example ways of characterising or identifying this type of hologram, other ways may be used. In summary, the hologram disclosed herein is characterised and identifiable by how the image content is distributed within light encoded by the hologram. Again, for the avoidance of any doubt, reference herein to a hologram configured to direct light or angularly-divide an image into a plurality of hologram channels is made by way of example only and the present disclosure is equally applicable to pupil expansion of any type of holographic light field or even any type of diffractive or diffracted light field. The system can be provided in a compact and streamlined physical form. This enables the system to be suitable for a broad range of real-world applications, including those for which space is limited and real-estate value is high. For example, it may be implemented in a head-up display (HUD) such as a vehicle or automotive HUD. In accordance with the present disclosure, pupil expansion is provided for diffracted or diffractive light, which may comprise diverging ray bundles. The diffracted light field may be defined by a “light cone”. Thus, the size of the diffracted light field (as defined on a two-dimensional plane) increases with propagation distance from the corresponding diffractive structure (i.e. display device). It can be said that the pupil expander / s replicate the hologram or form at least one replica of the hologram, to convey that the light delivered to the viewer is spatially modulated in accordance with a hologram. In some embodiments, two one-dimensional waveguide pupil expanders are provided, each onedimensional waveguide pupil expander being arranged to effectively increase the size of the exit pupil of the system by forming a plurality of replicas or copies of the exit pupil (or light of the exit pupil) of the spatial light modulator. The exit pupil may be understood to be the physical area from which light is output by the system. It may also be said that each waveguide pupil expander is arranged to expand the size of the exit pupil of the system. It may also be said that each waveguide pupil expander is arranged to expand / increase the size of the eye box within which a viewer’s eye can be located, in order to see / receive light that is output by the system. Light channelling The hologram formed in accordance with some embodiments, angularly-divides the image content to provide a plurality of hologram channels which may have a cross-sectional shape defined by an aperture of the optical system. The hologram is calculated to provide this channelling of the diffracted light field. In some embodiments, this is achieved during hologram calculation by considering an aperture (virtual or real) of the optical system, as described above. Figures 2 and 3 show an example of this type of hologram that may be used in conjunction with a pupil expander as disclosed herein. However, this example should not be regarded as limiting with respect to the present disclosure. Figure 2 shows an image 252 for projection comprising eight image areas / components, V1 to V8. Figure 2 shows eight image components by way of example only and the image 252 may be divided into any number of components. Figure 2 also shows an encoded light pattern 254 (i.e., hologram) that can reconstruct the image 252 - e.g., when transformed by the lens of a suitable viewing system. The encoded light pattern 254 comprises first to eighth sub-holograms or components, H1 to H8, corresponding to the first to eighth image components / areas, V1 to V8. Figure 2 further shows how a hologram may decompose the image content by angle. The hologram may therefore be characterised by the channelling of light that it performs. This is illustrated in Figure 3. Specifically, the hologram in this example directs light into a plurality of discrete areas. The discrete areas are discs in the example shown but other shapes are envisaged. The size and shape of the optimum disc may, after propagation through the waveguide, be related to the size and shape of an aperture of the optical system such as the entrance pupil of the viewing system. Figure 4 shows a system 400, including a display device that displays a hologram that has been calculated as illustrated in Figures 2 and 3. The system 400 comprises a display device, which in this arrangement comprises an LCOS 402. The LCOS 402 is arranged to display a modulation pattern (or ‘diffractive pattern') comprising the hologram and to project light that has been holographically encoded towards an eye 405 that comprises a pupil that acts as an aperture 404, a lens 409, and a retina (not shown) that acts as a viewing plane. There is a light source (not shown) arranged to illuminate the LCOS 402. The lens 409 of the eye 405 performs a hologram-to-image transformation. The light source may be of any suitable type. For example, it may comprise a laser light source. The viewing system 400 further comprises a waveguide 408 positioned between the LCOS 402 and the eye 405. The presence of the waveguide 408 enables all angular content from the LCOS 402 to be received by the eye, even at the relatively large projection distance shown. This is because the waveguide 508 acts as a pupil expander, in a manner that is well known and so is described only briefly herein. In brief, the waveguide 408 shown in Figure 4 comprises a substantially elongate formation. In this example, the waveguide 408 comprises an optical slab of refractive material, but other types of waveguide are also well known and may be used. The waveguide 408 is located so as to intersect the light cone (i.e., the diffracted light field) that is projected from the LCOS 402, for example at an oblique angle. In this example, the size, location, and position of the waveguide 408 are configured to ensure that light from each of the eight ray bundles, within the light cone, enters the waveguide 408. Light from the light cone enters the waveguide 408 via its first planar surface (located nearest the LCOS 402) and is guided at least partially along the length of the waveguide 408, before being emitted via its second planar surface, substantially opposite the first surface (located nearest the eye). As will be well understood, the second planar surface is partially reflective, partially transmissive. In other words, when each ray of light travels within the waveguide 408 from the first planar surface and hits the second planar surface, some of the light will be transmitted out of the waveguide 408 and some will be reflected by the second planar surface, back towards the first planar surface. The first planar surface is reflective, such that all light that hits it, from within the waveguide 408, will