Holographic computing for compact head-up displays

Abstract

A method for computing a sub-hologram of a virtual image point of an optical system, the optical system comprising a display device arranged to display the sub-hologram and a waveguide arranged to replicate the sub-hologram. The method comprises: determining a region bounded by a straight line path from the virtual image point to a periphery of an entrance pupil of an observer, wherein the region comprises a first region component on a first virtual replica of the display device and a second region component on a second virtual replica of the display device; determining a first sub-hologram component of the virtual image point within the first region component and a second sub-hologram component of the virtual image point within the second region component; and superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point. The method further comprises: applying a local phase ramp function to at least one of the first region component and the second region component.

Description

Technical Field

[0001] The present disclosure relates to pupil expansion or replication, particularly for diffracted light fields comprising diverging bundles of rays. More specifically, the present disclosure relates to methods for determining diffraction structures, such as holograms or kinoform patterns, for display by a display system comprising a waveguide pupil expander, and to methods for pupil expansion using waveguides. Some embodiments relate to two-dimensional pupil expansion using first and second waveguide pupil expanders. Some embodiments relate to picture generation units and heads-up displays, such as automotive heads-up displays (HUDs). Background Art

[0002] Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured, for example, on a photographic plate using well-known interference techniques to form a holographic recording or "hologram" consisting of interference fringes. The hologram can be reconstructed by illuminating it with appropriate light to form a two- or three-dimensional holographic reconstruction or replay image representing the original object.

[0003] Computer-generated holography can numerically simulate interference processes. Computer-generated holograms can be computed using techniques based on mathematical transformations such as the Fresnel or Fourier transforms. These types of holograms are referred to as Fresnel / Fourier transform holograms or simply Fresnel / Fourier holograms. Fourier holograms can be considered either Fourier domain / planar representations of an object or frequency domain / planar representations of an object. Computer-generated holograms can also be computed, for example, using coherent ray tracing or point cloud techniques.

[0004] The computer generated hologram may be encoded on a spatial light modulator arranged to modulate the amplitude and / or phase of the incident light. For example, light modulation may be achieved using electrically addressable liquid crystals, optically addressable liquid crystals, or micromirrors.

[0005] 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, multi-level, or continuous. Alternatively, the device may be continuous (i.e., comprise no pixels), so that the light modulation may be continuous across the device. A spatial light modulator may be reflective, meaning that the light is modulated to reflect the output. A spatial light modulator may also be transmissive, meaning that the light is modulated to transmit the output.

[0006] The system described here can be used to provide a holographic projector, which is already used in head-up displays (HUDs). Summary of the Invention

[0007] Various aspects of the disclosure are defined in the accompanying independent claims.

[0008] In general, the present disclosure relates to image projection. It relates to a method of image projection and an image projector including a display device. The present disclosure also relates to a projection system including an image projector and an observation system, wherein the image projector projects or relays light from the display device to the observation system. The present disclosure is equally applicable to monocular and binocular observation systems. The observation system may include one or more eyes of an observer. The observation system includes an optical element with optical power (e.g., the lens of a human eye) and an observation plane (e.g., the retina of a human eye). 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 each other. The observer forms or perceives the image on the 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 embodiments, the image is a real image formed by holographic reconstruction, and the image is projected or relayed to the observation plane. The image is formed by illuminating a diffraction pattern (e.g., a hologram) displayed on the display device.

[0009] A display device includes pixels. The pixels of the display device can display a diffraction pattern or structure of diffracted light. The diffracted light can form an image on a plane spatially separated from the display device. According to well-known optical principles, the magnitude of the maximum diffraction angle is determined by the size of the pixel and other factors, such as the wavelength of the light.

[0010] In an embodiment, the display device is a spatial light modulator, such as a liquid crystal on silicon ("LCOS") spatial light modulator (SLM). Light is transmitted from the LCOS to a viewing entity / system, such as a camera or an eye, over a range of diffraction angles (e.g., from zero to a maximum diffraction angle). In some embodiments, amplification techniques can be used to increase the range of available diffraction angles beyond the conventional maximum diffraction angle of the LCOS.

