Hologram Calculation For Compact Head-Up Display

Abstract

An optical system and a method of calculating a hologram of a virtual image for the optical system is described. The optical system comprises a display device arranged to display the hologram and a waveguide arranged to replicate the hologram. The method comprises determining a sub-hologram of a virtual image point within an area defined by straight line paths from the virtual image point to the perimeter of an entrance pupil of a viewer. The area comprises at least part of a virtual replica of the display device formed by the waveguide.

Claims

1. A method of calculating a hologram of a virtual image for an optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram, wherein the method comprises: determining a sub-hologram of a virtual image point within an area defined by straight line paths from the virtual image point to a perimeter of an entrance pupil of a viewer, wherein the area comprises at least part of a virtual replica of the display device formed by the waveguide.

2. The method of claim 1, further comprising: identifying a virtual surface between the virtual image and the waveguide, wherein the virtual surface comprises the display device and a plurality of virtual replicas of the display device formed by the waveguide; and identifying the area on the virtual surface.

3. The method of claim 1, wherein a first sub-hologram of a first virtual image point is determined within a first area of a first virtual replica of the display device.

4. The method of claim 1, wherein a first sub-hologram of a first virtual image point comprises a first sub-hologram component and a second sub-hologram component.

5. The method of claim 4, wherein the first sub-hologram component is determined within a first area of a first virtual replica of the display device and the second sub-hologram component is determined within a second area of a second virtual replica of the display device.

6. The method of claim 5, further comprising: superimposing the first sub-hologram component and second sub-hologram component to form the first sub-hologram of the first virtual image point.

7. The method of claim 4, wherein the first sub-hologram component is determined within a first area of a first virtual replica of the display device and the second sub-hologram component is determined within a second area of the display device.

8. The method of claim 7, further comprising: superimposing the first sub-hologram component and second sub-hologram component to form the first sub-hologram of the first virtual image point.

9. The method of claim 8, wherein at least one of (i) a sub-hologram component is discarded from the step of superimposing if its size is less than a threshold value, or (ii) any portions of the first sub-hologram component and second sub-hologram component that would overlap if superimposed are discarded from the step of superimposing.

10. The method of claim 1, further comprising: calculating a respective sub-hologram of each virtual image point of a plurality of virtual image points of the virtual image.

11. The method of claim 10, further comprising: superimposing the respective sub-holograms to form a hologram of the virtual image.

12. The method of claim 1, wherein each sub-hologram is a point cloud hologram determined by propagating a light wave from the corresponding virtual image point towards a viewer and determining a complex light field arriving at a corresponding position of the area, optionally, and wherein the light wave is a spherical light wave.

13. The method of claim 1, wherein each virtual replica of the display device formed by the waveguide is a different perpendicular distance from the display device such that a staggered virtual surface of virtual replicas of the display devices is formed.

14. The method of claim 13, further comprising: determining a position of each virtual replica of the display device by unfolding an optical path within the waveguide from the display device to the corresponding replica of the hologram formed by the waveguide.

15. The method of claim 1, wherein each virtual replica of the display device corresponds to a respective replica of the hologram formed by the waveguide.

16. The method of claim 15, further comprising: determining a position of each virtual replica of the display device by unfolding an optical path within the waveguide from the display device to the corresponding replica of the hologram formed by the waveguide.

17. A method of calculating a hologram of a virtual image for an optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram, wherein the method comprises: determining a sub-hologram of each virtual image point of the virtual image, wherein each sub-hologram is determined by: propagating a light wave from the respective virtual image point towards a viewer; defining an area of intersection of a propagating light wave at a virtual surface between the virtual image and the viewer, wherein the virtual surface comprises the display device and a plurality of virtual replicas of the display device formed by the waveguide, and wherein the defined area is bounded by straight line paths from the respective virtual image point to a perimeter of an entrance pupil of the viewer’s eye; identifying one or more sub-areas of the defined area of a complex light field, wherein each sub-area intersects the virtual surface at a position corresponding to a different one of the display device and the plurality of virtual replicas; and wherein each of the one or more sub-areas of the complex light field forms a respective component of the sub-hologram.