be reflected back towards the second planar surface. Therefore, some of the light may simply be refracted between the two planar surfaces of the waveguide 408 before being transmitted, whilst other light may be reflected, and thus may undergo one or more reflections, (or ‘bounces’) between the planar surfaces of the waveguide 408, before being transmitted. Figure 4 shows a total of nine “bounce” points, B0 to B8, along the length of the waveguide 408. Although light relating to all points of the image (V1-V8) as shown in Figure 2 is transmitted out of the waveguide at each “bounce” from the second planar surface of the waveguide 408, only the light from one angular part of the image (e.g. light of one of V1 to V8) has a trajectory that enables it to reach the eye 405, from each respective “bounce” point, B0 to B8. Moreover, light from a different angular part of the image, V1 to V8, reaches the eye 405 from each respective “bounce” point. Therefore, each angular channel of encoded light reaches the eye only once, from the waveguide 408, in the example of Figure 4. The waveguide 408 forms a plurality of replicas of the hologram, at the respective “bounce” points B1 to B8 along its length, corresponding to the direction of pupil expansion. As shown in Figure 5, the plurality of replicas may be extrapolated back, in a straight line, to a corresponding plurality of replica or virtual display devices 402’. This process corresponds to the step of “unfolding” an optical path within the waveguide, so that a light ray of a replica is extrapolated back to a “virtual surface” without internal reflection within the waveguide. Thus, the light of the expanded exit pupil may be considered to originate from a virtual surface (also called an “extended modulator” herein) comprising the display device 402 and the replica display devices 402’. Although virtual images, which require the eye to transform received modulated light in order to form a perceived image, have generally been discussed herein, the methods and arrangements described herein can be applied to real images. Two-Dimensional Pupil Expansion Whilst the arrangement shown in Figure 4 includes a single waveguide that provides pupil expansion in one dimension, pupil expansion can be provided in more than one dimension, for example in two dimensions. Moreover, whilst the example in Figure 4 uses a hologram that has been calculated to create channels of light, each corresponding to a different portion of an image, the present disclosure and the systems that are described herebelow are not limited to such a hologram type. Figure 5A shows a perspective view of a system 500 comprising two replicators, 504, 506 arranged for expanding a light beam 502 in two dimensions. In the system 500 of Figure 5A, the first replicator 504 comprises a first pair of surfaces, stacked parallel to one another, and arranged to provide replication - or, pupil expansion - in a similar manner to the waveguide 408 of Figure 4. The first pair of surfaces are similarly (in some cases, identically) sized and shaped to one another and are substantially elongate in one direction. The collimated light beam 502 is directed towards an input on the first replicator 504. Due to a process of internal reflection between the two surfaces, and partial transmission of light from each of a plurality of output points on one of the surfaces (the upper surface, as shown in Figure 5A), which will be familiar to the skilled reader, light of the light beam 502 is replicated in a first direction, along the length of the first replicator 504. Thus, a first plurality of replica light beams 508 is emitted from the first replicator 504, towards the second replicator 506. The second replicator 506 comprises a second pair of surfaces stacked parallel to one another, arranged to receive each of the collimated light beams of the first plurality of light beams 508 and further arranged to provide replication - or, pupil expansion - by expanding each of those light beams in a second direction, substantially orthogonal to the first direction. The first pair of surfaces are similarly (in some cases, identically) sized and shaped to one another and are substantially rectangular. The rectangular shape is implemented for the second replicator in order for it to have length along the first direction, in order to receive the first plurality of light beams 508, and to have length along the second, orthogonal direction, in order to provide replication in that second direction. Due to a process of internal reflection between the two surfaces, and partial transmission of light from each of a plurality of output points on one of the surfaces (the upper surface, as shown in Figure 5A), light of each light beam within the first plurality of light beams 508 is replicated in the second direction. Thus, a second plurality of light beams 510 is emitted from the second replicator 506, wherein the second plurality of light beams 510 comprises replicas of the input light beam 502 along each of the first direction and the second direction. Thus, the second plurality of light beams 510 may be regarded as comprising a two-dimensional grid, or array, of replica light beams. Thus, it can be said that the first and second replicators 504, 505 of Figure 5A combine to provide a two-dimensional replicator (or, “two-dimensional pupil expander”). Thus, the replica light beams 510 may be emitted along an optical path to an expanded eye-box of a display system, such as a head-up display. In the system of Figure 5A, the first replicator 504 is a waveguide comprising a pair of elongate rectilinear reflective surfaces, stacked parallel to one another, and, similarly, the second replicator 504 is a waveguide comprising a pair of rectangular reflective surfaces, stacked parallel to one another. In other systems, the first replicator may be a solid elongate rectilinear waveguide and the second replicator may be a solid planar rectangular shaped waveguide, wherein each waveguide comprises an optically transparent solid material such as glass. In this case, the pair of parallel reflective surfaces are formed by a pair of opposed major sidewalls optionally comprising respective reflective and reflective-transmissive surface coatings, familiar to the skilled reader. Figure 5B shows a perspective view of a system 500 comprising two replicators, 520, 540 arranged for replicating a light beam 522 in two dimensions, in which the first replicator is a solid elongated waveguide 520 and the second replicator is a solid planar waveguide 540. In the system of Figure 5B, the first replicator / waveguide 520 is arranged so that its pair of elongate parallel reflective surfaces 524a, 524b are perpendicular to