GB2630967A

GB2630967A - Hologram engine

Info

Publication number: GB2630967A
Application number: GB2308951.9A
Authority: GB
Inventors: Lin Ruisheng; Smeeton Timothy
Original assignee: Envisics Ltd
Current assignee: Envisics Ltd
Priority date: 2023-06-15
Filing date: 2023-06-15
Publication date: 2024-12-18
Anticipated expiration: 2043-06-15
Also published as: GB2630967B; WO2024256482A1

Abstract

Calculating a hologram of an image comprising a plurality of image points 1802 for reproduction by a display device comprises, for each image point: determining an area 1808 of the display device, determining two or more discrete sub-areas 1812, 1814 of the determined area, and determining a sub-hologram for the image point in the sub-areas. The determined area is determined based on the diffraction angle and the position of the image point. A holographic projection system comprising the display device and an optical component to received the hologram and to form a Fourier transform of an object at a focal plane of the optical component. The display device may be a spatial light modulator (SLM) and may comprise a plurality of pixels. The sub-holograms may be combined to form the image hologram. The hologram may be coupled into a pupil expander. A hologram engine which calculates the size or shape of at least one sub-area of the determined area based on characteristics of an optical system is additionally disclosed.

Description

HOLOGRAM ENGINE

FIELD

The present disclosure relates to a hologram engine, a driver for a display device, holographic projection system comprising said hologram engine, and methods of calculating a hologram. More specifically, the present disclosure relates to a hologram engine arranged to calculate a hologram of a picture comprising a plurality of image points. Even more specifically, the hologram comprises a sub-hologram for each image point and the sub-hologram has a shape selected to achieve a desired optical behaviour. 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.

In general terms, there is provided a hologram engine for calculating a hologram of a picture comprising a plurality of image points. The hologram engine is arranged to calculate a sub-hologram for each of the image points. The hologram engine may be arranged to calculate the hologram as a sum or superposition of the sub-holograms of each image point of the target picture. When the hologram is displayed on a display device and appropriately illuminated, a holographic wavefront may be formed which may form a holographic reconstruction of the picture. The sub-holograms are calculated such that each sub-hologram forms a respective image point of the holographic reconstruction.

The sub-hologram of each image point has a footprint on the display device. The inventors have surprisingly found that the footprint of the sub-hologram can be selected or engineered to achieve a desired effect. This is because a (Fourier) transform of the hologram has a (physical) shape or footprint and the inventors have surprisingly found that the (Fourier) transform of the hologram has a shape or footprint that depends on how the hologram was calculated. Specifically, the inventors have surprisingly found that the (Fourier) transform of the hologram has a shape or footprint that substantially corresponds to the shape or footprint of the sub-hologram used to form each image point. Thus, the shape or footprint of the (Fourier) transform of the hologram is typically different to the shape or footprint of the hologram per se. For example, the hologram may be rectangular (displayed on a rectangular display device). The footprint of each sub-hologram may conventionally be circular. The inventors have found that the (Fourier) transform of such a (rectangular) hologram may have a circular shape or footprint (corresponding to the shape of each of the sub-holograms rather than a rectangular shape). Thorough simulation and experimentation has lead the inventors to recognise that any arbitrary shape / footprint for (each of) the sub-holograms can be selected and the (Fourier) transform of the hologram will substantially correspond to that arbitrary shape / footprint. The inventors have thus recognised that the shape / footprint of (each of) the sub-holograms can be selected / engineered to achieve a desired effect (resulting from the (Fourier) transform of the hologram having a particular shape). In examples, the inventors have recognised that optical misalignments of an optical system comprising a display device displaying the hologram can be compensated for by selecting an appropriate footprint for each sub-hologram. Advantageously, this means that the optical misalignments can be corrected in software (i.e. the hologram calculation) rather than requiring a change in hardware. This may further advantageously mean that the corrections can be performed "on the fly" and an amount of correction can be adjusted dynamically. In examples, the inventors have recognised that the footprint of each sub-hologram can be selected to be convenient for spatial filtering (and with relatively high margins for error). In examples, the inventors have recognised that the footprint of each sub-hologram can be selected to be convenient for coupling different portions of a holographic wavefront to different optical components (and with relatively high margins for error).

In some embodiments, the hologram engine is arranged such that the footprint of each sub-hologram comprises a plurality of discrete sub-areas. As used herein, the sub-areas being discrete may mean that the sub-areas are distinguishable from one another. For example, the sub-areas may be at least partially spatially separated, optionally (completely) spatially separated. For example, the sub-areas may not be in contact with one another. A non-sub-hologram region may be defined between two discrete sub-areas of the sub-hologram. In embodiments in which each footprint comprises a plurality of discrete sub-areas, a (Fourier) transform of the hologram comprises corresponding discrete areas. Each area of the (Fourier) transform of the hologram may be referred to as a content area. The content areas may be (at least partially) spatially separated from one another. A non-content area may be defined between two (or more) content areas of the (Fourier) transform of the hologram. The non-content area may comprise noise. The inventors have recognised that there are many situations in which it may be advantageous for the (Fourier) transform of the hologram to have a footprint divided into a plurality of discrete sub-areas / content areas. For example, different portions of a holographic wavefront (associated with the discrete areas / content areas of the Fourier transform of the hologram) may conveniently be routed into different branches of an optical system. For example, a first (content) area of the Fourier transform of the hologram / first portion of a holographic wavefront may be coupled into a first waveguide and a second (content) area of the Fourier transform / second portion of the holographic wavefront may be coupled into a second waveguide. By (at least partially) spatially separating the discrete content areas, the need to precisely align the optical system, for example so first and second halves of the holographic wavefront are exactly aligned with a knife edge mirror, may be removed. Furthermore, in some examples, the shape of the footprint of each of the sub-holograms may advantageously be selected to compensate for optical misalignments in one or more branches of the optical system. In this way, the shape / orientation / position of one of the sub-areas of the footprint of each sub-hologram may be different to another discrete area of the sub-hologram, e.g. one of the sub-areas may be rotated relative to another discrete sub-area. This difference / rotation may be arranged to compensate for an optical misalignment that exists in only one of the branches. In some examples, spatial filtering may be applied to the (Fourier) transform of the hologram. The spatial filtering may be arranged to nullify a portion of the (Fourier) transform of the hologram. In this way, particular frequencies of the hologram can be nullified without affecting other frequencies of the hologram. In some examples, the spatial filer may be arranged to nullify zero-order / so called "DC" spot. The inventors have recognised that the footprint of the sub-holograms can be selected such that the DC spot is located in the non-content area of the (Fourier) transform of the hologram. The spatial filter may be arranged to process / nullify the non-content area of the (Fourier) transform of the hologram and so may nullify the DC spot / zero order light. Thus, when the DC spot is nullified (by a spatial filter) (e.g. absorbed or redirected away from a propagation axis of the optical system), substantially no holographic content of the (Fourier) transform of the hologram may be lost. In some examples, the spatial filter may be arranged to adjoin / re-join the discrete portions of the holographic wavefront after the spatial filtering has been performed. Again, this may typically require precise optical alignment to ensure that the discrete portions become correctly aligned. However, the inventors have recognised that these optical misalignments can be compensated for in the selection of the shape, size and position of the footprint, specifically the shape, size and position of the discrete sub-areas of the footprint.

The selection of the footprint of each sub-hologram may require the cropping of an area defined on the display device by the (maximum) diffraction angle of the display device and the position of the respective image point. In other words, the footprint of each sub-hologram on the display device may be smaller than a maximum area that may contribute to the formation of each image point. This is counterintuitive and unconventional. In particular, there is a general prejudice that the number of pixels contributing to each image point of a holographic reconstruction should be maximised. Cropping the or each area (associated with each image point) goes against this prejudice because the cropping reduces the number of pixels of the display device that contribute to the formation of each image point. However, the inventors have found that advantages of cropping the area to have a footprint having a desired shape and size to "engineer" the footprint, as described above, outweigh the need to maximise the number of pixels per image point. Furthermore, after thorough simulation and experimentation, the inventors have found that, even with cropping, there may still be a suitably large number of pixels per image point to allow for a good quality holographic reconstruction.

In a first aspect, there is provided a hologram engine. The hologram engine is arranged for calculating a hologram of a (target) picture. The hologram is for displaying on a display device. The picture comprises a plurality of image points. The plurality of image points may be said to be analogous to pixels. The hologram engine is arranged to, for each image point, define discrete first and second sub-areas on the display device. In some embodiments, the hologram engine may be arranged to define further discrete sub-areas on the display device for each image point. The (at least) first and second sub-areas are sub-areas of an area of the display device. The area of the display device is defined by the diffraction angle of the display device and the position of the image point. It may be said that the area is "diffraction limited" to reflect that the size of the area is limited by the laws of diffraction. Notably, the sub-areas are sub-areas of the area. That is, they fall within the area and are each smaller (e.g. comprise fewer pixels) than the area. In other words, each sub-area is smaller than the corresponding area. Further notably, in embodiments, there are a plurality of sub-areas. This is unconventional but the inventors have found this to be advantageous particularly in embodiments, such as holographic projection, in which imperfect optics are used to process the holographic wavefront and/or the holographic wavefront is directed down a plurality of different optical channels or branches such as different waveguides and / or different channels or branches of a spatial filter. In some embodiments, the sub-areas are spatially separated. That is, there are display device pixels providing spatial separation between the discrete sub-areas. In other embodiments, the sub-areas may touch or connect or adjoin in one or more places but may not completely connect or adjoin. In such embodiments, the discrete sub-areas may be said to be partially spatially separated. The term "discrete" is used to reflect that two clearly identifiable sub-areas are used to calculate the sub-hologram of each image point even when/if the sub-areas touch. The hologram engine is further arranged to, for each image point, determine a sub-hologram for the image point in the first and second sub-areas.

There is also provided a hologram engine for calculating a hologram of a picture for displaying on a display device, the picture comprising a plurality of image points, the hologram engine being arranged to define an area on the display device for each image point based on the diffraction angle of the display device and the position of the image point.

The hologram engine is further arranged to calculate a sub-hologram for the image point in the respective area. The hologram engine is further arranged to, for each image point, crop the respective area / sub-hologram to form (at least) first and second discrete sub-area of the respective sub-hologram on the display device. The reader should appreciate that the term "cropping" is used here as an alternative way of forming the plurality of "sub-areas" of hologram data from the diffraction-limited "area" corresponding to the image point.

The area on the display device defined by the diffraction angle may be defined by tracing back from the image point (or the (target) picture) (in the desired position of the image point, i.e. where the image point is desired to be holographically reconstructed) to the display device. This area may be defined by using (e.g. tracing) one or more straight lines from the image point to the display device. The area may be defined using a straight line (path) defined from the image point and that is normal to the display device. Thus, the straight line path may depend on the position of the image point. The area may be defined using a solid angle or diffraction cone around the straight line (that is normal to the display device). This may define a perimeter of the area on the display device. The hologram engine may be arranged to sweep the one or more straight lines around at an angle equal to the (maximum) diffraction angle of the display device (relative to a propagation axis / normal of the display device). In other words, the area may be defined in a way that is conventional in the calculation of a point cloud hologram. However, the method according to the present disclosure differs significantly from conventional cloud hologram calculation techniques because the sub-hologram (for each image point) is determined in discrete first and second sub-areas of the "conventional" area. In other words, the area on the display device defined by the diffraction angle may be considered to be cropped into (at least) two, separate, discrete sub-areas. Thus, the hologram engine may be arranged to crop the area of the display device defined by its diffraction angle to form the first and second (discrete) sub-areas. The hologram engine may be arranged to perform this cropping step before or after the sub-hologram is calculated. So, in some embodiments, the hologram engine may be arranged to crop the area to formed the (at least) first and second discrete sub-hologram areas and then calculate the sub-hologram for/ in those discrete sub-hologram areas. In other embodiments, the hologram engine may be arranged to calculate a sub-hologram for / in the entire area (defined by the diffraction angle) and then crop the area / sub-hologram by maintaining pixels of the sub-hologram only in the at least first and second discrete areas of the display device.