[0011] In some examples, an image (formed by a displayed diffraction pattern / hologram) is propagated to the eye. For example, spatially modulated light of an intermediate holographic reconstruction / image formed in free space between the display device and the observer or on a screen or other light-receiving surface can be propagated to the observer.

[0012] In embodiments, the image is an actual image. In other embodiments, the image is a virtual image perceived by one (or more) human eyes. The projection system or light engine can therefore be configured so that the observer looks directly at the display device. In such embodiments, the light encoded with the hologram is transmitted directly to the eye, and no intermediate holographic reconstruction is formed in the free space between the display device and the observer or on a screen or other light receiving surface. In such embodiments, the pupil of the eye can be considered the entrance aperture of the viewing system, and the retina of the eye can be considered the viewing plane of the viewing system. It is sometimes said that in this configuration, the lens of the eye performs the conversion of the hologram to the image.

[0013] In some other examples, (the light of) the diffraction pattern / hologram itself is transmitted to the eye. For example, spatially modulated light of a hologram (not yet fully converted into a holographic reconstruction, i.e., an image) - which can be informally said to be "encoded" with the hologram - is transmitted directly to the observer's eye. The observer can perceive a real or virtual image. In these embodiments, no intermediate holographic reconstruction / image is formed between the display device and the observer. It is sometimes said that in these embodiments, the lens of the eye performs the conversion or transformation of the hologram to the image. The projection system or light engine can be configured so that the observer effectively looks directly into the display device.

[0014] The "light field" mentioned here is a "composite light field". The term "light field" simply means a light pattern with finite size in at least two orthogonal spatial directions, such as x and y. The term "light field" simply means a light pattern with finite size in at least two orthogonal spatial directions (x and y). The word "complex" used here simply means that the light at each point in the light field can be defined by an amplitude value and a phase value, and can therefore be represented by a complex number or a pair of values. For the purpose of hologram calculation, the composite light field can be a two-dimensional array of complex numbers, where the complex numbers define the intensity and phase of light at multiple discrete locations within the light field.

[0015] According to well-known optical principles, the angular range of light propagating from a display device that can be observed by an eye or other observing entity / system varies with the distance between the display device and the observing entity. For example, at a viewing distance of 1 meter, only a small range of angles of light from an LCOS can propagate through the pupil of the eye to form an image on the retina at a given eye position. The angular range of light propagating from the display device that can successfully propagate through the pupil of the eye to form an image on the retina at a given eye position determines the portion of the image that is "visible" to the observer. In other words, not all portions 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 an eye box).

[0016] In some embodiments, the image perceived by the observer is a virtual image that appears upstream from the display device—that is, the observer perceives the image as being farther away from them than the display device itself. Conceptually, consider multiple different virtual image points of the virtual image. For each virtual image point, the distance from the virtual point to the observer is referred to herein as the virtual image distance. Of course, different virtual points can have different virtual image distances. Individual light rays within the light bundle associated with each virtual point may take different corresponding optical paths through the display device to reach the observer. However, only some portions of the display device, and therefore only some light rays from one or more virtual points in the virtual image, may be within the user's field of view. In other words, only some light rays from some virtual points on the virtual image will propagate through the display device to the user's eye and, therefore, will be seen by the observer. Therefore, conceptually, the observer can be thought of as viewing the virtual image through a "display-sized window," which can be very small, such as 1 cm in diameter, at a relatively large distance, such as 1 meter. Furthermore, the user will view the display-sized window through their pupil, which can also be very small. Consequently, the field of view is reduced at any given time, and the specific angular range that can be seen depends heavily on the position of the eye.

[0017] Pupil expanders address how to increase the angular range of light that propagates from a display device and that can successfully propagate through the pupil of the eye to form an image. Display devices are typically (relatively) small and have a (relatively) large projection distance. In some embodiments, the projection distance is at least one (such as at least two) orders of magnitude larger than the diameter or width of the entrance pupil and / or aperture of the display device (i.e., the size of the pixel array). Embodiments of the present disclosure relate to a configuration in which a hologram of an image is transmitted to the human eye rather than the image itself. In other words, the light received by the observer is modulated according to (or encoded with / by) a hologram of the image. However, other embodiments of the present disclosure may relate to configurations in which an image rather than a hologram is transmitted to the human eye—for example, through so-called indirect observation, in which light of a holographic reconstruction or "replayed image" formed on a screen (or even in free space) is transmitted to the human eye.