the plane of the second replicator / waveguide 540. Accordingly, the system comprises an optical coupler arranged to couple light from an output port of first replicator 520 into an input port of the second replicator 540. In the illustrated arrangement, the optical coupler is a planar / fold mirror 530 arranged to fold or turn the optical path of light to achieve the required optical coupling from the first replicator to the second replicator. As shown in Figure 5B, the mirror 530 is arranged to receive light -comprising a one-dimensional array of replicas extending in the first dimension - from the output port I reflective-transmissive surface 524a of the first replicator / waveguide 520. The mirror 530 is tilted so as to redirect the received light onto an optical path to an input port in the (fully) reflective surface of second replicator 540 at an angle to provide waveguiding and replica formation, along its length in the second dimension. It will be appreciated that the mirror 530 is one example of an optical element that can redirect the light in the manner shown, and that one or more other elements may be used instead, to perform this task. In the illustrated arrangement, the (partially) reflective-transmissive surface 524a of the first replicator 520 is adjacent the input port of the first replicator / waveguide 520 that receives input beam 522 at an angle to provide waveguiding and replica formation, along its length in the first dimension. Thus, the input port of first replicator / waveguide 520 is positioned at an input end thereof at the same surface as the reflective-transmissive surface 524a. The skilled reader will understand that the input port of the first replicator / waveguide 520 may be at any other suitable position. Accordingly, the arrangement of Figure 5B enables the first replicator 520 and the mirror 530 to be provided as part of a first relatively thin layer in a plane in the first and third dimensions (illustrated as an x-z plane). In particular, the size or “height” of a first planar layer - in which the first replicator 520 is located - in the second dimension (illustrated as the y dimension) is reduced. The mirror 530 is configured to direct the light away from a first layer / plane, in which the first replicator 520 is located (i.e. the “first planar layer"), and direct it towards a second layer / plane, located above and substantially parallel to the first layer / plane, in which the second replicator 540 is located (i.e. a “second planar layer”). Thus, the overall size or “height” of the system - comprising the first and second replicators 520, 540 and the mirror 530 located in the stacked first and second planar layers in the first and third dimensions (illustrated as an x-z plane) - in the second dimension (illustrated as the y dimension) is compact. The skilled reader will understand that many variations of the arrangement of Figure 5B for implementing the present disclosure are possible and contemplated. The image projector may be arranged to project a diverging or diffracted light field. In some embodiments, the light field is encoded with a hologram. In some embodiments, the diffracted light field comprises diverging ray bundles. In some embodiments, the image formed by the diffracted light field is a virtual image. In some embodiments, the first pair of parallel I complementary surfaces are elongate or elongated surfaces, being relatively long along a first dimension and relatively short along a second dimension, for example being relatively short along each of two other dimensions, with each dimension being substantially orthogonal to each of the respective others. The process of reflection / transmission of the light between / from the first pair of parallel surfaces is arranged to cause the light to propagate within the first waveguide pupil expander, with the general direction of light propagation being in the direction along which the first waveguide pupil expander is relatively long (i.e., in its “elongate” direction). There is disclosed herein a system that forms an image using diffracted light and provides an eye-box size and field of view suitable for real-world application - e.g. in the automotive industry by way of a head-up display. The diffracted light is light forming a holographic reconstruction of the image from a diffractive structure - e.g. hologram such as a Fourier or Fresnel hologram. The use diffraction and a diffractive structure necessitates a display device with a high density of very small pixels (e.g. 1 micrometer) - which, in practice, means a small display device (e.g. 1 cm). The inventors have addressed a problem of howto provide 2D pupil expansion with a diffracted light field e.g. diffracted light comprising diverging (not collimated) ray bundles. In some embodiments, the display system comprises a display device - such as a pixelated display device, for example a spatial light modulator (SLM) or Liquid Crystal on Silicon (LCoS) SLM - which is arranged to provide or form the diffracted or diverging light. In such aspects, the aperture of the spatial light modulator (SLM) is a limiting aperture of the system. That is, the aperture of the spatial light modulator - more specifically, the size of the area delimiting the array of light modulating pixels comprised within the SLM - determines the size (e.g. spatial extent) of the light ray bundle that can exit the system. In accordance with this disclosure, it is stated that the exit pupil of the system is expanded to reflect that the exit pupil of the system (that is limited by the small display device having a pixel size for light diffraction) is made larger or bigger or greater in spatial extend by the use of at least one pupil expander. The diffracted or diverging light field may be said to have “a light field size”, defined in a direction substantially orthogonal to a propagation direction of the light field. Because the light is diffracted I diverging, the light field size increases with propagation distance. In some embodiments, the diffracted light field is spatially-modulated in accordance with a hologram. In other words, in such aspects, the diffractive light field comprises a “holographic light field”. The hologram may be displayed on a pixelated display device. The hologram may be a computer-generated hologram (CGH). It may be a Fourier hologram or a Fresnel hologram or a point-cloud hologram or any other suitable type of hologram. The hologram may, optionally, be calculated so as to form channels of hologram light, with each channel corresponding to a different respective portion of an image that is intended to be viewed (or perceived, if it is a virtual image) by the viewer. The pixelated display device may