18. A hologram engine configured to calculate a hologram of a virtual image for an optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram, wherein the hologram engine is arranged to determine a sub-hologram of a virtual image point within an area defined by straight line paths from the virtual image point to a perimeter of an entrance pupil of a viewer, and wherein the area comprises at least part of a virtual replica of the display device formed by the waveguide.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Specific embodiments are described by way of example only with reference to the following figures:

[0078] FIG. 1 is a schematic showing a reflective SLM producing a holographic reconstruction on a screen;

[0079] FIG. 2 shows an image comprising a plurality of image areas (bottom) and corresponding hologram comprising a plurality of hologram components (top);

[0080] FIG. 3 shows a hologram characterised by the routing or channelling of holographically encoded light into a plurality of discrete hologram channels;

[0081] FIG. 4 shows a system arranged to route the light content of each hologram channel of FIG. 3 through a different optical path to the eye;

[0082] FIG. 5 shows a perspective view of a pair of stacked image replicators arranged for expanding a beam in two dimensions;

[0083] FIG. 6 shows an example visualisation of an “extended modulator” or “virtual surface” comprising a 3D array including a display device and a plurality of replicas of the display device formed by a waveguide;

[0084] FIG. 7 shows an arrangement for calculating a point cloud hologram using an extended modulator, showing the paths of waves propagated from first and second example image points of a desired virtual image to be holographically reconstructed by the hologram;

[0085] FIG. 8 shows the calculation of a sub hologram for the first example image point of the arrangement of FIG. 7;

[0086] FIG. 9 shows the calculation of a sub hologram for the second example image point of the arrangement of FIG. 7;

[0087] FIG. 10 illustrates a first criterion for including information from sub-areas of an example complex light pattern, at an area of intersection with an extended modulator, in a corresponding sub hologram;

[0088] FIG. 11A illustrates a second criterion for including information from sub-areas of another example complex light pattern, at an area of intersection with an extended modulator, in a corresponding sub hologram, and

[0089] FIG. 11B shows the sub hologram formed using the second criterion and the complex light pattern of FIG. 11A.

[0090] The same reference numbers will be used throughout the drawings to refer to the same or like parts.

DETAILED DESCRIPTION

[0091] 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.

[0092] Terms of a singular form may include plural forms unless specified otherwise.

[0093] 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.

[0094] 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.

[0095] 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.

[0096] Features of different embodiments may be partially or overall coupled to or combined with each other, and may be variously inter-operated with each other. Some embodiments may be carried out independently from each other, or may be carried out together in co-dependent relationship.

Optical Configuration

[0097] FIG. 1 shows an embodiment of a projector (optical system) 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.

[0098] 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 FIG. 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 examples, 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 example shown in FIG. 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.

[0099] 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.

[0100] In these embodiments of the projector, 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 FIG. 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.

Hologram Calculation

[0101] 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, embodiments relate to holograms calculated based on point cloud methods. British patent application GB 2112213.0 filed 26 Aug. 2021, incorporated herein by reference, discloses example hologram calculation methods that may be combined with the present disclosure. In particular, the earlier patent application describes methods for calculating a (special) type of hologram, described below with reference to FIGS. 2 and 3, that angularly divides/channels the image content.

[0102] In some embodiments of the projector, there is provided a real-time engine arranged to receive image data and calculate holograms in real-time using the algorithm. In some examples, the image data is a video comprising a sequence of image frames. In other embodiments of the projector, 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.

Light Modulation

[0103] The display system comprises a display device defining the exit pupil of the display system. The display device is a spatial light modulator. The spatial light modulation may be a phase modulator. The display device may be a liquid crystal on silicon, “LCOS”, spatial light modulator as well known in the art. A LCOS SLM comprises a plurality of pixels, such as an array of quadrilateral shaped LC pixels. The pixels may be addressed or encoded with a diffractive pattern comprising a hologram. It may be said that the LCOS SLM is arranged “display” a hologram. The LCOS SLM is arranged to be illuminated with light, and to output spatially modulated light in accordance with the hologram. The spatially modulated light output by the LCOS SLM comprises a diffracted or holographic light field as described herein.