[0018] Pupil expanders solve the problem of how to increase the angular range of light propagating from a display device that can successfully propagate through the pupil of the eye to form an image. Display devices are typically (relatively) small, while the projection distance is (relatively) large. In some embodiments, the projection distance is at least one order of magnitude larger, for example at least two orders of magnitude, than the diameter or width of the entrance pupil and / or aperture of the display device (i.e., the size of the pixel array). Embodiments of the present disclosure relate to a configuration in which a hologram of an image is transmitted to the human eye rather than the image itself. In other words, the light received by the observer is modulated according to (or encoded with / by) the hologram of the image. However, other embodiments of the present disclosure may relate to configurations in which an image rather than a hologram is transmitted to the human eye - for example, through so-called indirect viewing, in which light of a holographic reconstruction or "replayed image" formed on a screen (or even in free space) is transmitted to the human eye.

[0019] Waveguides are used to extend the field of view and, therefore, increase the maximum propagation distance over which the full diffraction angle of the display device can be used. Waveguides can also be used to increase the user's eyebox laterally, allowing for some eye movement while still allowing the user to see the image. For this reason, waveguides can be referred to as waveguide pupil expanders.

[0020] The use of a pupil expander laterally increases the viewing area (i.e., the user's eye box), thereby allowing for some eye movement while still allowing the user to see the image. As will be appreciated by those skilled in the art, in an imaging system, the viewing area (i.e., the user's eye box) is the area within which the viewer's eye can perceive the image. The present disclosure relates to non-infinite virtual image distances—i.e., near-field virtual images.

[0021] Traditionally, a two-dimensional pupil expander comprises one or more one-dimensional optical waveguides, each formed using a pair of opposing reflective surfaces, where the output light from the surfaces forms an observation window—e.g., an eyebox or gamma-ray box for an observer. Light received from a display device (e.g., spatially modulated light from an LCOS) is replicated by the or each waveguide to increase the field of view (or viewing area) in at least one dimension. In particular, the waveguide enlarges the observation window by generating additional light rays, or "replicas," by dividing the amplitude of the incident wavefront.

[0022] In some embodiments, the first pair of opposing surfaces of the waveguide are elongated or extended surfaces that are relatively long along a first dimension and relatively short along a second dimension, e.g., relatively short along each of two other dimensions, each dimension being substantially orthogonal to each of the corresponding other dimensions. The process of light reflecting / transmitting between / from the first pair of surfaces is arranged such that light propagates within the first waveguide pupil expander in a general direction that is the relatively long direction of the first waveguide pupil expander (i.e., in its "elongated" direction).

[0023] A system is disclosed herein that uses diffracted light to form images and provides an eyebox size and field of view suitable for real-world applications - for example in the automotive industry via heads-up displays. Diffracted light is light that forms a holographic reconstruction of an image from a diffractive structure - for example a hologram such as a Fourier or Fresnel hologram or a point cloud hologram. The use of diffraction and diffractive structures requires a high density of display devices with very small pixels (for example 1 micron) - which in practice means small display devices (for example 1 cm). The inventors have solved the problem of how to provide a diffracted light field (for example diffracted light comprising a diverging (non-collimated) beam of light) for 2D pupil expansion.

[0024] In some aspects, a display system includes a display device—such as a pixelated display device, e.g., a spatial light modulator (SLM) or a liquid crystal on silicon (LCoS) SLM—that is arranged to provide or form diffracted (e.g., divergent) light. In these aspects, the aperture of the spatial light modulator (SLM) is the limiting aperture of the system. That is, the aperture of the spatial light modulator—more specifically, the size of the area defining the array of light modulating pixels contained within the SLM—determines the size (e.g., spatial extent) of the bundle of light rays that can exit the system. In accordance with the present disclosure, it is stated that by using at least one pupil expander, the exit pupil of the system is expanded to reflect that the exit pupil of the system (which is limited by the small display device having a pixel size for light diffraction) becomes larger in spatial extension.