be configured to display a plurality of different holograms, in succession or in sequence. Each of the aspects and embodiments disclosed herein may be applied to the display of multiple holograms. The output port of the first waveguide pupil expander may be coupled to an input port of a second waveguide pupil expander. The second waveguide pupil expander may be arranged to guide the diffracted light field - including some of, preferably most of, preferably all of, the replicas of the light field that are output by the first waveguide pupil expander - from its input port to a respective output port by internal reflection between a third pair of parallel surfaces of the second waveguide pupil expander. The first waveguide pupil expander may be arranged to provide pupil expansion, or replication, in a first direction and the second waveguide pupil expander may be arranged to provide pupil expansion, or replication, in a second, different direction. The second direction may be substantially orthogonal to the first direction. The second waveguide pupil expander may be arranged to preserve the pupil expansion that the first waveguide pupil expander has provided in the first direction and to expand (or, replicate) some of, preferably most of, preferably all of, the replicas that it receives from the first waveguide pupil expander in the second, different direction. The second waveguide pupil expander may be arranged to receive the light field directly or indirectly from the first waveguide pupil expander. One or more other elements may be provided along the propagation path of the light field between the first and second waveguide pupil expanders. The first waveguide pupil expander may be substantially elongated and the second waveguide pupil expander may be substantially planar. The elongated shape of the first waveguide pupil expander may be defined by a length along a first dimension. The planar, or rectangular, shape of the second waveguide pupil expander may be defined by a length along a first dimension and a width, or breadth, along a second dimension substantially orthogonal to the first dimension. A size, or length, of the first waveguide pupil expander along its first dimension make correspond to the length or width of the second waveguide pupil expander along its first or second dimension, respectively. A first surface of the pair of parallel surfaces of the second waveguide pupil expander, which comprises its input port, may be shaped, sized, and / or located so as to correspond to an area defined by the output port on the first surface of the pair of parallel surfaces on the first waveguide pupil expander, such that the second waveguide pupil expander is arranged to receive each of the replicas output by the first waveguide pupil expander. The first and second waveguide pupil expander may collectively provide pupil expansion in a first direction and in a second direction perpendicular to the first direction, optionally, wherein a plane containing the first and second directions is substantially parallel to a plane of the second waveguide pupil expander. In other words, the first and second dimensions that respectively define the length and breadth of the second waveguide pupil expander may be parallel to the first and second directions, respectively, (or to the second and first directions, respectively) in which the waveguide pupil expanders provide pupil expansion. The combination of the first waveguide pupil expander and the second waveguide pupil expander may be generally referred to as being a “pupil expander”. It may be said that the expansion / replication provided by the first and second waveguide expanders has the effect of expanding an exit pupil of the display system in each of two directions. An area defined by the expanded exit pupil may, in turn define an expanded eye-box area, from which the viewer can receive light of the input diffracted or diverging light field. The eye-box area may be said to be located on, or to define, a viewing plane. The two directions in which the exit pupil is expanded may be coplanar with, or parallel to, the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. Alternatively, in arrangements that comprise other elements such as an optical combiner, for example the windscreen (or, windshield) of a vehicle, the exit pupil may be regarded as being an exit pupil from that other element, such as from the windscreen. In such arrangements, the exit pupil may be non-coplanar and non-parallel with the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. For example, the exit pupil may be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. The viewing plane, and / or the eye-box area, may be non-coplanar or non-parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. For example, a viewing plane may be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. In order to provide suitable launch conditions to achieve internal reflection within the first and second waveguide pupil expanders, an elongate dimension of the first waveguide pupil expander may be tilted relative to the first and second dimensions of the second waveguide pupil expander. Combiner shape compensation An advantage of projecting a hologram to the eye-box is that optical compensation can be encoded in the hologram (see, for example, European patent 2936252 incorporated herein by herein). The present disclosure is compatible with holograms that compensate for the complex curvature of an optical combiner used as part of the projection system. In some embodiments, the optical combiner is the windscreen of a vehicle. Full details of this approach are provided in European patent 2936252 and are not repeated here because the detailed features of those systems and methods are not essential to the new teaching of this disclosure herein and are merely exemplary of configurations that benefit from the teachings of the present disclosure. Light shuttering device A light shuttering device is described in this section. For the avoidance of doubt, embodiments of the present disclosure replace the functionality of the light shuttering device with a new approach. However, an understanding of the functionality of this component is useful for appreciating the functionality achieved by embodiments. The light shuttering device is more broadly referred to below as a control device. British patent application 2108456.1, filed 14 June 2021 and incorporated herein by reference, discloses in detail a holographic display system comprising at least one hologram replicator / waveguide pupil expander and the control device. A brief description is provided below, with reference to Figures 6A to 6J, for completeness. A holographic display using a hologram