As described above, in embodiments, a transform (e.g. Fourier transform) of a hologram calculated by the hologram engine, has a corresponding shape to that of the sub-holograms.

Thus, a (Fourier) transform of the hologram will comprise first and second discrete areas (corresponding, respectively, to the first and second sub-areas of each sub-hologram).

These sub-areas of the (Fourier) transform of the hologram may herein by referred to as content areas. Some of the advantages of the sub-hologram comprising these first and second sub-areas (such that the (Fourier) transform of the hologram comprises similarly shaped content areas) was described above. Specific examples / embodiments, and there associated advantages, will be described in more detail below.

In some embodiments, the hologram engine is arranged to form the hologram by combining the sub-holograms determined for each of the image points. In some embodiments, the hologram engine is arranged to output the formed hologram, for example to a display device.

Alternatively or additionally, the hologram engine may be arranged drive a display device to display the hologram.

In some embodiments, the area on the display device (defined by the diffraction angle of the display device and the position of the respective image point) for each image point comprises a contiguous group of pixels of the display device. In some embodiments, the first sub-area (of each sub-hologram) comprises / consists of a first subset of pixels of the respective contiguous group of pixels. The first subset of pixels may be contiguous. In some embodiments, the second sub-area (of each sub-hologram) comprises / consists of a second subset of pixels of the respective group of pixels. The second subset of pixels may be contiguous.

In some embodiments, each first sub-area is (at least partially) spatially separated from the respective second sub-area. In some embodiments, the hologram engine is arranged to exclude the sub-hologram from a region of the display device defined between the respective first and second sub-areas of the respective sub-hologram / image point. In some embodiments the first sub-area does not overlap with the second sub-area.

In some embodiments, each first sub-area has a first shape. In some embodiments, each first sub-area has a first size. In some embodiments, each second sub-area has a second shape. In some embodiments, each second sub-area has a second size. In some embodiments, the first shape of each first sub-area is congruent with the first shape of every other first sub-area. In some embodiments, the second shape of each second sub-area is congruent with the second shape of every other second sub-area. In some embodiments, each first shape is substantially the same size as the respective second shape.

In some embodiments, the hologram is arranged such that each first-area is positioned / orientated / scaled / skewed differently to each second-area. For example, the hologram may arranged such that each first sub-area is rotated relative to the respective second subarea. This difference / this rotation may be to compensate / correct for optical misalignments of a system comprising the display device.

In some embodiments, the first and second subareas are arranged such that each region defined between the first and second areas is substantially at the centre of the respective sub-hologram.

The hologram may be arranged such that, when the hologram is displayed on the display device of a system arranged to form a Fourier transform of the hologram, a DC / zero-order (bright) spot formed by the hologram may be substantially located in the non-content portion of the Fourier transform of the hologram. In some embodiments, the hologram is arranged such that a Fourier transform of the hologram has a first (content) area having the first shape and a second (content) area having the second shape, and wherein a non-content portion is defined between the first and second portions. The non-content portion may comprise noise such as zero order or so called "DC spot" light. This may advantageously be nullified by, for example, a spatial filter, without nullification of content in the content areas. In some embodiments, the first and second portions of the Fourier transform of the hologram are spatially separated.

According to a second aspect, there is provided a holographic projection system. The holographic projection system comprises a display device arranged to display a hologram of a picture comprising a plurality of image points. The hologram comprises a sub-hologram comprising discrete first and second sub-areas for each image point. The first and second sub-areas are sub-areas of an area of the display device defined by the (maximum) diffraction angle of the display device and the position of the respective image point. The display device is arranged to spatially modulate light in accordance with the hologram displayed thereon to form a holographic wavefront. In some embodiments, the holographic projection system comprises a hologram engine arranged to calculate the hologram, for example a hologram engine according to the first aspect. The holographic projection system further comprises an optical component. The optical component may be an imaging component such as a (thin) lens. The optical component is arranged to form a Fourier transform of an object. Specifically, the optical component is arranged to form a Fourier transform of an object at a first (front) focal plane of the optical component. The Fourier transform of the object may be formed at a second (back) focal plane of the optical component. The optical component is further arranged to receive the holographic wavefront (formed by light incident on the display device). In embodiments, the object may be the holographic wavefront (at the first focal plane).

The hologram may be arranged such that a Fourier transform of the hologram has a first (content) area or portion having the first shape (i.e. having a shape corresponding to the first sub-area of each sub-hologram). The hologram may be arranged such that a Fourier transform of the hologram has a second (content) area or portion having the second shape (i.e. having a shape correspond to the second sub-area of each sub-hologram). The first and second (content) portions or areas of the Fourier transform of the hologram may be spatially separated. A non-content portion or area nay be defined between the first and second (content) portions or area of the Fourier transform of the hologram. In some embodiments, the optical component is arranged to form a transform of the holographic wavefront (or hologram), such as a Fourier transform.

In some embodiments, the holographic projection system comprises an optical system arranged to relay the holographic wavefront to a viewing window. In some embodiments, the optical system comprises the optical component described above.

In some embodiments, the holographic projection system (or, optionally, the optical system of the holographic projection system) comprises a first pupil expander or replicator, such as a hologram replicator, such as a first waveguide. The holographic projection system may be arranged such that a (Fourier) transform of the hologram is coupled in to the pupil expander or replicator. Unless specified differently, herein, a hologram being coupled with or into a component can refer to either or both of a hologram displayed on the display device and a relayed hologram formed by the holographic wavefront downstream of the display device.

Similarly, a (Fourier) transform of a hologram being coupled with or into a component (such as the waveguide) can refer to either or both of a (Fourier) transform of a hologram displayed on the device or (Fourier) transform of a relayed hologram formed by the holographic wavefront downstream of the display device. In any case, such a holographic projection system can be characterised by the fact that the optical component is arranged such that a (Fourier) transform of the (relayed) hologram is coupled into a waveguide, rather than the (relayed) hologram per se being replicated by the waveguide (as is the convention).

The first pupil expander or replicator may replicate the holographic wavefront (e.g. may replicate the (Fourier) transform of the hologram coupled into (an input port of) the first pupil expander). The first pupil expander may be a first waveguide. The first waveguide may comprise a pair of opposing reflective surfaces. A first surface of the pair of opposing reflective surfaces surface may be partially transmissive / partially reflective. The first waveguide may be arranged to waveguide the holographic wavefront between the pair of opposing reflective surfaces. Replicas of the holographic wavefront may be emitted from the first surface. Conceptually, the result of this may be considered the creation of an array of replicas of the display device / replicas of the hologram displayed on the display device. The array of replicas may be said to exist on a "virtual surface" which may be staggered as explained in British patent application, GB2118911.3 filed on 23 December 2021. In particular, each replica may be a different perpendicular distance from the display device owing to different path lengths in the waveguide associated with each replica. Thus, the part of the virtual surface (e.g. in the x, y dimensions) associated with each replica is offset from the display device in the perpendicular direction (e.g. in the z dimension). A virtual image of the holographic reconstruction is visible when a viewing system (such as the eye of a user) is positioned at a viewing window downstream of the waveguide/s. The virtual image may be formed at a virtual image distance upstream of the display device. Typically, the virtual image distance may be between about 1 metre and about 10 or 20 metres.

In some embodiments, the holographic projection system is arranged such that the holographic reconstruction forms a holographic reconstruction (of the picture) downstream of the display device. In some embodiments, the optical component may be positioned such that the holographic reconstruction is between the display device and the optical component.

In some embodiments, the optical component may be positioned between the holographic reconstruction and the waveguide (when present). In some embodiments, the optical component is arranged to form a virtual image of the holographic reconstruction upstream of the display device. In some embodiments: either a distance between the holographic reconstruction and the optical component is less than a focal length of the optical component such that the image of the holographic reconstruction is a virtual image formed upstream of the display device; or the optical system further comprises an optical relay between the display device and waveguide, the optical relay comprising two lens arranged in cooperation to form a relayed holographic reconstruction, wherein the relayed holographic reconstruction is an image of the holographic reconstruction formed by the hologram displayed on the display device, and wherein a distance between the relayed holographic reconstruction and the optical component is less than a focal length of the optical component such that the virtual image of the holographic reconstruction formed by the optical component is a virtual image of the relayed holographic reconstruction. As explained in GB2302916.8 (filed on 28 February 2023), such an optical arrangement may substantially reduce or minimise a visual impact of the virtual surface of replicas. In general terms, the optical component (e.g. lens) is arranged to form: a) a virtual image of the holographic reconstruction; and b) an image (e.g. real image at a finite distance or virtual image at infinity) of the displayed hologram / display device. The optical component is arranged such that a magnitude of the separation of the virtual image of the holographic reconstruction and the image of the displayed hologram / display device is greater than a virtual image distance of the virtual image of the holographic reconstruction. As such, the image of the displayed hologram / display device is far removed from the virtual image of the holographic reconstruction. This was found to improve the viewing experience. In some examples, a virtual image of the display device is formed at infinity such that the effective distance between the virtual image of the display device and the virtual image of the holographic reconstruction (which is at a finite image distance) is infinite. In such examples, the (virtual image of) the display device may be referred to as being "at infinity". In other examples, a real image of the display device is formed downstream of the optical component, again far removed from the virtual image of the holographic reconstruction (which will be upstream of the optical component). In such examples, the (virtual image of) the display device may be referred to as being "beyond infinity". Thus, the optical system may be described as being arranged to form an image of the display device "at or beyond infinity". Arranging the optical component in this way advantageously significantly reduces the impact of artifacts of the virtual surface from obstructing / distracting a viewer at the viewing window. In particular, the optical component can be arranged to either form the image of the hologram / display device at infinity (far beyond the virtual image of the holographic reconstruction) or at a position downstream of the optical component (typically behind the viewing system). In either set of examples, the viewer is not required to look through or past the image of the hologram / display device to view the virtual image of the holographic reconstruction when the optical component is arranged in this way.

As above, the holographic projection system described above may be characterized by the (first) waveguide being arranged to replicate a (Fourier) transform of the hologram rather than the hologram per se. The inventors have recognised that, because the (Fourier) transform of the hologram is replicated, the sub-hologram for each point can be selected to result in a shape or footprint of the (Fourier) transform of the hologram at the waveguide that is advantageous. For example, the shape or orientation of the sub-hologram can be chosen to ensure that the (Fourier) transform of the hologram is correctly aligned with an input port of the (first) waveguide. For example, one or both of the discrete sub-areas may be rotated to ensure alignment of the (Fourier) transform of the hologram with the input port of the (first) waveguide. The rotation may pre-compensate for a rotational misalignment of the holographic projection system.