[0025] A diffracted (eg, diverging) light field may be referred to as having a "light field size," which is defined in a direction substantially orthogonal to the direction of propagation of the light field. Because light is diffracted / diverged, the light field size increases with propagation distance.

[0026] In some embodiments, the diffracted light field is spatially modulated according to a hologram. In other words, in these aspects, the diffracted light field comprises a "holographic light field". The hologram can be displayed on a pixelated display device. The hologram can be a computer-generated hologram (CGH). It can be a Fourier hologram or a Fresnel hologram or a point cloud hologram or any other suitable type of hologram. Optionally, the hologram can be calculated so as to form channels of holographic light, each channel corresponding to a different part of the image that the observer wants to observe (or perceive, in the case of a virtual image). The pixelated display device can be configured to display multiple different holograms continuously or sequentially. Each of the aspects and embodiments disclosed herein can be applied to the display of multiple holograms.

[0027] The output port of the first waveguide pupil expander can be coupled to the input port of the second waveguide pupil expander. The second waveguide pupil expander can be arranged to guide the diffracted light field (including some, preferably most, and preferably all replicas of the light field output by the first waveguide pupil expander) from its input port to the corresponding output port by internal reflection between a third pair of parallel surfaces of the second waveguide pupil expander.

[0028] The first waveguide pupil expander can be arranged to provide pupil expansion or replication in a first direction, and the second waveguide pupil expander can be arranged to provide pupil expansion or replication in a second, different direction. The second direction can be substantially orthogonal to the first direction. The second waveguide pupil expander can be arranged to maintain the pupil expansion already provided by the first waveguide pupil expander in the first direction and expand (or replicate) some, preferably most, or preferably all of the copies it receives from the first waveguide pupil expander in the second, different direction. The second waveguide pupil expander can be arranged to receive the light field directly or indirectly from the first waveguide pupil expander. One or more other elements can be provided along the propagation path of the light field between the first and second waveguide pupil expanders.

[0029] The first waveguide pupil expander can be substantially elongated (e.g., rod-shaped), while the second waveguide pupil expander can be substantially planar (e.g., rectangular). The elongated shape of the first waveguide pupil expander can be defined by a length along a first dimension. The planar or rectangular shape of the second waveguide pupil expander can be defined by a length along the first dimension and a width or breadth along a second dimension substantially orthogonal to the first dimension. The size or length of the first waveguide pupil expander along its first dimension corresponds to the length or width of the second waveguide pupil expander along its first or second dimension, respectively. A first surface of a pair of parallel surfaces of the second waveguide pupil expander, including its input port, can be shaped, sized, and / or positioned to correspond to an area defined by an output port on the first surface of a pair of parallel surfaces on the first waveguide pupil expander, such that the second waveguide pupil expander is arranged to receive each replica output by the first waveguide pupil expander.

[0030] The first and second waveguide pupil expanders can 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 defining the length and width, respectively, of the second waveguide pupil expander can be parallel to the first and second directions, respectively (or to the second and first directions, respectively), wherein the waveguide pupil expander provides pupil expansion. The combination of the first waveguide pupil expander and the second waveguide pupil expander can generally be referred to as a "pupil expander."

[0031] It can be said that the expansion / replication provided by the first and second waveguide expanders has the effect of expanding the exit pupil of the display system in each of two directions. The area defined by the expanded exit pupil can, in turn, define an expanded eyebox region from which an observer can receive light of the input diffracted or diverging light field. The eyebox region can be said to be located in or define the viewing plane.

[0032] The two directions of exit pupil expansion can be coplanar or parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. Alternatively, in an arrangement that includes other elements such as an optical combiner, such as a vehicle's windshield, the exit pupil can be considered to be the exit pupil from the other element, such as the windshield. In such an arrangement, the exit pupil can be non-coplanar and non-parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. For example, the exit pupil can be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion.

[0033] The viewing plane and / or the eyebox region can 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, the viewing plane can be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion.