replicator may require a control device (e.g. light shuttering device) to control the delivery of light from a light channelling hologram to the viewer. The holographic projector may further comprise a control device arranged to control the delivery of angular channels to the eye-box position. The reader will understand from at least this prior disclosure that the optical configuration of the control device is fundamentally based upon the eye-box position of the user and is compatible with any hologram calculation method that achieves the light channeling described herein. It may be said that the control device is a light shuttering or aperturing device. The light shuttering device may comprise a 1D array of apertures or windows, wherein each aperture or window independently switchable between a light transmissive and a light non-transmissive state in order to control the deliver of hologram light channels, and their replicas, to the eye-box. Each aperture or window may comprise a plurality of liquid crystal cells or pixels. Figure 6A shows an image that is desired for a viewer’s left eye, split into 4 zones, labelled respectively as L1, L2, L3 and L4. Figure 6B shows an image that is desired for the viewer’s right eye, split into 4 zones, labelled respectively as R1, R2, R3 and R4. To ensure that both eyes receive all the desired image content within a short time window, but that no image content is received by both eyes at the same angle at exactly the same time, a control device such as a waveguide aperture is provided that is configured to be dynamically switched between a first phase and a second phase, which are complementary to one another. Figure 6C shows the target image for hologram calculation for phase 1 and Figure 6D shows the target image for hologram calculation for phase 2. That is, the target image in Figure 6C is used to calculate a first hologram that is reconstructed during phase 1 and the target image in Figure 6D is used to calculate a second hologram that is reconstructed during phase 2. The target images used ensure that each eye receives content tailored to its position / perspective of the image (i.e. picture or field of view). The first phase can be understood more fully from Figures 6E to 6G. The waveguide aperture 650 is arranged in a first configuration 600A in the first phase, with 3 open portions 651,653, 655 and two closed portions 652, 654. The waveguide aperture 650 is provided in a display system, or light engine. The waveguide aperture 650 may be tilted with respect to an entrance pupil plane defined by the viewer’s left 606 and right 608 eyes, such that the waveguide aperture 650 is substantially parallel to the waveguide 604 from which it receives spatially modulated light. Other aspects of the display system, such as the display device displaying a hologram or holograms calculated as described herein, are not shown. In the first phase, the first open portion 651 permits light of zone 1 of the right eye view image to reach the right eye - thus image content “R1” is received. The second open portion 653 permits light from zone 3 of the right eye view image to reach the right eye - thus image content “R3” is received. The second open portion 653 also permits light from zone 2 of the left eye view image to reach the left eye - thus, image content “L2” is received. Finally, the third open portion 655 permits light from zone 4 of the left eye view image to be received by the left eye - thus, image content “L4” is received. Figure 6F therefore shows the image content received by the right eye 608 and Figure 6G shows the image content received by the left eye 606, in the first phase. The second phase can be understood more fully from Figures 6H to 6J. The waveguide aperture 650 is in a second phase 600B, with 2 open portions 652’, 654’ and three closed portions 651’, 653’, 655’. Again, other aspects of the display system would be present in practice but are not shown in Figure 6H. In the second phase, the first open portion 652’ permits light of zone 2 of the right eye view image to reach the right eye - thus image content “R2” is received. The first open portion 652’ also permits light of zone 1 of the left eye view image to reach the left eye - thus image content “L1” is received. The second open portion 654’ permits light of zone 4 of the right eye view image to reach the right eye - thus, image content “R4” is received. Finally, the second open portion 654’ also permits light of zone 3 of the left eye view image to be received by the left eye - thus, image content “L3” is received. Figure 6i therefore shows the image content received by the right eye 608 and Figure 6J shows the image content received by the left eye 606, in the second phase. The waveguide aperture 650 may be controlled to switch between the first and second phases quickly, for example more quickly than the typical integration time of the human eye, so that the respective image contents received by the viewer in each phase - as shown in combination in Figures 6C and 6D, respectively - are interlaced with one another. Hence, the viewer perceives that they have seen the full image with both eyes, each from its own unique perspective according to its position. However, the viewer does not perceive the image deterioration, nor do they encounter any confusion, that actually receiving common, or overlapping, image content at both eyes at the same time at the same angle would have caused. Hence, the control device works in combination with the calculated hologram(s), as described herein, to create clear and accurate holographically constructed images for the viewer. It does so in a simple yet effective way. Interleaved replicas of different holograms Figure 7A represents an example of replica of a single hologram displayed on a relatively large display device. The display device is described as being relatively large because it has more pixels than necessary to form a good quality holographic reconstruction. Figure 7A shows a spatial light modulator 700 forming a holographic wavefront 701 by spatially modulating light in accordance with a hologram displayed thereon. The holographic wavefront 701 comprises a range of light ray angles in accordance with the diffractive process. This range of angles is represented by a maximum diffraction angle 703 (e.g. positive angle) and a minimum diffraction angle 705 (e.g. negative angle) with respect to a surface normal of the spatial light modulator 700. Holographic wavefront 701 is received by a waveguide 704. The spatial light modulator 700 and waveguide 704 are configured with respect to one another (e.g. angled) such that the holographic wavefront 701 is at least partially waveguided by a pair of parallel