In some embodiments, the hologram is arranged such that a first shape of the first sub-area and / or a second shape of the second sub-area compensates for an optical misalignment of the optical system. In some embodiments, the first shape is rotated relative to the second shape to compensate for rotational misalignments of the optical system. This may be particularly advantageous if the holographic projection system comprises different optical paths or branches and the different areas of the (Fourier) transform of the hologram are coupled into the different optical paths or branches. For example, the existence / magnitude / direction of an optical misalignment may be different for the different optical paths or branches of the holographic projection system. The hologram may be arranged such the first shape of the first sub-area of each hologram (pre-) compensates for an optical misalignment of a first branch of the holographic projection system (into which the corresponding first area of the (Fourier) transform of the hologram is coupled). The hologram may be arranged such that the second shape of the second sub-area of each hologram (pre-) compensates for an optical misalignment of a second branch of the holographic projection system (into which the corresponding second area of the (Fourier) transform of the hologram is coupled).

In some embodiments, the holographic projection system comprises a first pupil expander and a second pupil expander. As above, the first pupil expander may be a first waveguide. The second pupil expander may be a second waveguide. The first pupil expander may be arranged to expand an exit pupil thereof in a first direction of a first dimension. The second pupil expander may be arranged to expand an exit pupil thereof in a second direction of the first dimension. The second direction may be opposite to the first direction. In other words, both the first and second pupil expanders may provide pupil expansion in different (opposing) directions of a first dimension. The expanded pupils of the first and second pupil replicators may combine / both contribute to a continuous viewing window of the holographic projection system. Another way of saying this is that the first pupil replicator expands an eye-box of the holographic projection system in a first direction of a first dimension (of the eye-box). The second pupil replicator expands an eye-box of the holographic projection system in a second direction of the first dimension of the eye-box. The first and second pupil expanders / waveguides may be tilted with respect to the viewing plane in opposite directions. This tilting may be to ensure that emission from the first and second pupil expanders / waveguides is substantially parallel. Using first and second pupil expanders (each arranged to expand in the first dimension) advantageously allows for a more compact composite pupil expander structure than using a single pupil expander in the first dimension (for a given amount of expansion in the first dimension). In particular, the size in the second dimension e.g. height or light propagation direction may be reduced, and thus the volume required thereby, may be reduced.

In some embodiments, the optical system of the holographic projection system comprises the first pupil expander and the second pupil expander. In some embodiments, a first branch of the optical system comprises the first pupil expander. In some embodiments, a second branch of the optical system comprises the second pupil expander. In some embodiments, the first area of the (Fourier) transform of the hologram is coupled into the first pupil expander arid the second area of the (Fourier) transform of the hologram is coupled into the second pupil expander. In some embodiments, the hologram is arranged such that the first and / or second sub-areas of each sub-hologram are arranged to (pre) compensate for an optical misalignment of the first and / or second branch of the optical system, for example such that the first and second area of the (Fourier) transform of the hologram are aligned with an input port of the respective first and / or second pupil expander. Both the first and second areas of the (Fourier) transform of the hologram may comprise all the information required to holographically reconstruct the target picture. Thus, the replicas formed by either the first or second pupil expander may contain all the information needed to reconstruction the target picture and so a viewer in the viewing window, receiving light via a replica of one of the first or second pupil expanders may view a reconstruction of the full target picture/ field of view.

In some embodiments, the holographic projection system further comprises a third pupil expander, such as a third waveguide. The third pupil expander may be arranged to receive the output of the first and / or second pupil expanders (first and / or second waveguides). The third pupil expander may be arranged to expand a pupil thereof in a second dimension. The second dimension may be perpendicular to the first dimension. Similarly, the third pupil expander may be arranged to expand an eye-box in the second dimension. In this way, the holographic projection system may be arranged to expand an exit pupil of the system / eye-box in two dimensions.

In some embodiments, the holographic projection system further comprises a spatial filter.

The spatial filter may be arranged to receive the holographic wavefront. The spatial filter may be arranged to process the holographic wavefront. In some embodiments, the spatial filter is optically coupled to a (back) focal plane of the optical component. In this way, the spatial filter may receive or be coupled with a Fourier transform of the hologram. Thus, the spatial filter may process a Fourier transform of the hologram (or holographic wavefront). The spatial filter may operate on (such as nullify) areas in space corresponding to particular frequencies of the hologram. The spatial filter may be arranged to nullify a portion of the holographic wavefront. For example, the spatial filter may be arranged to nullify a portion of the holographic wavefront corresponding to zero-order or so-called "DC" light. The spatial filter may be coupled to the (back) focal plane of the optical component.

In some embodiments, the spatial filter comprises an input side. The input side may be arranged to receive the holographic wavefront along a first plane. The input side may be further arranged to divide the holographic wavefront into first and second portions. The input side may be further arranged to nullify a third portion of the holographic wavefront that is located between the first portion and the second portion. In embodiments, the first portion of the holographic wavefront forms / corresponds to the first area of the Fourier transform of the hologram (described above). In embodiments, the second portion of the holographic wavefront forms / corresponds to the second area of the Fourier transform of the hologram. Thus, in such embodiments, the spatial filter may be arranged to divide the first and second areas or portions of the Fourier transform of the hologram. The skilled reader will appreciate, that the discrete sub-areas of the hologram can be selected such that the first and second areas or portions of the Fourier transform of the hologram are properly aligned with the input side of the spatial filter to ensure that this divide is achieved. The discrete sub-areas of the hologram can further be selected such that an area or sub-region between the first and second sub-areas results in a corresponding non-content region in the Fourier transform of the hologram. Specifically the discrete sub-areas of the hologram can be selected such that a non-content region in the Fourier transform is nullified by the spatial filter. In some embodiments, the input side comprises: a first surface arranged to receive the first portion of the holographic wavefront; a second surface arranged receive the second portion of the holographic wavefront; and a discontinuity between the first surface and the second surface arranged to receive and nullify the third portion of the holographic wavefront.

In some embodiments, the spatial filter may comprise the first and second pupil expanders / waveguides, described above. In such cases, an input of the first pupil expander and an input of the second pupil expander may form the first and second surfaces of the input surface. The first and second pupil expanders may be arranged such that there is a discontinuity between the respective inputs of respective pupil expanders. This discontinuity may form the discontinuity of the input surface of the spatial filter.

In some embodiments, the spatial filter is arranged such that the first portion of the holographic wavefront is directed away from the first plane at the first surface of the input side in a first direction and the second portion of the holographic wavefront is directed away from the first plane at the second surface of the input side in second direction that is different to the first direction. In some embodiments, the spatial filter is further arranged to relay the first and second portions to an output side such that a processed holographic wavefront is formed. The processed holographic wavefront may comprise the first portion adjoined to the second portion. In this case, the (Fourier) transform of the hologram (after processing of the holographic wavefront) may comprise the first area adjoined to the second area. In such embodiments, the holographic projection system may comprise a spatial filter and a separate pupil expander (or pupil expanders). For example, the holographic projection system may comprise a spatial filter arranged to process the holographic wavefront arid a pupil expander (waveguide) arranged to receive and replicate the processed holographic wavefront. The inventors have recognised that, in such embodiments, it is important that the first and second portions of processed holographic wavefront are correctly aligned with one another (e.g. so that the first and second areas of the (Fourier) transform of the hologram are aligned). This alignment of the processed holographic wavefront may ensure a good quality and properly aligned holographic reconstruction. Without proper alignment, a discontinuity may appear in the holographic reconstruction viewable at a viewing window, for example. However, many spatial filters comprise a plurality of branches and each branch may comprise multiple surfaces. A misalignment of any of the surfaces may result in a misalignment in a portion of the holographic wavefront and so a misalignment in the processed holographic wavefront. It would be very time consuming, expensive and laborious to ensure that all of the surface of the spatial filter are correctly aligned during manufacture.

Furthermore, the surfaces may come out of alignment over time and / or because of temperature changes or vibrations, for example. However, the inventors have recognised that the first and second areas of the sub-hologram for each point can be selected to have a footprint / shape / size / orientation that (pre-)compensates for a misalignment of one or more branches of the spatial filter. Thus, the sub-hologram can be arranged to ensure that the processed holographic wavefront is correctly aligned. Advantageously, this is a software solution. Thus, the arrangement of the sub-hologram can be changed to compensate for changes in the misalignment of the spatial filter over time.

The inventor has recognised that there is a particular need for the above described spatial filter (which processes a holographic wavefront by nullifying the third portion (comprising DC light) and adjoining the first and second portions to form a processed holographic wavefront) when a (Fourier) transform of the hologram / holographic wavefront is coupled into a waveguide and replicated. In more conventional arrangements (in which the hologram per se is replicated), the zero order / DC light can be removed by blocking or masking that light in a Fourier transform of the hologram. Because, conventionally, the hologram per se is replicated, the "hole" or blocked / masked region in the Fourier transform of the hologram is not apparent in the virtual surface / extended modulator. However, when the Fourier transform of the hologram is instead replicated (as described above), each replica of the Fourier transform of the hologram will comprise a dark region associated with the blocked / masked region. In other words, an array of dark regions may be formed in the virtual surface. While this dark region may not be visible in the actual holographic reconstruction viewed at the eye-box, the inventors have found that the human eye is particularly sensitive to artefacts in the virtual surface / extended modulator. In particular, the human eye may be able to detect the presence of the array of dark regions in the virtual surface. This may adversely affect the viewing experience. A spatial filter which adjoins the first and second portions of the holographic wavefront may advantageously result the removal of a "dark" region in the processed holographic wavefront and so may advantageously not result in an array of dark regions on the virtual surface.

In some embodiments, the spatial filter is arranged to have a reflective mode of operation or arrangement. In such embodiments, the spatial filter may comprise a plurality of reflective surfaces arranged to receive the holographic wavefront, redirect the first and second portions of the holographic wavefront and recombine / adjoint the first and second portions of the holographic wavefront.

In some embodiments, the spatial filter is arranged to have a refractive mode of operation or arrangement. In such embodiments, the spatial filter may comprise an optical element having a refractive index, n > 1. The optical element may comprise a first pair of parallel of surfaces comprising a first input surface (wherein the input side of the device comprises the first input surface) and a first output surface (wherein the output side of the device comprises the first output surface). The optical element may further comprise a discontinuity adjacent to the first input surface, wherein said discontinuity is arranged to receive and to nullify a third portion of the holographic wavefront, wherein said third portion is located between the first portion and the second portion. The first input surface may be arranged to receive the first portion of the holographic wavefront and arranged such that there is a first acute angle between a normal to the first input surface and a normal to the first plane. The optical element may be arranged such that the first portion and the second portion of the holographic wavefront are adjoined to one another at the output side to form the processed holographic wavefront.

In some embodiments, each sub-hologram comprises a subset of pixels of the display device. In some embodiments each subset of pixels comprises less than 5% of the total number of pixels of the display device, optionally less than 2% of the total number of pixels of the display device. In some embodiments, each subset of pixels comprises less than 100,000 pixels, optionally less than 25,000 pixels, optionally less than 5,000 pixels, optionally less than 1,000 pixels, optionally less than 500 pixels, optionally less than 200 pixels, optionally less than 100 pixels. This may advantageously result in the holographic reconstruction being formed relatively close to the display device. For example, the hologram may be arranged such that a distance between the display device and the holographic reconstruction is 20 millimetres or less, optionally 10 millimetres or less, optionally 5 millimetres of less. In some embodiments, each subset of pixels may overlap with one or more of the (other) subsets. In other words, any given pixel of the display device may be present in a plurality of subsets of pixels (and so may form part of a plurality of sub-holograms).