[0034] In order to provide suitable launch conditions to achieve internal reflections within the first and second waveguide pupil expanders, the elongated dimension of the first waveguide pupil expander may be tilted relative to the first and second dimensions of the second waveguide pupil expander.

[0035] In order to provide suitable launch conditions to achieve internal reflections within the first and second waveguide pupil expanders, the elongated dimension of the first waveguide pupil expander may be tilted relative to the first and second dimensions of the second waveguide pupil expander.

[0036] The display device can have an active or pixel display area having a first dimension of less than 10 centimeters, such as less than 5 centimeters or less than 2 centimeters. The propagation distance between the display device and the viewing system can be greater than 1 meter, such as greater than 1.5 meters or greater than 2 meters. The optical propagation distance within the waveguide can be up to 2 meters, such as up to 1.5 meters or up to 1 meter. The method can receive an image and determine a corresponding hologram of sufficient quality in less than 20 milliseconds, such as less than 15 milliseconds or less than 10 milliseconds.

[0037] In some embodiments—described solely by way of example using diffractive or holographic light fields according to the present disclosure—a hologram is configured to route light into multiple channels, each corresponding to a different portion (i.e., subregion) of an image. The hologram can be displayed, for example, on a display device such as a spatial light modulator. When displayed on an appropriate display device, the hologram can spatially modulate light that can be converted into an image by a viewing system. The channels formed by the diffractive structure (including the hologram) are referred to herein as "hologram channels" simply to reflect that they are channels of light encoded by the hologram with image information. The light of each channel can be said to be in the holographic domain, rather than in the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram, and thus the hologram domain is the Fourier or frequency domain. The hologram can also be a Fresnel or Fresnel transform hologram. The hologram is described herein as routing light into multiple hologram channels simply to reflect that the image reconstructible from the hologram has a finite size and can be arbitrarily divided into multiple image subregions, with each hologram channel corresponding to each image subregion. Importantly, the hologram of this example is characterized by how it distributes the image content when illuminated. Specifically, the hologram divides the image content by angle. That is, every point on the image is associated with a unique 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 holographic behavior is not conventional. When illuminated, the spatially modulated light formed by this particular type of hologram can be arbitrarily divided into multiple hologram channels, where each hologram channel is defined by a range of ray angles (in two dimensions). It will be understood from the above that any hologram channel (i.e., a sub-range of ray angles) that can be considered in the spatially modulated light will be associated with a corresponding part or sub-region of the image. That is, all the information required to reconstruct that part or sub-region of the image is contained within the angular sub-range of the spatially modulated light formed by the hologram of the image. When the spatially modulated light is observed as a whole, there is not necessarily any evidence of multiple discrete light channels. However, in some arrangements, multiple spatially separated hologram channels are formed by intentionally leaving regions of the target image of the computational hologram blank or empty (ie, without image content).

[0038] However, the hologram can still be identified. For example, if only a continuous portion or subregion of the spatially modulated light formed by the hologram is reconstructed, only a subregion of the image should be visible. If a different continuous portion or subregion of the spatially modulated light is reconstructed, a different subregion of the image should be visible. Another identifying feature of this type of hologram is that the shape of the cross-sectional area of any hologram channel substantially corresponds to the shape of the entrance pupil (i.e., substantially the same), although the dimensions may differ—at least at the correct plane from which the hologram is calculated. Each light / hologram channel propagates from the hologram at a different angle or range of angles. While these are example ways to characterize or identify this type of hologram, other approaches may also be used. In summary, the (particular type of) hologram disclosed herein is characterized and identified by how the image content is distributed within the light encoded by the hologram. Furthermore, for the avoidance of doubt, references herein to holograms configured to direct light or angularly divide an image into multiple hologram channels are by way of example only, and the present disclosure is equally applicable to any type of holographic light field or even any type of diffraction or pupil expansion of a diffracted light field.

[0039] In summary, a system for providing pupil expansion for an input light field is disclosed, wherein the input light field is a diffracted or holographic light field comprising a diverging bundle of light rays. As described above, pupil expansion (also referred to as "image replication," "replication," or "pupil replication") increases the size of the region in which an observer can see an image (or can receive light from a hologram, with the observer's eye forming the image) by creating one or more replicas of the input light rays (or bundles of light rays). Pupil expansion can be provided in one or more dimensions. For example, two-dimensional pupil expansion can be provided, wherein each dimension is substantially orthogonal to a respective other dimension.