reflective surfaces of the waveguide 704. A first reflective surface 706 of the waveguide 704 is partially transmissive, partially reflective such that a plurality of replicas of the holographic wavefront 701 are emitted therefrom. Whilst a general holographic projection axis 707 is shown in Figure 7A, the full range of diffraction angles emitted by the spatial light modulator 700 are waveguided by waveguide 704. Figure 7A shows a first replica 711, a second replica 712 and a third replica 713 by way of example only. The person skilled in the art will appreciate that any number of replicas may be emitted, as required, in accordance with this scheme. As explained in the Summary section above, the display device is larger (more specifically, has more pixels) than necessary to form a good holographic image in order to prevent to occurrence of image artefacts that adversely affect the viewing experience. This oversize is represented by the arrow labelled x in Figure 7A. This condition results from a relationship between the size of the pupil replicated by the waveguide and the size of the pupil of the viewing system (e.g. human eye) that has been identified, and understood, during the course of extensive experimental and simulation work. Figure 7B shows a field of view 750 encoded by the hologram displayed on the spatial light modulator 700 of Figure 7A. For the avoidance of doubt, the first holographic wavefront 701, and the full range of diffraction angles associated therewith including maximum diffraction angle 703 and a minimum diffraction angle 705, encode the entire field of view 750. In fact, the size of the field of view 750 may correspond to the maximum diffraction angle of the display device 700. In accordance with the present disclosure, the hologram is arranged to divide the spatial content of the field of view 750 by angle such that a first side 753 of the field of view 750 corresponds to the maximum diffraction angle 703 and a second side 755 of the field of view 750 corresponds to the minimum diffraction angle of 705. Whilst the arrangement of Figure 7 eliminates the occurrence of the image artefacts described above, it is inefficient in some respects because the display device, and therefore hologram, are larger (more pixels) than necessary for the holographic process. An embodiment of the present disclosure is shown in Figure 8A. Figure 8A shows a first spatial light modulator 810, a second spatial light modulator 820 and a third spatial light modulator 830. Each spatial light modulator forms a corresponding holographic wavefront as shown in Figure 8A. Each holographic wavefront is replicated as described in relation to Figure 7A. Notably, Figure 8A shows three spatial light modulators by way of example only and the present disclosure is equally applicable to displaying the three different holograms on three different subsets of pixels of a single / common spatial light modulator. Unless stated to the contrary, the term “replica” is used in the following paragraphs to refer to a replica of a holographic wavefront formed by division during waveguiding, or the input holographic wavefront before any division. Figure 8A shows first plurality of first replicas 811,812, 813 corresponding to the first hologram of the first spatial light modulator 810. Figure 8A further shows second plurality of second replicas 821,822, 823 corresponding to the second hologram of the second spatial light modulator 820 and a third plurality of third replicas 831,832, 833 corresponding to the third hologram of the third spatial light modulator 830. Figure 8A further shows a one-dimensional array 850 of interleaved replicas 821,812, 831,822, 813, 832, 823. Figure 8A shows how the first, second and third replicas alternate. The first, second and third replicas are interleaved or spatially-interlaced. In this example, each spatial light modulator 810, 820, 830 of Figure 8A is one third of the size of the spatial light modulator 700 shown in Figure 7A. It has been found that this configuration does not introduce the image artefacts described above because the three adjacent spatial light modulators 810, 820, 830 effectively, and collectively, form a single pupil that satisfies the minimum size in relation the size of the pupil of the viewing system (e.g. human eye). It may be said that embodiments of the present disclosure interleave a plurality of different hologram replicas or plurality of different holographic wavefronts. Figures 8B, 8C and 8D illustrate how the arrangement of Figure 8A may be used to provide a further technical advancement. Specifically, the arrangement of Figure 8A may be used to eliminate the needed for the light shuttering device described in relation to Figures 6. Each of Figures 8B to 8D effectively show the “input image” used to calculate the corresponding hologram. In embodiments, each hologram is a channelling hologram that divides spatial content in the spatial domain by angle in the hologram domain. A first hologram, H1, is displayed on the first spatial light modulator 810. Figure 8B shows a first part or sub-area 812 of the field of view 750. For the purpose of calculating the first hologram, the rest of the field of view 750 is effectively blanked. It may be said that the pixel values of the rest of the field of view 750 are nullified (e.g. zeroed). The input image to the hologram engine for calculating the first hologram, H1, therefore comprises the first sub-area 812 of the field of view 750 shown in hatching in Figure 8B and a blank sub-area shown in white in Figure 8B. Accordingly, the first hologram H1 therefore only contains some of the image content of the field of view 750. In embodiments, each hologram is a so-called channelling hologram (that divides the spatial content of the “input image” by angle in the hologram domain) so the first holographic wavefront formable from the first hologram (i.e. by displaying and illuminating the first hologram) comprises only a subset (namely, one third in this example) of the range of diffraction angles formable by the pixel structure of the spatial light modulator. A second hologram, H2, is displayed on the second spatial light modulator 820. Figure 8C shows a second sub-area 822 of the field of view that is retained for calculation of the second hologram. As for the first hologram, the other pixels are nullified such that diffractions angles of the holographic wavefront corresponding to these parts of the image / field of view are not formed (i.e. used) by the second hologram. Likewise, the third hologram. H3, is formed by retaining only a third sub-area 832 of the image pixel values. The third hologram, H3, is displayed on the third spatial light modulator 830. Each