Conventionally, much larger numbers of pixels of the display device are used to form each of image point (for example, in point cloud holography). The inventors have recognised that by using such relatively small areas on the display device to form each image point, the holographic reconstruction can be formed relatively very close to the display device. For example, in some embodiments, the hologram is arranged such that a distance between the display device and the holographic reconstruction is 20 millimetres or less, optionally 10 millimetres or less, optionally 5 millimetres or less. In some embodiments, the distance between the display device and the holographic reconstruction is less than a width and / or a height of the display device. Optionally, a width or height of a display area of the display device, wherein the display device comprises the plurality of pixels arranged in an array. The key advantage of being able to form the holographic reconstruction so close to the display device is that the optical system can be made compact (the optical axis of the optical system being relatively short) while still achieving an arrangement in which the holographic reconstruction is formed within a focal length of the lens, while the display device is at or beyond the focal length of the lens. As described above, such an arrangement advantageously significantly reduces the impact of artifacts of the virtual surface from obstructing / distracting a viewer at the viewing window. However, such arrangements are unconventional. It is particularly unconventional to have constraints on both the position of the display device and the position of the holographic reconstruction with respect to a lens and so the inventors were faced with an unusual problem when trying to implement such an arrangement in a compact way. Furthermore, the technical field is prejudiced against forming a holographic reconstruction so close to the display device by using few display pixels to form each image point because of concerns of loss of quality of the holographic reconstruction. The generally held view is that high numbers of pixels per image point are needed to form high quality holographic reconstructions. So, the inventors have gone against the prejudice of the technical field and surprisingly found / shown through simulation and experimentation that a good quality holographic reconstruction can be achieved using a relatively low number of display pixels per image point.

In a third aspect there is provided a driver for a display device comprising a plurality of pixels. The driver is arranged to drive the display device to display a hologram of a picture on the plurality of pixels such that, when the display device is suitably illuminated, a holographic reconstruction of the picture is formed. The holographic reconstruction comprises a plurality of image points. The hologram is arranged such that each image point of the holographic reconstruction is formed by sub-hologram comprising a respective discrete first and second sub-area of an area of the display device defined by the diffraction angle and the position of the image point.

In a fourth aspect there is provided a method of calculating a hologram of a picture comprising a plurality of image points. The method comprises, for each image point of the picture: defining discrete first and second sub-areas on a display device, the first and second sub-areas being sub-areas of an area defined by the diffraction angle and the position of the image point. The method further comprises (for each respective image point) determining a sub-hologram for the image point in the first and second sub-areas.

In a fifth aspect, there is provided a hologram engine for calculating a hologram of a picture for displaying on a display device of a holographic projection system comprising an optical system arranged to relay light from the display device to a viewing window. The picture comprises a plurality of image points. The hologram engine is arranged to, for each image point: define at least one sub-area on the display device in an area, wherein the area is defined by the diffraction angle and the position of the image point; and determine a sub-hologram for the image point in the respective sub-area. The hologram engine is arranged to determine a shape and size of each sub-area based on a property or feature of the optical system. The sub-area may have a shape that is arranged to compensate for a misalignment or aberration of the optical system. Each sub-area may have a non-circular shape. Each sub-hologram may comprise a plurality of sub-areas (e.g. a first and second sub-area as described above, for example with respect to the first aspect).

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 2-rr) 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 rr/2 will retard the phase of received light by Tr/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 6 is a cross-sectional schematic view of the optical components of an optical system; Figure 7 is a cross-sectional schematic view of the optical components of another optical system, the optical system comprising an optical relay and being arranged to form a virtual image of a relayed hologram at infinity; Figure 8 shows a cross-sectional schematic ray diagram showing features of the optical system of Figure 7; Figure 9 is a cross-sectional schematic view of the optical components of yet another optical system, the optical system comprising an optical relay and being arranged to form a real image of a relayed hologram; Figure 10 shows a cross-sectional schematic ray diagram showing features of the optical system of Figure 9; Figure 11 shows a schematic view of an extended modulator comprising a plurality of replicas of a display device, each replica having a substantially rectangular shape; Figure 12 represents a point cloud-type hologram calculation in which circular wavelets are used; Figure 13 is a schematic view of a portion of a phase-only hologram calculated using a point cloud-type hologram technique utilising circular wavelets; Figure 14 shows a schematic view of an extended modulator comprising a plurality of replicas of a Fourier transform of a hologram, each replica having a substantially circular shape; Figure 15 represents a point cloud-type hologram calculation in which square wavelets are used; Figure 16 is a schematic view of a portion of a phase-only hologram calculated using a point cloud-type hologram technique utilising square wavelets; Figure 17 shows a schematic view of an extended modulator comprising a plurality of replicas of a Fourier transform of a hologram, each replica having a substantially square shape; Figure 18 represents a point cloud-type hologram calculation in which "broken square" wavelets comprising two spatially separated discrete sub-areas are used; Figure 19 shows a sub-hologram calculated in the "broken square" wavelet area on the display device for an individual image point of the picture; Figure 20 is a schematic view of a portion of a phase-only hologram calculated using a point cloud-type hologram technique utilising the broken square wavelets of Figure 18; Figure 21 is a schematic view of a Fourier transform of the hologram of Figure 20; Figure 22 is a schematic view of an example holographic projection system comprising first and second pupil replicators coupled to different portions of a holographic wavefront and which also acts as a spatial filter; Figure 23 is a schematic view of a second example spatial filter for use in a holographic projection system; Figure 24 is a schematic view of a third example spatial filter for use in a holographic projection system; Figure 25A shows a modified sub-hologram of Figure 19, modified such that one sub-area of the sub-hologram has been rotated to compensate for an optical misalignment of a holographic projection system; and Figure 25B shows a Fourier transform of a hologram calculated using sub-holograms according to Figure 25B.

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 codependent 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 proiection 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.

Lame 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 / 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 eye-box.) 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 non-infinite 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 sub-area 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 / 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 one-dimensional 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, VI 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, BO 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, BO 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 / 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 / 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 how to 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 / 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.

Control device The present disclosure is also compatible with optical configurations that include 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. British patent application 2108456.1, filed 14 June 2021 and incorporated herein by reference, discloses the at least one waveguide pupil expander and control device. 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.

Image Formation Figure 6 is a cross-sectional schematic view of the optical components of an optical system 600 in which a relayed hologram is coupled into and replicated by a waveguide 611.

An optical axis of the optical system 600 is shown by dotted line 602 in Figure 6. The optical system 600 comprises a display device 604 which, in this example, is a liquid crystal on silicon spatial light modulator. The display device 604 is arranged to display a hologram of a picture. Downstream of the display device 604 is an optical relay 606. The optical relay 606 comprises a first lens 608 and a second lens 610. The optical system 600 further comprises a waveguide 611 downstream of the second lens 610 of the optical relay 606. The waveguide 611 comprises a pair of opposing surfaces 622, 624 arranged to provide waveguiding of light therebetween in accordance with the previously described examples.

The first lens 608 of the optical relay 606 comprises a front focal plane 612 and a back focal plane 614. The front focal plane 612 is upstream of the first lens 608 and the back focal plane 614 is downstream of the first lens 608. The second lens 608 of the optical relay 606 comprises a front focal plane 616 and a back focal plane 618. The front focal plane 616 is upstream of the second lens 610 and the back focal plane 618 is downstream of the second lens 610. Normals of the front and back focal planes of each of the first and second lenses 608, 610 are parallel to the optical axis 602 and a distance from each of the front and back focal planes to the respective first or second lens is equal to the focal length f of the respective lens. In this example, the display device 604 is positioned substantially at the front focal plane 612 of the first lens 608. In this example, the front focal plane 616 of the second lens 610 is substantially coplanar with the back focal plane 614 of the first lens 608.

In this example, the waveguide 611 is arranged such that back focal plane 618 of the second lens 610 is between the first and second surfaces of the waveguide 622, 624. In the example shown in Figure 6, the focal length f of the first and second lenses 608, 610 is the same. As such, the optical relay forms a 4f system (i.e. the length of the optical relay is equal to four times the focal length of either the first and second lens 608, 610). However, in other embodiments, the focal length of the first lens 608 may be different to the focal length of the second lens 610. In such cases, the optical relay may form a magnifying (or demagnifying) telescope.

The optical system 600 further comprises a coherent light source such as a laser. The coherent light source is not shown in Figure 6. In operation of the optical system 600, the coherent light is arranged to illuminate the display device 604. Said light may thus be spatially modulated in accordance with the hologram of the picture displayed on the display device. The spatially modulated light may be received by the first lens 608 and relayed to the second lens 610. A holographic reconstruction 626 of the picture is formed at the back focal plane 612 of the first lens 608, between the first and second lenses 608, 610. The second lens 610 relays the spatially modulated light to the waveguide 611. As described in relation to earlier Figures, the waveguide 611 replicates the light received from the display device so as to form a plurality of replicas or copies of the hologram displayed on display device 604 such that each replica comprises light spatially modulated in accordance with the hologram on the display device. In embodiments, the optical system further comprises a second waveguide (not shown in the drawings) to provide waveguiding and replication in a second direction such that a two-dimensional array of replicas is output by the second waveguide. The spatially modulated light is relayed from the output of the second waveguide to an eye-box / viewing plane (which is expanded as a result of replication achieved by the waveguides). When a viewing system (such as the eye of a user) is placed at the eye-box / at the viewing plane, the viewing system receives the spatially modulated light which forms a virtual image of the picture of the hologram displayed on the display device at a virtual image distance which is encoded in the hologram.

The optical system 600 is able to provide a good virtual image of the picture of the hologram when a viewing system is positioned in the viewing plane / eye-box. However, artifacts may be formed / appear at the viewing plane (i.e. the plane comprising the plurality of replicas). The artifacts may comprise dark bands resulting from the display device being illuminated with non-uniform intensity light and / or may result from the physical features of the display device (for example, scattering off features of the display device). In any case, the artifacts may be replicated by the waveguide(s) to form a repeating pattern of the artifacts at the viewing plane. Thus, while the virtual image of the picture / holographic reconstruction per se may be good quality, the view of the virtual image of the picture at the viewing plane may appear obstructed by the repeating pattern of artifacts. The viewing system may have to effectively "look through" the repeating pattern of artifacts to observe the virtual image.

Separation of hologram image and holographic reconstruction image Figure 7 is a cross-sectional schematic view of the optical components of a first optical system 700 which is arranged such that an image of the hologram / display device is far removed from a virtual image of a holographic reconstruction of the hologram, thus reducing or eliminating the appearance of the above-described artifacts. The first optical system 700 is arranged such that a Fourier transform of the hologram displayed on the display device 704 is coupled into the waveguide 711 (rather the hologram per se). As explained below, this is because of the presence of a lens 750 between a relayed hologram and the waveguide 711.

The optical system 700 comprises an optical axis represented by dotted line 702 in Figure 7.

The optical system 700 comprises a display device 704 which, in this example, is a liquid crystal on silicon spatial light modulator. The display device 704 is arranged to display a hologram of a picture. Downstream of the display device 704 is an optical relay 706. The optical relay 706 comprises a first lens 708 and a second lens 710.

The display device 704 and the optical relay 706 of the optical system 700 are very similar to the display device 604 and optical relay 706 of the optical system 600. For example, the first lens 708 of the optical relay 706 comprises a front focal plane 712 and a back focal plane 714. The front focal plane 712 is upstream of the first lens 708 and the back focal plane 714 is downstream of the first lens 708. The second lens 708 of the optical relay 706 comprises a front focal plane 716 and a back focal plane 718. The front focal plane 716 is upstream of the second lens 710 and the back focal plane 718 is downstream of the second lens 710.