[0040] The system can be provided in a compact and streamlined physical form. This makes the system suitable for a wide range of real-world applications, including those where space is limited and real estate is at a high value. For example, it can be implemented in a head-up display (HUD), such as a vehicle or automotive HUD.

[0041] According to the present disclosure, pupil expansion is provided for diffraction or diffracted light, which may include a diverging bundle of light rays. The diffracted light may be output by a display device, such as a pixelated display device, such as a spatial light modulator (SLM) arranged to display a diffractive structure (e.g., a hologram). The diffracted light field may be defined by a "light cone." Thus, the size of the diffracted light field (as defined in a two-dimensional plane) increases with propagation distance from the corresponding diffractive structure (i.e., the display device).

[0042] The spatial light modulator can be arranged to display a hologram (or a hologram including a diffraction pattern). The diffracted or diverged light can include light encoded with or by the hologram, rather than light reconstructed from an image or hologram. Thus, in such an embodiment, the pupil expander can be said to replicate the hologram or form at least one replica of the hologram to convey that the light transmitted to the observer is spatially modulated according to the hologram of the image, rather than the image itself. That is, the diffracted light field is propagated to the observer.

[0043] In some embodiments, two one-dimensional waveguide pupil expanders are provided, each of which is arranged to effectively increase the size of the system's exit pupil by forming multiple copies or replicas of the spatial light modulator's exit pupil (or the light of the exit pupil). The exit pupil can be understood as the physical area from which the system outputs light. Alternatively, each waveguide pupil expander can be arranged to expand the size of the system's exit pupil. Alternatively, each waveguide pupil expander can be arranged to expand / increase the size of the eyebox within which an observer's eye can be positioned in order to see / receive the light output by the system.

[0044] In summary, a method for computing a hologram of a virtual image point of a virtual image of an optical system is provided. The optical system comprises a display device arranged to display the hologram. The optical system further comprises a waveguide arranged to replicate the hologram. The method may comprise determining an area bounded by a straight line path from the virtual image point to the periphery of an entrance pupil of an observer. The area comprises at least a portion of a virtual replica of the display device formed by the waveguide. The straight line path may represent a light wave. Methods for computing holograms comprising propagating light waves from the image point, such as point cloud holography, are known per se. However, methods involving the application of such methods for computing holograms to optical systems comprising waveguides (particularly waveguide pupil expanders) are still in their infancy. The inclusion of waveguides in the optical system introduces complexity to the computation of the hologram and there are a number of hurdles in ensuring that a clear and high quality image formed by the computed hologram is received / observed at the entrance pupil. The inventor is one of very few people who has worked on solving the problem in the apparatus, which involves applying point cloud holography to an optical system including a waveguide pupil expander configured to deliver a hologram (not an image) to the eye.

[0045] As described above, the exit pupil of an optical system can be expanded by a waveguide to generate multiple virtual replicas of a display device, each virtual replica corresponding to a calculated hologram and formed by a waveguide. An optical system including a first waveguide can expand the exit pupil in a first dimension. If the first and second waveguides are properly arranged, an optical system including a first waveguide and a second waveguide can expand the exit pupil in a first dimension and a second dimension orthogonal to the first dimension. If an optical system including one or more waveguides is correctly arranged, a one-dimensional or two-dimensional array of replicas can be generated. Generating a hologram that provides a clear and high-quality image that is observed by an observation system (e.g., an observer's eye) through such an array of replicas is difficult.

[0046] For example, when waveguides are combined with non-infinite virtual image distances (i.e., near-field virtual images), so-called "ghosting" can occur due to the potentially different light propagation paths through the waveguides. A ghost image is a low-intensity replica of the primary image. The primary (e.g., highest intensity) image can be referred to as the primary image. Each ghost image can be referred to as a secondary image. The presence of ghosting can significantly reduce the perceived quality of the virtual image. Ghost images can make the primary image appear blurry. Furthermore, for a given position of an observation system (e.g., a user's eye) within an extended exit pupil, light associated with a particular virtual image point can be received from multiple replicas of the display device. However, due to the optical path distance through one or more waveguides, different replicas have different optical path lengths, and therefore the depths of the corresponding virtual replicas (measured from the exit pupil) are different. The method for calculating a hologram to be displayed and subsequently replicated on a display device should preferably take this depth difference of the virtual replicas into account.