hologram therefore uses a different sub-range of diffraction angles in the hologram domain. In other words, the first holographic wavefront comprises (only) a first sub-range of diffraction angles, the second holographic wavefront comprises (only) a second sub-range of diffraction angles and the third holographic wavefront comprises (only) a third sub-range of diffraction angles. The first, second and third sub-ranges of diffraction angles may be non-overlapping. For the avoidance of doubt, the size (i.e. number of pixels) of the “input image” for each hologram calculation is not decreased by the division of the field of view shown in Figures 8B to 8D. That is, the first hologram, second hologram and third hologram of Figures 8 each have the same number of pixels as the hologram of Figures 7. Figure 8A shows a first plurality of replicas of a first holographic wavefront emitted from a first plurality of locations on a first surface of the pair of reflective surfaces of the waveguide, a second plurality of replicas of a second holographic wavefront being emitted from a second plurality of locations on the first surface and a third plurality of replicas of a third holographic wavefront being emitted from a third plurality of locations on the first surface. The first, second and third pluralities are spatially separated and / or interleave or spatially interlaced. The reader will understand that the teachings of this disclosure are applicable to the interleaving of any number of different holographic wavefronts including just two. Figures 8 show an arrangement in which the field of view is evenly divided between a plurality of holograms. However the division of the field of view is not necessarily even. For example, the sizes of the different sub-areas may be different, such as uneven or irregular, and the number of different sub-areas used for each hologram may be different, such as uneven or irregular. Figure 9 shows an arrangement in which a nonlinear optical combiner 930 (e.g. vehicle windscreen) is incorporated between the waveguide 904 and viewer 970. Specifically, Figure 9 shows a first spatial light modulator 910 arranged to display a first hologram, a second spatial light modulator 920 arranged to display a second hologram and a third spatial light modulator 930 arranged to display a third hologram. As described in relation to other embodiments, the waveguide 904 is arranged to output a plurality of interleaved and alternating holographic wavefront, or hologram, replicas 950. Figure 9 shows how the nonlinear optical combiner 930 causes the angles of the different hologram replicas to be changed by different amounts. The linear spacing of the hologram replicas shown in Figures 8 is therefore disrupted by the nonlinear optical combiner 930. Arrow 960 in Figure 9A shows an array of disrupted hologram replicas heading towards the viewer 970. In embodiments including a nonlinear optical combiner, the division of field of view may be irregular Figures 9B, 9C and 9D show an example of irregular division of the field of view. Figure 9B shows a first division of the field of view used for calculation of a first hologram displayed on the first spatial light modulator 910. Figure 9B shows a first subset of pixels 912 and a second subset of pixels 914. The first subset of pixels 912 and second subset of pixels 914 are spatially displaced. The first subset of pixels 912 is larger (i.e. contains more pixels) than the second subset of pixels 914, in this example. Figure 9C shows a third subset of pixels 922 used to form the second hologram. Figure 9C shows a fourth subset of pixels 932 and a fifth subset pixels 934 used to calculate the third hologram. Again, as in earlier embodiments, the other pixels of each “input image” are nullified so as to exclude sub-ranges of diffraction angles - specifically, sub-ranges of diffraction angles that could cause replica crosstalk. Notably, the inventor has found that by subdividing the field of view and calculating different holograms thereof, as described in relation to Figure 9, the problem of replica crosstalk can be eliminated without needing a light shuttering device as described in relation to Figure 6. Specifically, the inventor has demonstrated that using this technique, it is possible to ensure that each diffraction angle (therefore, each part of the field of view) is not delivered to the viewer by more than one replica (at least within the integration time of the viewing system). In particular, the inventor has demonstrated that using technique it is possible to eliminate crosstalk between the two eyes of a human viewer caused by the formation of a plurality of replicas of each part of the image I diffraction angle. It may be said that embodiments of the present disclosure are advantageous because they address the problem of replica crosstalk using a software based solution that does not require a light shuttering device. The divisions of field of view shown in Figures 8 and 9 are disclosed herein by way of example only and the person skilled in the art of optical design will understand how any number of different techniques, such as techniques based on optical simulation or ray-tracing, may be used to identify how the field of view should be divided between the different holograms for any given viewing position within the permitted viewing window. Additional features The methods and processes described herein may be embodied on a computer-readable medium. The term “computer-readable medium” includes a medium arranged to store data temporarily or permanently such as random-access memory (RAM), read-only memory (ROM), buffer memory, flash memory, and cache memory. The term "computer-readable medium" shall also be taken to include any medium, or combination of multiple media, that is capable of storing instructions for execution by a machine such that the instructions, when executed by one or more processors, cause the machine to perform any one or more of the methodologies described herein, in whole or in part. The term "computer-readable medium" also encompasses cloud-based storage systems. The term "computer-readable medium" includes, but is not limited to, one or more tangible and non-transitory data repositories (e.g., data volumes) in the example form of a solid-state memory chip, an optical disc, a magnetic disc, or any suitable combination thereof. In some example embodiments, the instructions for execution may be communicated by a carrier medium. Examples of such a carrier medium include a transient medium (e.g., a propagating signal that communicates instructions). It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. The present disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.