Normals of the front and back focal planes of each of the first and second lenses 708, 710 are parallel to the optical axis 702 and a distance from each of the front and back focal planes to the respective first or second lens is equal to the focal length f of the respective lens. In this example, the display device 704 is positioned substantially at the front focal plane 712 of the first lens 708. In this example, the front focal plane 716 of the second lens 710 is substantially coplanar with the back focal plane 714 of the first lens 708. In the example shown in Figure 7, the focal length f of the first and second lenses 708, 710 is the same. As such, the optical relay forms a 4f system (i.e. the length of the optical relay is equal to four times the focal length f of either the first and second lens 708, 710). However, in other embodiments, the focal length of the first lens 708 may be different to the focal length of the second lens 710. In such cases, the optical relay may be form a magnifying (or demagnifying) telescope.

Unlike the optical system 600, the optical system 700 further comprises an optical component 750 between the second lens 710 and a waveguide 711. The optical component 750 in this example is a (third) lens. In this example, the third lens 750 is a Fourier lens. A front focal plane 754 of the third lens 750 is upstream of the third lens 750 and is substantially co-planar with the back focal plane 718 of the second lens 710. A back focal plane 757 of the third lens 750 positioned between first and second surfaces 722,724 of the waveguide 711.

In this example, the focal length f of the third lens 750 is the same as the focal length f of the first and second lenses 708, 710. As such, the optical relay 706 and the third lens 750 collectively define a 6f system (in which the separation between the front focal plane 712 of the first lens 708 and the back focal plane 757 of the third lens 750 is equal to six times the focal length of the first / second or third lens 708, 710, 752). However, in other examples, the focal length of the third lens 750 may be different to the focal length of the first lens 708 and / or second lens 710.

So, an important difference between the optical system 600 and the optical system 700 according to the disclosure is that the optical system 700 according to the disclosure comprises an additional lens 750 between the display device 704 and the waveguide 711.

Another important difference between the optical system 600 and the optical system 700 is that, in the optical system 700, the hologram displayed on the display device 704 is arranged such that a holographic reconstruction 756 of the picture of the hologram is formed downstream of the display device when the display device 704 is illuminated with coherent light from a coherent light source such as a laser. This is holographic reconstruction 756 which is formed without the use of a physical lens between the display device 704 and the holographic reconstruction 756. Instead, the hologram is calculated to form the holographic reconstruction 756 at this location. In particular, the hologram is calculated / arranged such that the holographic reconstruction 756 is formed such that a distance between the holographic reconstruction 756 and the first lens 708 is less than the focal length f of the first lens 708 while the distance between the display device 704 and the first lens 708 is equal to the focal length f of the first lens 708.

The optical relay 706 is arranged to relay the hologram on the display device to form a relayed hologram 760 downstream of the second lens 710 and to form a relayed holographic reconstruction 758 downstream of relayed hologram 760. The relayed hologram 760 corresponds to the display device (comprising the displayed hologram of the picture). The relayed holographic reconstruction 758 corresponds to the holographic reconstruction 756.

In this example, the relayed holographic reconstruction 758 is formed such that a distance between the relayed holographic reconstruction 758 and the third lens 750 is less than the focal length of the third lens 750 while the distance between the relayed hologram 760 and the third lens 750 is equal to the focal length of the third lens 750. By positioning the relayed hologram 760 and the relayed holographic reconstruction 758 with respect to the third lens 750 in this way, the third lens 750 can form images of the relayed hologram and relayed holographic reconstruction that are far removed from one another. This is explained in more detailed in relation to Figure 8.

Figure 8 shows a cross-sectional schematic view of the third lens 750 and the waveguide 711 of Figure 7 (as well as the relayed hologram 760 and relayed holographic reconstruction 758). These components are shown separately from the other optical components of the optical system 700 (such as the display device 704 and the optical relay 706). Figure 8 is a schematic ray diagrams showing rays from the relayed hologram 760 and the relayed holographic reconstruction 758.

As the skilled person will understand, a (convex) lens (such as the third lens 750) will form a virtual image of an object at infinity when the object to be imaged is positioned at the focal length of the lens. As above, the relayed hologram 760 is formed (by the optical relay 706) at the focal length f of the third lens 750 (in particular, at the front focal plane 752 of the third lens 750). Thus, the third lens 750 is arranged to form a virtual image of the relayed hologram 760 at infinity. The virtual image at infinity is upstream of the display device 704 / third lens 750. The formation of this virtual image is represented by the rays coming from the relayed hologram 760 to the third lens 750 and then extending parallel. Said rays are shown by the broken lines comprising dots and dashes in an alternating configuration in Figure 8.

The skilled person will also understand that a (convex) lens (such as the third lens 750) will form a virtual image of an object at a finite image distance upstream of said lens when the object to be imaged is positioned such that a distance between the object and the lens is less than the focal length of the lens. As above, the relayed holographic reconstruction 758 is formed (by the optical relay 706) such that the distance between the relayed holographic reconstruction 758 arid the third lens 750 is less than the focal length of the third lens 750. In other words, the relayed holographic reconstruction 758 is positioned between the front focal plane 752 of the third lens 750 and the third lens 750 itself By forming the relayed holographic reconstruction 758 here, the third lens 750 is arranged to form a virtual image 800 of the relayed holographic reconstruction 758 upstream of the third lens 750 and at a finite image distance. The formation of this virtual image 800 is represented by the rays coming from the relayed holographic reconstruction 758 to the third lens 750 and then converging upstream of the third lens 750. Said rays are shown by broken lines comprising dots only in Figure 8.

Both the virtual image of the relayed hologram 760 and the virtual image 800 of the relayed holographic reconstruction 758 are upstream of the third lens 750. However, the virtual image distance of the virtual image of the relayed hologram 760 is at infinity whereas the virtual image distance of the virtual image 800 of the relayed holographic reconstruction 758 is finite. Thus, the two virtual images are far removed from one another (in fact, the separation between the two virtual images is effectively infinite). The artifacts (described above) may be features in the virtual image of the relayed hologram 760. The appearance of the artifacts may not be present / apparent in the virtual image 800 of the relayed holographic reconstruction 758. The inventors have found that, by separating the two virtual images as described, the prominence of the artifacts in a viewing system's field of view may be substantially reduced or even eliminated. Without wishing to be bound by theory, it is believed that this is because the virtual image of the relayed hologram 760 (comprising the artifacts) is far removed from the virtual image of the relayed holographic reconstruction 758 and, in this case, projected right out to infinity, beyond the virtual image of the relayed holographic reconstruction 758. Thus, the viewing system is not required to "look through" the virtual image of the relayed hologram 760 to view the virtual image of the relayed holographic reconstruction 758.

Figure 9 is a cross-sectional schematic view of the optical components of a second optical system 900 that is arranged such that an image of the hologram / display device is far removed from the virtual image of the holographic reconstruction, thus reducing or eliminating the appearance of the above-described artifacts. The second optical system 900 is similar to the first optical system 700 in that the second optical system 900 is arranged such that a relayed hologram and relayed holographic reconstruction are formed at positions with respect to a third lens so that images of the two are far removed from one another.

However, in the second optical system 900, the image of the relayed hologram is a real image formed downstream of the waveguide (for example, behind a viewing system) rather than at infinity and upstream of the third lens. This is described in more detail below.

Like the first optical system 700, the second optical system 900 is arranged such that a Fourier transform of the hologram displayed on the display device 904 is coupled into the waveguide 911 (rather the hologram per se).

The optical system 900 comprises an optical axis represented by dotted line 902 in Figure 9.

The optical system 900 comprises a display device 904 which, in this example, is a liquid crystal on silicon spatial light modulator. The display device 904 is arranged to display a hologram of a picture. Downstream of the display device 904 is an optical relay 906. The optical relay 906 comprises a first lens 908 and a second lens 910. The optical system 900 further comprises a third lens 950.

The display device 904, the optical relay 906 and the third lens 950 of the optical system 900 are very similar to the display device 704, optical relay 706 and third lens of the first optical system 700. For example, the first lens 908 of the optical relay 906 comprises a front focal plane 912 and a back focal plane 914. The front focal plane 912 is upstream of the first lens 908 and the back focal plane 914 is downstream of the first lens 908. The second lens 910 of the optical relay 906 comprises a front focal plane 916 and a back focal plane 918. The front focal plane 916 is upstream of the second lens 910 and the back focal plane 918 is downstream of the second lens 910. Normals of the front and back focal planes of each of the first and second lenses 908, 910 are parallel to the optical axis 902 and a distance from each of the front and back focal planes to the respective first or second lens is equal to the focal length f of the respective lens. In this example, the front focal plane 916 of the second lens 910 is substantially coplanar with the back focal plane 914 of the first lens 908. In the example shown in Figure 9, the focal length f of the first and second lenses 908, 910 is the same. As such, the optical relay forms a 4f system (i.e. the length of the optical relay is equal to four times the focal length f of either the first and second lens 908, 910). However, in other embodiments, the focal length of the first lens 908 may be different to the focal length of the second lens 910. In such cases, the optical relay may form a magnifying (or demagnifying) telescope. As in the first optical system 700, the third lens 950 is a Fourier lens. A front focal plane 954 of the third lens 950 is upstream of the third lens and is substantially co-planar with the back focal plane 918 of the second lens 910. A back focal plane 957 of the third lens 950 positioned between first and second surfaces of the waveguide 911. In this example, the focal length f of the third lens 950 is the same as the focal length of the first and second lenses 908, 910. As such, the optical relay 906 and the third lens 950 collectively define a 6f system (in which the separation between the front focal plane 912 of the first lens 908 arid the back focal plane 957 of the third lens 950 is equal to six times the focal length of the first / second or third lens 908, 910, 952). However, in other examples, the focal length of the third lens 950 may be different to the focal length of the first lens 908 and / or second lens 910.

The key difference between the first optical system 700 and the second optical system 900 is that, in the second optical system 900, the display device 904 is not positioned substantially at the front focal plane 912 of the first lens 908 (as is the case in the first optical system 700). Instead, the distance between the display device 904 and the first lens 908 is greater than the focal length f of the first lens 908. However, like in the first optical system 700, in the second optical system 900, the hologram displayed on the display device 904 is arranged such that a holographic reconstruction 956 of a picture of the hologram is formed downstream of the display device such that a distance between the holographic reconstruction 956 and the first lens 908 is less than the focal length f of the first lens 908.

As such, a distance between the display device 904 and the holographic reconstruction 956 in the second optical system 900 is greater than a distance between the display device 704 and the holographic reconstruction 756 in the second optical system 700.

The optical relay 906 is arranged to relay the hologram on the display device to form a relayed hologram 960 downstream of the second lens 910 and to form a relayed holographic reconstruction 958 downstream of relayed hologram 960. The relayed hologram 960 corresponds to the display device (comprising the displayed hologram of the picture). The relayed holographic reconstruction 958 corresponds to the holographic reconstruction 956.

In this example, the relayed holographic reconstruction 958 is formed such that a distance between the relayed holographic reconstruction 958 and the third lens 950 is less than the focal length of the third lens 950 while the distance between the relayed hologram 960 and the third lens 950 is greater than the focal length of the third lens 950. By positioning the relayed hologram 960 and the relayed holographic reconstruction 986 with respect to the third lens 950 in this way, the third lens 950 can form images of the relayed hologram and relayed holographic reconstruction that are far removed from one another. This is explained in more detailed in relation to Figure 10.

Figure 10 shows a cross-sectional schematic view of the third lens 950 and the waveguide 911 of Figure 9 (as well as the relayed hologram 960 and relayed holographic reconstruction 958). These components are shown separately from the other optical components of the optical system 900 (such as the display device 904 arid the optical relay 906). Figure 10 is a schematic ray diagrams showing rays from the relayed hologram 960 and the relayed holographic reconstruction 958.