Light Channelling

[0104] The optical system disclosed herein is applicable to pupil expansion with any diffracted light field. In some embodiments of the optical system, the diffracted light field is a holographic light field -that is, a complex light field that has been spatially modulated in accordance with a hologram of an image, not the image itself. In some embodiments of the optical system, the hologram is a special type of hologram that angularly divides/channels the image content. This type of hologram is described further herein merely as an example of a diffracted light field that is compatible with the present disclosure. Other types of hologram may be used in conjunction with the display systems and light engines disclosed herein.

[0105] A display system and method are described herebelow, which comprise a waveguide pupil expander. As will be familiar to the skilled reader, the waveguide may be configured as a ‘pupil expander’ because it can be used to increase the area over (or, within) which the light emitted by a relatively small light emitter – such as a relatively small SLM or other pixelated display device as used in the arrangements described herein – can be viewed by a human viewer or other viewing system that is located at a distance, such as a relatively large distance, away from the light emitter. The waveguide achieves this by increasing the number of transmission points from which the light is output, towards the viewer. As a result, the light may be seen from a plurality of different viewer locations and, for example, the viewer may be able to move their head, and therefore their line of sight, whilst still being able to see the light from the light emitter. Thus, it can be said that the viewer’s ‘eye-box’ or ‘eye-motion box’ is enlarged, through use of a waveguide pupil expander. This has many useful applications, for example but not limited to head-up displays, for example but not limited to automotive head-up displays.

[0106] A display system as described herein may be configured to guide light, such as a diffracted light field, through a waveguide pupil expander in order to provide pupil expansion in at least one dimension, for example in two dimensions. The diffracted light field may comprise light output by a spatial light modulator (SLM), such as an LCOS SLM. For example, that diffracted light field may comprise light that is encoded by a hologram displayed by the SLM. For example, that diffracted light field may comprise light of a holographically reconstructed image, corresponding to a hologram displayed by the SL M. The hologram may comprise a computer-generated hologram (CGH) such as, but not limited to, a point-cloud hologram, a Fresnel hologram, or a Fourier hologram. The hologram may be referred to as being a ‘diffractive structure’ or a ‘modulation pattern’. The SLM or other display device may be arranged to display a diffractive pattern (or, modulation pattern) that comprises the hologram and one or more other elements such as a software lens or diffraction grating, in a manner that will be familiar to the skilled reader.

[0107] The hologram may be calculated to provide channelling of the diffracted light field. This is described in detail in each of GB2101666.2, GB2101667.0, and GB2112213.0, all of which are incorporated by reference herein. In general terms, the hologram may be calculated to correspond to an image that is to be holographically reconstructed. That image, to which the hologram corresponds, may be referred to as an ‘input image’ or a ‘target image’. The hologram may be calculated so that, when it is displayed on an SLM and suitably illuminated, it forms a light field (output by the SLM) that comprises a cone of spatially modulated light. In some embodiments the cone comprises a plurality of continuous light channels of spatially modulated light that correspond with respective continuous regions of the image. However, the present disclosure is not limited to a hologram of this type.

[0108] Although we refer to a ‘hologram’ or to a ‘computer-generated hologram (CGH)’ herein, it will be appreciated that an SLM may be configured to dynamically display a plurality of different holograms in succession or according to a sequence. The systems and methods described herein are applicable to the dynamic display of a plurality of different holograms.

[0109] FIGS. 2 and 3 show an example of a type of hologram that may be displayed on a display device such as an SLM, which can be used in conjunction with a pupil expander as disclosed herein. However, this example should not be regarded as limiting with respect to the hologram calculation method of the present disclosure.