Claims

05 06 251. A holographic display comprising:a display system arranged to form a first holographic wavefront and a second5 holographic wavefront; anda waveguide arranged to receive the first holographic wavefront and second holographic wavefront, and waveguide each between a pair of at least partially reflective surfaces thereof,wherein a first plurality of replicas of the first holographic wavefront are emitted10 from a first plurality of locations on a first surface of the pair of reflective surfaces of thewaveguide and a second plurality of replicas of the second holographic wavefront are emitted from a second plurality of locations on the first surface,wherein the first holographic wavefront corresponds to a first hologram of a first part of a picture and the second holographic wavefront corresponds to a second15 hologram of a second part of the picture.

2. A holographic display as claimed in claim 1 wherein the first plurality of locations and second plurality of locations are at least partially spatially separated.20 3. A holographic display as claimed in claim 1 or 2 wherein the first plurality of locations andsecond plurality of locations are spatially interleaved.

4. A holographic display as claimed in any preceding claim wherein the first part and second part of the picture are substantially non-overlapping.

255. A holographic display as claimed in claim 4 wherein the first part and second part of the picture collectively form the entire picture.

6. A holographic display as claimed in any of claims 1 to 5 wherein the first part comprises a 30 first plurality of spatially separated sub-areas of the picture and the second part comprises asecond plurality of spatially separated sub-areas of the picture.

7. A holographic display as claimed in any of claims 1 to 6 wherein the first part and secondpart of the picture are immediately adjacent parts of the picture.

8. A holographic display as claimed in any preceding claim wherein each hologram is arranged to divide the spatial content of the picture, or respective part of the picture, by angle05 06 25such that a diffraction angle within the holographic wavefront formed by the hologram corresponds to a spatial coordinate of the picture.

9. A holographic display as claimed in any preceding claim further comprising a controller5 arranged to determine the first part and second part of the picture such that a viewer downstream of the waveguide only receives each diffraction angle once within an integration time of the viewer.

10. A holographic display as claimed in any of claims 1 to 8 further comprising a controller10 arranged to determine the first part and second part of the picture such that a viewer downstream of the waveguide only receives each diffraction angle from one location of the first and / or second plurality of locations on the first surface of the pair of reflective surfaces of the waveguide.

11. A holographic display as claimed in claim 9 or 10 further comprising a viewer tracking15 system that determines a viewing position of the viewer within a viewing area, wherein the determined viewing position is input to the controller in order to determine the first part and second part of the picture.

12. A holographic display as claimed in any preceding claim further comprising an optical20 combiner between the waveguide and viewing area, optionally, wherein the optical combiner has curvature such as spatially variant curvature.

13. A holographic display as claimed in any preceding claim wherein the display system comprises a first spatial light modulator arranged to display the first hologram and a second25 spatial light modulator arranged to display the second hologram.

14. A method of holographic display comprising:receiving a first holographic wavefront and a second holographic wavefront into a pupil expander; and30 forming a first plurality of replicas of the first holographic wavefront at a firstplurality of locations on a first surface of the pupil expander and forming a second plurality of replicas of the second holographic wavefront at a second plurality of locations on the first surface, wherein the first holographic wavefront corresponds to a first hologram of a first part of a picture and the second holographic wavefront corresponds to35 a second hologram of a second part of the picture.

15. A method of holographic display as claimed in claim 14 wherein the first plurality of locations and second plurality of locations are spatially interleaved.

16. A method of holographic display as claimed in claim 15 wherein the first part and second 5 part of the picture are substantially non-overlapping.

17. A method of holographic display as claimed in claim 16 wherein the first part and second part of the picture collectively form the entire picture.10 18. A method of holographic display as claimed in any of claims 15 to 17 wherein eachhologram is arranged to divide the spatial content of the picture, or respective part of the picture, by angle such that a diffraction angle within the holographic wavefront formed by the hologram.05 06 25

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