As the skilled person will understand, a (convex) lens (such as the third lens 958) will form a real image of an object when the object to be imaged is positioned beyond the focal length of the lens. Said real image will be formed at a finite image distance downstream of said lens. As above, the relayed hologram 960 is formed (by the optical relay 906) beyond the focal length f of the third lens 950. In particular, the distance between the relayed hologram 960 and the third lens 950 is greater than the focal length f of the third lens. Thus, the third lens 950 is arranged to form a real image 1002 of the relayed hologram 960 downstream of the third lens 950. The formation of this real image 1002 is represented by the rays coming from the relayed hologram 960 to the third lens 950 and then converging at a point which is downstream of the third lens 950 (and waveguide 911). Said rays are shown by the broken lines comprising dots and dashes in an alternating configuration in Figure 10.

In both the first and second optical systems 700,900, the relayed holographic reconstruction is formed (by the optical relay) such that the distance between the relayed holographic reconstruction and the third lens is less than the focal plane of the third lens. Thus, like in the first optical system 700, in the second optical system 900, the third lens 950 is arranged to form a virtual image 1000 of the relayed holographic reconstruction 958 upstream of the third lens 950 and at a finite image distance. The formation of this virtual image 100 is represented by the rays coming from the relayed holographic reconstruction 958 to the third lens 950 and then converging at a point which is upstream of the third lens 950. Said rays are shown by the broken lines comprising dots only in Figure 10.

So, the third lens 950 (and optical system 900 more generally) is arranged to form a virtual image of the relayed holographic reconstruction 958 upstream of the third lens and a real image of the relayed hologram 960 downstream of the waveguide 911. In this way, the two images (virtual and real) are far removed from one another.

In examples, the real image of the relayed hologram 960 is downstream of a viewing window / eyebox (which is not shown in the Figures but which would be located between the waveguide 911 and the real image of the relayed hologram 960). Thus, because, as above, it is believed that the artifacts are visible / apparent in the image of relayed hologram 960 and not the relayed holographic reconstruction 958, the prominence of the artifacts in a viewing system's field of view may be substantially reduced or even eliminated. In particular, the image of the relayed holographic reconstruction 958 is in front of the viewing system and the relayed hologram 960 is behind the viewing system such that the viewing system is not required to "look through" an image of the relayed hologram (comprising the artifacts) when viewing the virtual image of the holographic reconstruction 958.

The first and second optical systems 700,900 (according to the disclosure) described above each comprise an optical relay 702,902. The optical relay in each example forms a relayed hologram 760,960 and a relayed holographic reconstruction 758,958 of a picture of the hologram. The third lens 750,950 in each examples then forms images of the relayed hologram and relayed holographic reconstruction. Some examples according to the disclosure do not comprise the optical relay. These examples comprise a (single) lens which forms images of the hologram / display device per se and the holographic reconstruction per se, rather than relayed versions of the hologram and holographic reconstruction. However, the principal is substantially the same as previously described in that the hologram / display device and holographic reconstruction are positioned with respect to the (single) lens so that the image of the hologram / display device is far removed from the image of the holographic reconstruction such that the appearance I impact of the above-described artifacts is reduced / eliminated.

Virtual replicas of the display device formed by the waveguide or wavequides As described above, in relation to Figure 6, the waveguide 611 of the optical system 600 replicates the light received from the display device so as to form a plurality of replicas or copies of the hologram displayed on display device 604 such that each replica comprises light spatially modulated in accordance with the hologram on the display device. The optical system further comprises a second waveguide (not shown in the drawings) to provide waveguiding and replication in a second direction such that a two-dimensional array of replicas is output by the second waveguide. A portion of this two-dimensional array of replicas is shown in Figure 11 which is a perspective view.

As noted above with reference to Figure 4, a one-dimensional waveguide 408 may be arranged to expand the exit pupil of a display system. The display system comprises a display device 402 displaying a hologram, which is output at "bounce" point BO of waveguide 408. In addition, the waveguide forms a plurality of replicas of the hologram, at respective "bounce" points B1 to B8 along its length, corresponding to the direction of pupil expansion.

As shown in Figure 4, 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'.

Figure 11 shows an example visualisation of an "extended modulator" or "virtual surface" comprising a 3D array including a hologram formed on a display device and a plurality of replicas of the hologram formed by a waveguide. Figure 11 shows an extended modulator array formed by the optical system 600 of Figure 6. Position (0,0) of the array may correspond to the display device. Each of the subsequent components of the array (to position (4,2)) are replicas of the display device. Due to the optical path distance through the one or more waveguides, the depths of the virtual replicas (measured from the eye-box) are different. This results in the "staggering" of the replicas in z direction, as shown in Figure 11. For the avoidance of doubt, these different virtual replicas of the display device contribute to the same reconstructed virtual image which therefore appears at the same depth to the viewer from all positions within the eye-box.

When the extended modulator or virtual surface is formed by the optical system 600 of Figure 6, each replica is a replica of the display device 604 and so has a shape corresponding to the shape of the display device 604. In this example, the display device 604 has a rectangular shape and so the replicas of the extend modulator (being replicas of the display device 604) also have a rectangular shape. The inventors have found that this is not the case when each replica is instead a replica of the Fourier transform of the (relayed) hologram (as in Figure 7, for example). In that case, the shape of the Fourier transform of the (relayed) hologram is dependent on how the hologram was calculated, rather than the shape of the display device. For example, the inventors have found that, when a point cloud-type calculation method is used to determine the displayed hologram, the shape of the Fourier transform of the hologram is dependent on / corresponds to the shape of the wavelet traced back to the display device from image points of a target image in a ray-tracing calculation. In particular, in point cloud-type calculations, a wavelet is traced back from each point of a target image to the display device to define a sub-area of the display device. A sub-hologram is typically calculated for each sub-area of the display device. When the sub-hologram is suitably illuminated, that sub-hologram is arranged to form a particular image point. Conventionally, the wavelet used in point cloud-type holography calculations takes the form of a light cone which forms a circular footprint on the display device for each image point. Thus, each sub-hologram / sub-area on the display device conventionally has a circular shape. The inventors have surprisingly found that the Fourier transform of the (relayed) hologram coupled into the waveguide and replicated has a corresponding circular shape such that the extended modulator comprises an array of circular replicas. The inventors have therefore recognised that the shape of the wavelet can be modified to modify the shape of the Fourier transform of the hologram (and so, because it is this Fourier transform of the hologram that is replicated, modify the shape of the replicas forming the extended modulator). This is explained in relation to circular and square wavelets herein.

Figure 12 represents a conventional point cloud-type calculation in which circular wavelets 1206 are used. More specifically, a light cone is propagated from the image point 1202 towards the display device computationally by ray tracing. In this example, as is convention, the range of angles (represented by 1212 in Figure 12) of the simulated / computationally modelled light cone is substantially equal to the maximum diffraction angle of the display device / optical system. Because the ray tracing is using a cone of light as the wavelet 1206, the wavelet 1206 may be described as circular and the footprint 1208 of the light cone on the display device is circular.

Figures 13 shows an example portion of a phase hologram 1304. Figure 13 is phase plot, representing the phase delay applied to incident light. Greater amounts of phase delay are represented by darker regions of the plot. The hologram 1304 is of a target picture. Figure 13 shows a portion of a hologram 1304 that has been calculated using a conventional point cloud-type method using circular wavelets for each image point. So, the hologram effectively comprises a plurality of circular sub-holograms or wavelets 1310. A circular wavelet 1310 is identified in Figure 13 by the dashed / broken circular line. The circular wavelet 1310 encodes an image point of a target image. The hologram has been calculated such that a holographic reconstruction of the hologram is formed 10 millimetres away from the hologram.

Figure 14 shows a schematic view of an extended modulator formed by the optical system 700 or 900 (of Figure 7 or 9) when a conventionally calculated hologram is displayed on a display device (i.e. with circular wavelets). Figure 14 is a view of the extended modulator from viewing plane described above (which is in a plane parallel to the x-y plane). In other words, Figure 14 is a "head-on" schematic view of the extended modulator. As shown in Figure 14, the inventors have found that the replicas 1402 formed by optical systems 700,900 (when a conventionally calculated hologram is displayed on the respective display device) have a circular shape. That is, a perimeter of each of the replicas has a circular shape. In other words, a Fourier transform of the (conventionally calculated) hologram has a circular shape, which is replicated.

Figure 15 represents a point cloud-type calculation in which square wavelets 1506 are used. More specifically, a light cone is propagated from the image point 1502 towards the display device computationally by ray tracing. In this example, as is convention, the range of angles (represented by 1512 in Figure 15) of the simulated / computationally modelled light cone 1510 is substantially equal to the maximum diffraction angle of the display device / optical system (in the diagonal direction). Because the ray tracing is using a square (rather than circular) wavelet 1506, the footprint 1508 of the wavelet 1506 on the display device is square.

Figures 16 shows an example portion of a phase hologram 1604. Like Figure 13, Figure 16 is a phase plot, representing the phase delay applied to incident light. Greater amounts of phase delay are represented by darker regions of the plot. The hologram 1604 is of the target picture as the hologram of Figure 13. Figure 16 shows a portion of a hologram 1604 that has been calculated using square wavelets for each image point (instead of circular wavelets as in Figure 13). A square wavelet 1610 is identified in Figure 16 by the dashed / broken circular line. The square wavelet 1610 encodes an image point of a target image.

The hologram has been calculated such that a holographic reconstruction of the hologram is formed 10 millimetres away from the hologram.

Figure 17 shows a schematic view of an extended modulator formed by the optical system 700 or 900 (of Figure 7 or 9) when a hologram is displayed on the respective display device 704,904 that is a point cloud-type hologram that has been calculated using square wavelets. Figure 17 is a corresponding "head-on" view of the extended modulator as shown in Figure 14. Because the hologram in Figure 17 has been calculated using square wavelets, each sub-hologram on the display device has a square shape. Thus, the Fourier transform of the hologram also has a square shape and the extended modulator (formed of replicas of the Fourier transform of the hologram) comprises an array of square replicas 1702.

Sub-holograms formed in a plurality of sub-areas The inventors have recognised that any arbitrary wavelet shapes can be used to "engineer" the Fourier transform of the hologram to have a corresponding (arbitrary) shape. For example, the inventors have recognised that a wavelet comprising first and second sub-areas that are discrete and spatially separated can be used in the hologram calculation and that this will result in a Fourier transform of the hologram having a corresponding first and second area (being discrete and spatially separated). The inventors have recognised that there are a number of scenarios / examples in which such an unconventional shape would be desirable.

Figure 18 represents a point cloud-type calculation in which broken square wavelets 1806 are used. More specifically, light rays are propagated from the image point 1802 towards the display device computationally by ray tracing. Initially, the ray tracing forms a square wavelet 1806 in the same way as described in relation to Figure 15. However, the sub-hologram that is calculated does not fill this square wavelet / area. Instead, the square wavelet 1806 is cropped into two discrete sub-areas comprising a left sub-area 1812 and a right sub-area 1814. The left and right sub-areas 1812, 1814 are discrete and spatially separated. A sub-hologram (for forming point 1802) is then calculated for / in the left and right sub-areas 1812,1814 (but not outside the left and right sub-areas). A sub-hologram 1900 formed in this way is shown more clearly in Figure 19. The sub-hologram 1900 comprises a first (left) portion 1902 and a second (right) portion 1904. An area / region 1906 is defined between the first and second portions 1902,1906. No hologram / diffractive content is present in / calculated for the area / region 1906.