[0110] FIG. 2 shows an image 252 for projection comprising eight image areas/components, V1 to V8. FIG. 2 shows eight image components by way of example only and the image 252 may be divided into any number of components. FIG. 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. FIG. 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 FIG. 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 the entrance pupil of the viewing system.

[0111] FIG. 4 shows a system 400, including a display device that displays a hologram that has been calculated as illustrated in FIGS. 2 and 3.

[0112] 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.

[0113] 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.

[0114] In brief, the waveguide 408 shown in FIG. 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.

[0115] FIG. 4 shows a total of nine “bounce” points, B0 to B8, along the length of the waveguide 408. Although light relating to all points of the image (V1-V8) as shown in FIG. 2 is transmitted out of the waveguide at each “bounce” from the second planar surface of the waveguide 408, only the light from one angular part of the image (e.g. light of one of V1 to V8) has a trajectory that enables it to reach the eye 405, from each respective “bounce” point, B0 to B8. Moreover, light from a different angular part of the image, V1 to V8, reaches the eye 405 from each respective “bounce” point. Therefore, each angular channel of encoded light reaches the eye only once, from the waveguide 408, in the example of FIG. 4.

[0116] The methods and arrangements described above can be implemented in a variety of different applications and viewing systems. For example, they may be implemented in a head-up-display (HUD) or in a head or helmet mounted device (HMD) such as an Augmented Reality (AR) HMD.

[0117] 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 above can be applied to real images.

Two-Dimensional Pupil Expansion

[0118] Whilst the arrangement shown in FIG. 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 FIG. 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.

[0119] FIG. 5 shows a perspective view of a system 500 comprising two replicators, 504, 506 arranged for expanding a light beam 502 in two dimensions.

[0120] In the system 500 of FIG. 5, 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 FIG. 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 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 FIG. 5), 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.

[0121] 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 FIG. 5), 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.

[0122] Thus, it can be said that the first and second replicators 504, 505 of FIG. 5 combine to provide a two-dimensional replicator (or, “two-dimensional pupil expander”).

Virtual Replicas of the Display Device Formed by the Waveguide or Waveguides

[0123] Conventionally, for calculation of a point cloud hologram of an image (such as a virtual image), the image is broken down into (i.e. represented by) a plurality of individual points -referred to herein as ‘virtual points’. A light wave – e.g. spherical wave – (or ‘wavelet’) is then propagated computationally – i.e. using a model or other theoretical tool – from each virtual point, at its intended or desired location, within the virtual image, to the plane of the hologram e.g. display device that will be used to display the hologram – such as the plane of the LCOS, in the examples described hereabove. The wavelets from a plurality of virtual image points are combined with one another and the resulting amplitude and/or phase distribution/pattern at the display device is calculated. The display device can then be configured, in a manner that is well known and so will not be described herein, to display the hologram, in order to recreate the wavelets, and thus to create a reconstruction of the image.

[0124] However, as described herein, in certain display system applications, one or more waveguides are used for pupil expansion. The inventors have recognised that pupil expansion using light ray replication has the effect of creating “virtual replicas” of the display device in a two-dimensional array and that the location of these replicas may be used to help eliminate ghost images that can appear because of the plurality of different light propagation paths within the waveguide. The inventors have further realised that, 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 and the method disclosed herein must account for these differences. 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.

[0125] Accordingly, the present disclosure proposes a new method for calculating a hologram of the virtual image, such that, for a particular target eye position, the displayed hologram creates a wavefront, after the pupil expander, as if it was generated by the target image.

[0126] FIG. 6 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.

[0127] As noted above with reference to FIG. 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 B0 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 FIG. 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′.

[0128] The proposed method of calculating a hologram defines a so-called “extended modulator”, in which the display device (e.g. LCOS SLM) is “extended” by an array of virtual replicas thereof, which would be formed by one or more waveguide pupil expanders, to form an “extended modulator” or “virtual surface” (e.g. as shown in FIG. 4). For example, the display device (e.g. LCOS SLM) may be located at position (0, 0) of the extended modulator shown in FIG. 6, and (virtual) replicas (i.e. replica display devices) that would be formed by two one-dimensional pupil expanders are located at positions extending to (0,2) in a first direction of pupil expansion and (4, 0) in a second direction of pupil expansion. The direction of the optical path is shown by arrow 601, which is perpendicular to the first and second directions of pupil expansion.