Figures 20 shows an example portion of a phase hologram 2004. Figures 20 is a phase plot, representing the phase delay applied to incident light. Greater amounts of phase delay are represented by darker regions of the plot. The hologram is of the same target picture as in Figures 13 and 17. Figure 20 shows a portion of a hologram 2004 that has been calculated using the broken square wavelets (shown in Figure 18) for each image point. Two broken square wavelets 2010,2012 are identified in Figure 20 by the dashed / broken line. Each broken square wavelet 2010,2012 encodes an image point of a target image. Because the hologram comprises a superposition of all sub-holograms / wavelets for all points, many of the sub-holograms / wavelets overlap one another. Thus, the area / region 1906 of an individual wavelet that is "empty" during the calculation of the sub-hologram may appear to be filled with the diffractive content of one or more other sub-holograms / wavelets when the various sub-holograms are combined to form hologram 2004. This is the case for wavelet 2010 in particular (out of wavelets 2010 and 2012). The hologram has been calculated such that a holographic reconstruction of the hologram is formed 10 millimetres away from the hologram.

Figure 21 represents a Fourier transform of the hologram 2004 when the hologram 2004 is displayed on a display device, appropriately illuminated and transformed by an optical component (for example, as formed by the optical systems of Figure 7 or 9). Figure 21 shows how the Fourier transform of the hologram 2004 comprises a left area 2102 and a right area 2104. The shape, size and orientation of the left and right area 2102,2104 correspond, respectively to the shape, size and orientation of the left and right sub-areas 1902,1904 / 1812,1814 of each sub-hologram / wavelet used in the hologram calculation. Thus, there is similarly an empty region 2106 between the left and right areas 2102,2104. However, unlike in the sub-hologram, the empty region 2106 comprises a bright spot 2108. The bright spot 2108 corresponds to zero order / so called "DC spot" light. This bright spot 2108 may be considered noise and it is advantageous to prevent this bright spot 2108 from being received by a viewing system using a spatial filter. The inventors have recognised that the shape, size and orientation of the left and right sub-areas 1812,1814 of the wavelet used in the hologram calculation can be selected such that the bright spot 2108 falls in the empty region 2106 (as shown in Figure 21). Thus, it is straightforward to nullify (e.g. absorb / mask) the bright spot 2108 without nullifying content of the left and right areas 2102,2104. In some examples of holographic projection systems, it is advantageous to couple the left and right areas 2102,2104 into different optical branches of the holographic projection system. By spatially separating the left and right area 2102, 2104 (such that the empty region 2106 is formed between the left and right areas 2102,2104) the left and right areas 2102, 2104 can be independently aligned with the respective input ports of the different optical branches of the holographic projection system. There is no need, for example, for a knife edge mirror and for the (Fourier transform of the hologram) to be exactly aligned with the knife edge mirror and / or the bright spot 2108 can be removed using a spatial filter. Several examples of this are described below.

Example 1 -Double waveQuide with spatial filter Figure 22 shows a first example of a holographic projection system 2200 comprising a spatial filter optimised for use with a hologram calculated using wavelets as shown in Figures 18 and 19. Figure 22 is a schematic cross-sectional view that is perpendicular to the view of, for example, Figure 7 (and is from above). The system 2200 comprises a display device 2204 arranged to display the hologram 2004. The system further comprises an optical component which, in this example, is a lens 2250. The lens 2250 has a front focal plane 2252 coupled to the display device 2204 and a back focal plane 2254. The hologram 2004 is arranged to form a holographic reconstruction 2210 a relatively short distance from the display device 2204 (within the focal length of the lens 2250). The system further comprises a first waveguide 2260 and a second waveguide 2270. The first waveguide 2262 comprises a first input port 2262 and the second waveguide 2270 comprises a second input port 2272. The first and second input ports 2262,2272 are coupled to the back focal plane 2254 of the lens 2250.

The system 2200 is arranged such that a Fourier transform of the hologram 2004 displayed on the display device 2204 is formed at back focal plane 2254. The Fourier transform of the hologram 2004 comprises left and right areas 2102,2104 (as described above). The first input port 2262 of the first waveguide 2260 is coupled to the first area 2102 and the second input port 2272 of the second waveguide 2270 is coupled to the second area 2104. Thus, the first waveguide 2260 is arranged to replicate the first area 2102 of the Fourier transform of the hologram and the second waveguide 2270 is arranged to replicate the second area 2104. Because the first and second areas 2102,2104 of the Fourier transform of the hologram are spatially separated, the first and second input ports 2262,2272 can also be spatially separated. In fact, it is preferable for there to be discontinuity between the first and second input ports 2262,2272 (as shown in Figure 22). The system is arranged such that the discontinuity is aligned with the empty region 2106. Light incident on the discontinuity may be nullified (e.g. absorbed). Thus, the bright spot 2108 of Figure 21 can be nullified. In this way, the double waveguide arrangement can simultaneously expand a pupil in two (opposing) directions of the same dimension while also acting as a spatial filter. In this example, the first waveguide 2260 may be considered to form a first branch of the optical system and the second waveguide 2270 may be considered to form a second branch of the optical system.

Example 2 -Reflective spatial filter Figure 23 shows a second example of holographic projection system, specifically, Figure 23 shows spatial filter 2300 of the holographic projection system. Spatial filter 2300 comprises a holographic wavefront splitter-recombiner 2312 and first to fourth receiving surfaces 2302 to 2308 which combined operate to eliminate the bright spot 2108 / DC spot and recombine first and second portions of a holographic wavefront. In this example, the wavefront splitter recombiner 2312 is optically coupled to the back focal plane 2254 of the lens 2250. In some examples, the wavefront splitter recombiner 2312 takes the place of the first and second waveguides 2260,2270 shown in Figure 22.

In this example, the holographic wavefront splitter-recombiner 2312 comprises a solid, substantially triangular block or prism. The triangle has an isosceles shape in this example, with the base 2313 of the triangle shape facing away from the lens 2250 and a first edge 2314 (which is indicated by a corner, or apex, in the cross-sectional view of Figure 23) which is nearest to the lens 2250 and is substantially coincident with the back focal plane 2254 of the lens 2250. A first input surface 2316 of the holographic wavefront splitter-recombiner 2212 slopes upwards, away from the lens 2250 and away from the first edge 2214. The first input surface 2316 may thus be described as being on the positive (+) side of the wavefront splitter-recombiner 2312. A second input surface 2318 slopes downwards, away from the lens 2250 and away from the first edge 2314. The second input surface 2318 may thus be described as being on the negative (-) side of the wavefront splitter-recombiner 2312. The first input surface 2318 is arranged to receive / be coupled to the left area 2102 of the Fourier transform of the hologram (shown in Figure 21).

There is a discontinuity, or gap, in the holographic wavefront splitter-recombiner 2312, which substantially coincides with the first edge 2314 and therefore prevents the first 2316 and second 2318 input surfaces from physically touching or abutting one another. This discontinuity extends from the first edge 2314, substantially towards the core of the holographic wavefront splitter-recombiner 2312 -but not the whole way across the holographic wavefront splitter-recombiner 2312. The discontinuity therefore appears as a slit, or opening, 2320 in an input side of the holographic wavefront splitter-recombiner 2312. The holographic wavefront splitter-recombiner 2312 is aligned such that the slit 2320 runs substantially along the central optical axis of the system, and therefore receives light of the DC spot / bright spot 2108, when the holographic wavefront splitter-recombiner 2312 is correctly aligned with the focal plane of the lens 2250. The light of the DC spot is therefore trapped within the slit 2320 and is unable to travel on towards the viewer.

The first input surface 2316 is a reflective surface. It extends at approximately 45 degrees to the substantially central optical axis, in a positive direction. The reflective first input surface 2316 is configured to reflect the light received from the lens 2250 that is above the slit 2320 and to direct it, substantially perpendicular to the central axis, towards the first receiving surface 2302. This is the light / portion of the holographic wavefront that is associated with / forms the left area 2102 of the Fourier transform of the hologram. The first input surface 2316 therefore directs all light on a first side of the substantially central optical axis (apart from the light closest to that axis, which includes the light of the DC spot and which is trapped by the slit 2320), towards the first receiving surface 2302.

The first receiving surface 2302 is reflective and is configured to direct the light in a direction that is substantially parallel to the central optical axis of the system, towards a second receiving surface 2304. In this example, both the first and second receiving surface 2302,2304 are substantially planar reflective surfaces of triangular blocks or prisms. The first and second receiving surfaces 2302 are both angled at 45 degrees to the central optical axis 600. In turn, the second receiving surface 2304 is configured to direct the light back down in a direction perpendicular to the central optical axis 600 and towards a receiving surface 2330 of a recombiner system of the holographic wavefront splitter-recombiner 2312. The recombiner system further comprises beam splitter 2334 comprising a partially reflective-partially transmissive first surface 2336. The receiving surface 2330 of the recombiner system is another planar reflective surface and is arranged to redirect the light to the first surface 2336 of the beam splitter 2334.

The second input surface 2318 is also a reflective surface. The second input surface 2318 is arranged to receive / be coupled to the right area 2104 of the Fourier transform of the hologram (shown in Figure 21). Light forming or contributing to the right area 2104 may be referred to as a second portion of a holographic wavefront. The second input surface 2318 also extends at approximately 45 degrees to the substantially central optical axis of the system 600, but in a negative direction. The reflective second input surface 2318 is configured to reflect the light from the lens 2350 that is below the slit 2320 and to direct it, substantially perpendicular to the central axis, towards a third receiving surface 2306. The second input surface 2316 directs all light on a second, opposite side of the substantially central optical axis (apart from the light closest to that axis, which includes the light of the DC spot and which is trapped by the slit 2320) towards the third receiving surface 2306.

The third receiving surface 2306 is reflective and is configured to direct the light in a direction that is substantially parallel to the central optical axis of the system 600, towards a fourth receiving surface 1508. In turn, the fourth receiving surface 2308 is configured to direct the light back up in a direction perpendicular to the central optical axis 600 to the first surface 2336 of the beam splitter 2334.

The first surface 2336 of the beam splitter 2334 is partially-transmissive and partially-reflective. As such, when the light of the first portion of the holographic wavefront is received at the first surface 2336 from the recombiner receiving surface 2330, a first component 2340 of the light is transmitted by the first surface 2336 and a second component 2342 of the light is reflected by the first surface 2336. The transmitted first component 2340 continues to propagate in a direction substantially parallel to the central optical axis 600. Similarly, when the light of the second portion of the holographic wavefront is received at the first surface 2336 from the fourth receiving surface 2308, a first component 2344 of the light is reflected by the first surface 2336 and a second component 2346 of the light is transmitted by the first surface 2336.

The first to fourth receiving surfaces 2302 to 2308 and the holographic wavefront splitterrecombiner 2312 are arranged such that the transmitted first component 2340 of the (positive) first portion of the holographic wavefront is recombined with the reflected first component 2344 of the (negative) second portion of the holographic wavefront. The two portions of holographic wavefront are recombined substantially without a gap therebetween. Therefore, the first and second portions of the holographic wavefront, that propagate onwards from the first surface 2336 (which forms an output side of the holographic wavefront splitter recombiner 2312), may be referred to as being adjoined.

Optionally, wavefront splitter recombiner 2312 comprises a second combiner receiving surface 2350 which is arranged to receive the (positive) reflected second component 2342 and the (negative) transmitted second component 2346. The second combiner receiving surface 2350 is arranged to redirect the second components 2342, 2346 in a direction parallel to the central optical axis 600. The two components can be combined in a similar way to the two first components, as described above. In this way, a second processed holographic wavefront may be generated comprising adjoined first and second portions of the input holographic wavefront. The advantage of this arrangement is that the (positive) reflected second component 2342 and the (negative) transmitted second component 1546 can usefully be recovered. The light of these components might otherwise be lost and wasted.