[0129] Accordingly, an extended modulator is defined comprising: (i) a first offset between replicas generated in a first waveguide pupil expander (e.g. an elongate waveguide) defined by an angle (in space) and corresponding direction of pupil expansion, (ii) a second offset between replicas generated in a second waveguide pupil expander (e.g. planar waveguide) defined by an angle (in space) and corresponding direction of pupil expansion; (iii) any skew between the direction of the first offset and the second offset – creating the general parallelogram shape in FIG. 6, and (iv) the optical path length (difference) between display device replicas and the eye position – in the direction 601 shown in FIG. 6.

Hologram Calculation Using an Extended Modulator Comprising Virtual Replicas

[0130] FIG. 7 shows an arrangement for calculating a point cloud hologram using an extended modulator, such as the extended modulator shown in FIG. 6, in accordance with an embodiment of the present disclosure.

[0131] The arrangement comprises a virtual image 700 at a desired virtual image position in space, and a viewing system comprising an eye 720 having a pupil forming an entrance aperture 730 of the viewing system. The arrangement shows one position of the eye 720 within the eye-box. Thus, the point cloud hologram is associated with a particular eye-box position. In addition, the arrangement comprises an extended modulator (or virtual surface) 710 positioned between the virtual image 700 and the eye 720. As the skilled person will appreciate, in FIG. 7, the optical path is effectively “unfolded” within the waveguide.

[0132] In accordance with conventional techniques for calculating a point hologram well known in the art, spherical waves (or ‘wavelets’) are propagated along a path from each virtual image point to the plane of a display device. The point cloud hologram is determined based on (e.g. by combining/superimposing) the complex light pattern (i.e. a complex light field having an amplitude and phase distribution) formed by the wavelets propagating from each virtual image point at its respective area of intersection with the plane of the display device.

[0133] It may be said that the complex light pattern of the wavelets associated with each virtual image point is “captured” at the corresponding area of intersection with the plane of the display device.

[0134] However, in accordance with the present disclosure, the point cloud hologram is determined based on (e.g. by combining/superimposing) the complex light pattern (i.e. amplitude and or phase distribution) formed by the wavelet propagating from each virtual image point at its respective area of intersection with the extended modulator or virtual surface. Moreover, only the parts of the wavelets propagating from the virtual image points that reach the viewer’s eye are considered.

[0135] FIG. 7 shows first and second example virtual image points 701, 702 of a virtual image 700 positioned at a desired distance from a viewer’s eye 720. As shown by dashed lines, (expanding) spherical waves or wavelets are propagated from each example virtual image point 701, 702 through the extended modulator 710 to the entrance aperture 730 of the viewer’s eye 720. A first pair of straight lines 711 extend from first virtual image point 701 to opposite extreme positions of the entrance aperture 730 (i.e. left and right hand sides in the drawing) representing the edges/perimeter of (the relevant part of) the associated wavelet. Similarly, a second pair of straight lines 721 extend from second virtual image point 702 to opposite extreme positions/edges of the entrance aperture 730 (i.e. left and right hand sides in the drawing) representing the edges/perimeter of (the relevant part of) the associated wavelet. The first and second pairs of straight lines 711, 721 have respective areas of intersection 800, 900 with the extended modulator 710 (or virtual surface). Thus, the first and second pairs of straight lines 711, 721 “delineate” (i.e. form a boundary around) the desired (part of the) wavelet, in accordance with this disclosure, associated with the first and second virtual image points 701, 702, respectively, that can pass through the entrance aperture 730 (i.e. pupil) of the viewer’s eye 720 at the particular eye-box position. In the following description, references to the ‘wavelet’ propagating from a virtual image point relate to the part of the propagating wave that is delineated by straight lines, as described above.

[0136] Since the extended modulator is “staggered”, as described herein, the area of intersection of the wavelet propagating from each virtual image point is at different perpendicular distance (to the plane of the display device) – or different distance in the propagation direction. In particular, the wavelets propagating from different virtual image points pass thought different “replicas” (of the display device) of the extended modulator 710. Some wavelets – e.g. the one associated with virtual image point 701 – may intersection a plurality of replicas, whilst other wavelets – e.g. the one associated with virtual image point 702 –intersection only a single replica, as described further below. For example, FIG. 7 shows a first area of intersection 800 with the extended modulator 710 of a first wavelet, delineated/bounded by first pair of lines 711, propagating from first virtual image point 701 to the eye 720. Similarly, FIG. 7 shows a second area of intersection 900 with the extended modulator 710 of a second wavelet, delineated/bounded by the second pair of lines 721, propagating from second virtual image point 702 to the eye 720. These areas of intersection are described below with reference to FIGS. 8 and 9.

[0137] FIG. 8 shows the first area of intersection 800 with extended modulator 710 of the first wavelet, delineated by the first pair of lines 711, propagating from first virtual image point 701 in more detail. In particular, the first wavelet intersects in an area comprising two adjacent virtual replicas of the extended modulator 710 – these virtual replicas are shown as horizontal lines in FIG. 7 and vertical lines in FIG. 8. As noted above, different virtual replicas of the extended modulator are in different planes at different perpendicular distances. Accordingly, the complex light pattern at an area of intersection with each virtual replica of the extended modulator is determined separately. This is necessary because the parts of the wavelet intersecting the two adjacent virtual replicas will have propagated different distances from the virtual image point 791 and so have different complex light patterns or wavefronts on arrival at the extended modulator.

[0138] Reference is made in the following to a “complex light pattern” to refer to a spatial distribution of pairs of amplitude and phase values representative of the light field that arrives at the extended modulator from each virtual image point. In other words, the “complex light pattern” corresponds to the wavefront of the wavelet at the point or points it intersections the extended modulator. In embodiments, the “complex light pattern” is an array of pairs of amplitude and phase values. In some examples, the display device is a phase modulator in which case amplitude values may ultimately be ignored or discarded. The “complex light pattern” may also be referred to as a “complex light field”.

[0139] Accordingly, FIG. 8 shows a first complex light pattern 810′ formed by the wavelet at the intersection with a first virtual replica of the extended modulator 710 (shown at the top of the drawing). The first complex light pattern 810′ is “captured” at the plane of the first virtual replica and forms a first sub-hologram component 810 associated with first virtual image point 701. In addition, FIG. 8 shows a second complex light pattern 811′ formed by the wavelet at the intersection with a second virtual replica of the extended modulator 710 (shown at the bottom of the drawing). The second complex light pattern 811′ is “captured” at the plane of the second virtual replica and forms second sub-hologram component 811 associated with first virtual image point 701. Notably, the area of intersection at each of the first and second virtual replicas of the extended modulator 710 is shown as (a part of) a circle or ellipse. This corresponds to a “primary contributory area” because it corresponds to light rays that pass through the entrance pupil of the viewing system. In some cases, this ensures that a primary image (and not “ghost image”) is formed by the viewing system. In some embodiments, the shape of the primary contributory area corresponds to (e.g. has the same general shape but not necessarily the same size as) that of the entrance pupil of the viewing system. Since the complex light patterns 810′, 811′ formed by the wavelet are positioned at the edges of the respective virtual replicas, the primary contributory area is at the top and bottom edges of the sub-hologram 820 of virtual image point 701.