Like example 1, example 2 utilises the (broken square) form of the Fourier transform of the hologram to process the holographic wavefront in a convenient way. In example 2, the first input surface 2316 may be considered to direct light into a first branch of the optical system (the first branch comprising first input surface 2316, first and second receiving surfaces 2302, 2304 and receiving surface 2330). The second input surface 2318 may be considered to direct light into a second branch of the optical system (the second branch comprising second input surface 2318, third and fourth receiving surfaces 2306, 2308 and partially reflective-partially transmissive first surface 2336).

Example 3 -Refractive spatial filter Figure 24 shows another example of a holographic wavefront splitter recombiner 2412. This holographic wavefront splitter recombiner 2412 utilizes refraction to process a holographic wavefront, rather than reflection between various (reflective) receiving surfaces, as in the previous example.

The holographic wavefront splitter recombiner 2412 of Figure 24 is formed substantially of a solid slab 2402 of transparent material having a refractive index of greater than 1 (in this example). The holographic wavefront splitter recombiner 2412 comprises an input side 2404 and an output side 2406. The solid slab 2402 of transparent material is formed of glass in this embodiment and comprises a first slab portion 2408 and a second slab portion 2410. In this example, the first slab portion 2408 may be considered to form a first branch of the optical system and the second slab portion 2410 may be considered to form a second branch of the optical system. The first slab portion 2408 comprises a first pair of parallel surfaces comprising a first input surface 2412 and a first output surface 2414. The second slab portion 2410 comprises a second input surface 2416 and a second output surface 2418. Both the first and second input surfaces 2412, 2416 are at an acute angle to the central optical axis 600 but one of the acute angles is measured in a clockwise direction and the other is measured in an anti-clockwise direction such that the overall shape of the solid slab 2402 is a chevron shape. Between the first and second input surfaces 2412, 2416 is a chamfered edge 2420.

The holographic wavefront splitter recombiner 2412 is arranged to receive a holographic wavefront along the central optical axis and is arranged such that a first portion 2422 of the holographic wavefront is received by the first input surface 2412 and a second portion 2424 of the holographic wavefront is received by the second input surface 2416. Again, the first portion 2422 of the holographic wavefront is a portion that contributes to / forms the left area 2102 of the Fourier transform of the hologram and the second portion 2424 of the holographic wavefront is a portion that contributes to / forms the right area 2104 of the Fourier transform of the hologram.

A third portion 2426 of the holographic wavefront comprising the bright spot 2108 / DC spot light is received at the chamfered edge 2422 between the first and second input surfaces.

The chamfered edge 2422 is angled / arranged such that light of the third portion 2426 of the holographic wavefront is totally internally reflected between either the first input surface 2412 and the first output surface 2414 or between the second input surface 2416 and the second output surface 2418 (the latter is shown by light ray 1248 in Figure 16). The light may then substantially escape out of an end surface of the slab 2402.

In this example, the slab 2402 (in particular, the angle of the first and second surfaces) is arranged such that light of the first and second portions 2422,2424 of the holographic wavefront is substantially transmitted through the slab 2402 from the first or second input surface to the respective first or second output surface. Because the slab 2402 comprises a material having a refractive index greater than 1, and the light is travelling from air into the slab, light is bent towards the normal of the respective first and second input surface 2412,2416 on entry into the slab. Because the first and second slab portions of the slab2402 form a chevron shape, light of the first portion2422 of the holographic wavefront is bent towards a different direction to light of the second portion 2424. When the light of the first and second portions 2422,2424 reaches the respective output surfaces 2414,2418, the light of each portion returns to parallel. This is represented by the dotted lines representing the light rays defining the edge of each of the first and second portions 2422,2424 in Figure 24. Note that the holographic wavefront in Figure 24 again comprises diverging light. However, the light rays represented by the dotted lines in Figure 24 are central rays of diverging wave bundles at the edges of the respective first and second portions 2422,2424 such that these (central) light rays remain substantially parallel to one another.

The slab 2402 is arranged such that, by the time the light rays of the respective first and second portions 2422,12424 reaches the output surface 2414,2418 the first and second portions 2422,2424 of the holographic wavefront are adjoined to one another to form a processed holographic wavefront in which the third portion 2426 has been nullified.

Correction for Optical Misalignments Examples 2 and 3 described above both process a holographic wavefront such that the first and second portions of the holographic wavefront (corresponding to the left and right areas 2102,2104 of Figure 21) are sent down different branches of the optical system and processed so as to be adjoined to one another. Assuming the respective branches of the optical system are correctly aligned, the output of both the second and third examples will appear as is shown in Figure 25A. However, it can be difficult / time consuming to ensure that both branches are correctly aligned. If there is an optical misalignment, the first and second portions of the holographic wavefront will not be correctly adjoined (i.e. will be misaligned). This will adversely affect the quality of a holographic reconstruction formed by the system.

The inventors have recognised that the wavelet used in the sub-hologram calculation can be adjusted to (pre-) compensate for these optical misalignments. For example, Figure 25A shows how a first sub-area 2502 can be rotated relative to a second sub-area 2504. Figure 25B shows how, when using such a wavelet, the Fourier transform of the hologram 2510 comprises first and second areas 2512, 2514 having a corresponding shape (in particular, in which the first area 2512 is rotated relative to the second area 2514). The rotation is selected such that, when the first and second areas 2512 are coupled into the respective branches of the respective optical system, the rotation pre-compensates for a rotation caused by a misalignment in the first branch. The skilled reader should appreciate that either or both of the sub-areas could be rotated and that other adjustments could be applied to either of the sub-areas of the wavelet to compensate for optical misalignments (for example, repositioning, scaling, skewing).

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

CLAIMS1. A hologram engine for calculating a hologram of a picture for displaying on a display device, the picture comprising a plurality of image points, the hologram engine being arranged to, for each image point: define discrete first and second sub-areas on the display device, the first and second sub-areas being sub-areas of an area defined by the diffraction angle and the position of the image point; and determine a sub-hologram for the image point in the first and second sub-areas.
2. A hologram engine as claimed in claim 1, wherein the hologram engine is arranged to define the area on the display device for each image point using a straight line path from the image point to the display device, optionally, wherein the straight line path is normal to a surface of the display device.
3. A hologram engine as claimed in claim 1 or 2, wherein each first sub-area is at least partially spatially separated from the respective second sub-area.
4. A hologram engine as claimed in any one of the preceding claims, wherein the area on the display device for each image point comprises a contiguous group of pixels of the display device, wherein the first sub-area comprises a first subset of pixels of the respective contiguous group of pixels; and wherein the second sub-area comprises a second subset of pixels of the respective group of pixels.
5. A hologram engine as claimed in any one of the preceding claims, wherein the hologram engine is arranged to output a hologram by combining the sub-holograms determined for each of the image points, optionally, wherein combining comprises adding.
6. A hologram engine as claimed in any one of the preceding claims, wherein each first sub-area has a first shape and wherein each second sub-area has a second shape, optionally, wherein the first shape and second shape are substantially the same or complementary/opposing.
7. A hologram engine as claimed in claim 6, wherein the first shape of each first sub-area is congruent with the first shape of every other first sub-area; and wherein the second shape of each second sub-area is congruent with the second shape of every other second sub-area.
8. A hologram engine as claimed in claim 6 to 7, wherein the hologram is arranged such that a Fourier transform of the hologram has a first area having the first shape and a second area having the second shape.
9. A hologram engine as claimed in claim 8, wherein the Fourier transform of the hologram further comprises a non-content portion defined between the first and second 10 areas.
10. A holographic projection system comprising: a display device arranged to display a hologram of a picture comprising a plurality of image points, the hologram comprising a sub-hologram comprising discrete first and second sub-areas for each image point, the first and second sub-areas being sub-areas of an area of the display device defined by the diffraction angle of the display device and the position of the respective image point; wherein the display device is arranged to spatially modulate light in accordance with the hologram displayed thereon to form a holographic wavefront; and further comprising an optical component arranged to form a Fourier transform of an object at a focal plane of the optical component, the optical component being arranged to receive the holographic wavefront.
11. A holographic projection system as claimed in claim 10, wherein the hologram is arranged such that a first shape of the first sub-area and / or a second shape of the second sub-area compensates for an optical misalignment of the optical system.
12. A holographic projection system as claimed in claim 10 or 11, wherein the optical component is arranged to form a transform of the holographic wavefront, such as a Fourier transform.
13. A holographic projection system as claimed in any one of claims 10 to 12, wherein the hologram is arranged such that a Fourier transform of the hologram has a first area having a first shape corresponding to a shape of each first sub-area and a second area having a second shape corresponding to a shape of each second sub-area.
14. A holographic projection system as claimed in claim 13, wherein the optical system comprises a first pupil expander and a second pupil expander, and wherein the optical system is arranged such that the first area of the transform of the hologram is coupled into the first pupil expander and the second area of the transform of the hologram is coupled into the second pupil expander.
15. A holographic projection system as claimed in claim 14, wherein the first pupil expander is arranged to expand an exit pupil thereof in a first direction of a first dimension and wherein the second pupil expander is arranged to expand an exit pupil thereof in a second direction of the first dimension.
16. A holographic projection system as claimed in any one of claims 10 to 15, wherein the holographic projection system comprises a spatial filter arranged to process the holographic wavefront.
17. A holographic projection system as claimed in claim 16, wherein the spatial filter comprises an input side arranged to: receive the holographic wavefront along a first plane; divide the holographic wavefront into first and second portions; and nullify a third portion of the holographic wavefront that is located between the first portion and the second portion.
18. A holographic projection system as claimed in claim 17, wherein the input side comprises: a first surface arranged to receive the first portion of the holographic wavefront; a second surface arranged receive the second portion of the holographic wavefront; and a discontinuity between the first surface and the second surface arranged to receive and nullify the third portion of the holographic wavefront.
19. A driver for a display device comprising a plurality of pixels, the driver being arranged to drive the display device to display a hologram of a picture on the plurality of pixels such that, when the display device is suitably illuminated, a holographic reconstruction of the picture is formed; wherein the holographic reconstruction comprises a plurality of image points and the hologram is arranged such that each image point of the holographic reconstruction is formed by a sub-hologram comprising a respective discrete first and second sub-area of an area of the display device defined by the diffraction angle and the position of the image point.
20. A method of calculating a hologram of a picture comprising a plurality of image points, the method comprising, for each image point of the picture: defining discrete first and second sub-areas on a display device, the first and second sub-areas being sub-areas of an area defined by the diffraction angle and the position of the image point; and determining a sub-hologram for the image point in the first and second sub-areas.
21. A hologram engine for calculating a hologram of a picture for displaying on a display device of a holographic projection system comprising an optical system arranged to relay light from the display device to a viewing window, the picture comprising a plurality of image points, the hologram engine being arranged to, for each image point: define at least one sub-area on the display device in an area, wherein the area is defined by the diffraction angle and the position of the image point; and determine a sub-hologram for the image point in the respective sub-area; wherein the hologram engine is arranged to determine the size and shape of each sub-area based on a property or feature of the optical system.
22. A hologram engine as claimed in claim 21, wherein each sub-area has a shape that is arranged to compensate for a misalignment or aberration of the optical system.
23. A hologram engine as claimed in claim 21 or 22, wherein each sub-area has a non-circular shape.