[0140] FIG. 8 shows that the first sub-hologram component 810 and the second sub-hologram component 811 are combined – in particular superimposed – to form a sub-hologram 820 associated with first virtual image point 701. In particular, spatial information (on the display device) associated with each complex light pattern 810′, 811′ is retained in the step of superimposing. That is, first complex light pattern 810′ is formed at a position corresponding to a lower region of the display device and so appears at the corresponding lower region of the final sub-hologram 820 of this virtual image point 701. Likewise, second complex light pattern 811′ is formed at a position corresponding to an upper region of the display device and so appears at the corresponding upper region of the final sub-hologram 820 of this virtual image point 701. In this example, the first complex light pattern 810′ and second complex light pattern 811′ are non-overlapping – and so can be superimposed to form the final sub-hologram 820 for this virtual image point without any further processing.

[0141] FIG. 9 shows an area of intersection 900 with extended modulator 710 of the second wavelet, delineated by the second pair of lines 721, propagating from second virtual image point 702 in more detail. In particular, the wavelet intersects in an area of a single virtual replica of the extended modulator 710 – this virtual replica is shown as a horizontal line in FIG. 7 and a vertical line in FIG. 9. Accordingly, the complex light pattern 920′ at the area of intersection at the (single) plane of the virtual replica of the extended modulator 710 is captured and forms a sub-hologram 920 associated with second virtual image point 702. Once again, the area of intersection at the virtual replica of the extended modulator 710 is shown as a circle or ellipse. This corresponds to a “primary contributory area” for the second virtual image point 702. Since the complex light pattern formed by the wavelet is positioned at the centre of the virtual replica, the primary contributory area is at the centre of the sub-hologram 920 for this virtual image point 702.

[0142] A point cloud hologram is determined for the entire virtual image 700 by combining/superimposing (e.g. by vector addition) the sub-holograms e.g. 820, 920 associated with each virtual image point e.g. 701, 702 of the virtual image 700.

[0143] Since the improved method of calculation of the point cloud hologram uses an extended modulator, it automatically takes into account the differences in (i) first offsets between replicas in a first dimension, (ii) second offsets between replicas in a second dimension and (iii) any skew between replicas generated by one or more waveguide pupil expanders, as well as (iv) optical path length differences between replicas to the eye position, as described above.

[0144] Furthermore, the improved method of calculation of the point cloud hologram only takes into account wavelets/light rays from the virtual image that can pass through the entrance pupil of the viewer’s eye at the relevant eye position. Thus, only light rays that contribute to the “main image” (and not ghost image) are considered - i.e. the primary contributory areas at the intersection of the wavelets with the extended modulator. In consequence, the improved method automatically avoids the undesirable formation of “ghost images”, as described above. Furthermore, since the method only propagates wavelets/light rays from the virtual image that can pass through the entrance pupil of the viewer’s eye at the relevant eye position, the computational complexity is reduced. In this way, the speed of calculating the point cloud hologram is reduced, as is the consumption of computational resources.

Further Advancements

[0145] The method of calculating the point cloud hologram described above may utilise the wavefront information (i.e. complex light pattern) for the areas of intersection of all wavelets on the extended modulator from virtual image points that can pass through the entrance pupil of the viewer’s eye. That is, all the sub holograms 820, 920 (including sub-hologram components 810, 811) associated with all virtual image points may be combined/superimposed to form the point cloud hologram for the virtual image 700.

[0146] However, in some embodiments, certain criteria may be used to determine whether or not to include captured wavefront information in the final sub-hologram of a virtual image point. Two such criteria are described below with reference to FIGS. 10 and 11.

[0147] A first criterion is to include wavefront information (captured complex light pattern) in the final sub-hologram based on a threshold minimum size of area of intersection at the extended modulator. FIG. 10 shows an example of a complex light pattern (shown as a circle), associated with a wavelet propagating from a virtual image point, captured at an area of intersection with an extended modulator. The area of intersection of the complex wavefront/light pattern comprises first, second third and fourth sub areas 1001, 1002, 1003, 1004 on respective, first, second, third and fourth adjacent “virtual replicas” R1, R2, R3, R4 of extended modulator. As described above, the virtual replicas R1, R2, R3 R4 are offset in different planes. The size of each sub area of intersection may be compared to a threshold value. For example, the threshold value may represent a minimum size of complex light pattern needed to form a wavefront of acceptable quality. If a sub area of intersection does not exceed the threshold value, the complex information may be discarded and may not be included in the final sub-hologram. Accordingly, this criterion eliminates any wavefront information that does not positively contribute to the point cloud hologram, and may reduce consumption of computational resources and/or memory - as well as significantly improving image quality

[0148] A second criterion is to include wavefront information (captured complex light pattern) in the final sub-hologram only if it is “visible” in only one replica of the extended modulator. Based on this criterion, the final sub-hologram (of the virtual image point) does not include wavefront information from overlapping areas of intersection. Including wavefront information from overlapping areas is undesirable, as “ghost” images/image points may be created from the (final) sub-hologram due to the different light ray paths through the pupil expander associated with each hologram replica. FIG. 11A shows an example of a complex light pattern (shown bounded by a circle), associated with a wavelet propagating from a virtual image point, captured at an area of intersection with an extended modulator. FIG. 11B shows the final sub-hologram determined using this criterion.

[0149] Referring to FIG. 11A, the area of intersection of the complex wavefront/light pattern comprises first to fifth sub areas 1101, 1102, 1103, 1104, 1105 on first, second and third “virtual replicas” R1, R2, R3 of an extended modulator. As described above, the virtual replicas R1, R2, R3 are offset in different planes. The second virtual replica R2 is adjacent, and positioned between, each of the first and third virtual replicas R1, R3. First sub area 1101 of the complex light pattern is located at the centre of the second virtual replica R2 and does not overlap with the sub areas 1102, 1103, 1104, 1105 of the complex light pattern on the first and third virtual replicas R1, R3. Thus, in accordance with this criterion, the complex light pattern in the first sub area 1001 is included in the sub-hologram, as shown in FIG. 11B. However, the second sub area 1102 of the complex light pattern – in a region at the top of second/middle virtual replica R2 – overlaps with the third sub area 1103 of the complex light pattern – in an equivalent region at the top of third virtual replica R3. Similarly, the fourth sub area 1104 of the complex light pattern – in a region at the bottom of the first virtual replica R1 – overlaps with the fifth sub area 1105 of the complex light pattern – in an equivalent region at the bottom of second/middle virtual replica R2. Thus, in accordance with this criterion, the complex light pattern in the overlapping second and third sub areas 1102, 1103 and the overlapping fourth and fifth sub areas 1104, 1105 are not included in the sub-hologram, as shown in FIG. 11B. The method therefore comprises discarded sub-hologram component information that overlaps with or uses or corresponds to or requires the same part of the display device.

[0150] The embodiments described above relate to the calculation of a point cloud hologram. However, the skilled person will appreciate that the present disclosure may be used for the calculation of other types of holograms of a virtual image for an optical system comprising a display device and waveguide. In particular, the skilled person will understand how to apply the concept of a virtual surface comprising virtual image points (e.g. a staggered virtual surface of virtual replicas) at the hologram plane in methods of calculating other types of holograms.

Additional Features

[0151] In embodiments of the projector (optical system), the holographic reconstruction is colour. In some embodiments, an approach known as spatially-separated colours, “SSC”, is used to provide colour holographic reconstruction. In other embodiments, an approach known as frame sequential colour, “FSC”, is used.

[0152] Examples describe illuminating the SLM with visible light but the skilled person will understand that the light sources and SLM may equally be used to direct infrared or ultraviolet light, for example, as disclosed herein. For example, the skilled person will be aware of techniques for converting infrared and ultraviolet light into visible light for the purpose of providing the information to a user. For example, the present disclosure extends to using phosphors and/or quantum dot technology for this purpose.

[0153] Some arrangements describe 2D holographic reconstructions by way of example only. In other arrangements, the holographic reconstruction is a 3D holographic reconstruction. That is, in some arrangements, each computer-generated hologram forms a 3D holographic reconstruction.

[0154] 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.

[0155] 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).

[0156] 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.