[0047] A method for calculating a hologram of a virtual image point of a virtual image has been previously developed specifically for an optical system including a display device configured to display a hologram and a waveguide configured to replicate the hologram. This method eliminates ghosting and accounts for depth differences between different virtual replicas. The method includes determining a sub-hologram of the virtual image point within a region defined by a straight line path from the virtual image point to the periphery of an observer's entrance pupil. The virtual image point can be one of multiple virtual image points in the virtual image. The region of the sub-hologram can be determined by propagating light waves from the corresponding virtual image point toward the observer. The region can be defined as the intersection of light waves propagating at a virtual surface between the virtual image and the observer. A virtual surface can be identified between the virtual image and the waveguide. The virtual surface can include the display device and multiple replicas of the display device formed by the waveguide. The method can include identifying a region on the virtual surface. The virtual surface can also be referred to as an extended modulator. The virtual surface can be an interleaved virtual surface of the virtual replicas. The region can include at least a portion of the virtual replica of the display device formed by the waveguide. In some embodiments, a first sub-hologram for a first virtual image point is determined within a first region of a first virtual replica of the virtual replicas. In other embodiments, the first sub-hologram for the first virtual image point includes a first sub-hologram component and a second sub-hologram component. In one example, the first sub-hologram component is determined within a first region of a first virtual replica of the display device, and the second sub-hologram component is determined within a second region of a second virtual replica of the display device. The methods of these embodiments may further include superimposing the first sub-hologram component and the second sub-hologram component to form the first sub-hologram for the first virtual image point.

[0048] The above method only considers light rays from the virtual image that can pass through the entrance pupil of the observation system (e.g., the observer's eye) at a specific location within the eye box. Therefore, when calculating the hologram, only light rays that contribute to the "main image" (and not the ghost image) are considered. As a result, the above method of calculating the hologram prevents the formation of undesirable ghost images. In addition, since the method only propagates wavelets / rays from the virtual image that can pass through the entrance pupil of the observer's eye at the relevant eye location, the computational complexity is reduced. This reduces the speed of calculating the point cloud hologram and also reduces the consumption of computing resources. In addition, the method takes into account the depth differences between different replicas in the replica array.

[0049] Thus, the hologram calculation method devised above solves many problems associated with providing a clear and high-quality image formed by a calculated hologram when a waveguide is included in an optical system. However, after simulations and experiments to test the robustness of the above method, the inventors surprisingly discovered another problem that affects the clarity and quality of the hologram / image received at the eyebox. Specifically, the inventors have identified a problem when an image point is formed from light encoded with a calculated sub-hologram that is determined within a region spanning multiple replicas, for example, including a first sub-hologram component and a second sub-hologram component determined within first and second regions of first and second virtual replicas, respectively. The inventors unexpectedly discovered that, even after accounting for any offsets between replicas and differences in the optical paths of different replicas, the formed image point appears elongated relative to the virtual image point on which the hologram calculation is based (i.e., the elongation is an error). This degrades the quality of the image formed by the hologram and the resolution of the display device, as fewer pixels can be displayed per unit area, which is undesirable. The present disclosure provides a method for improving image quality by eliminating or reducing the elongation effect.

[0050] In a first aspect, a method for computing sub-holograms of a virtual image point of a virtual image of an optical system is provided. The optical system includes a display device configured to display a hologram and a waveguide configured to replicate the hologram. The method includes determining an area bounded by a straight line path from the virtual image point to a periphery of an observer's entrance pupil. The area bounded by the straight line path includes a first area component on a first virtual replica of the hologram displayed on the display device and a second area component on a second virtual replica of the hologram displayed on the display device. The first virtual replica may be adjacent to the second virtual replica. The method also includes determining a first sub-hologram component of the virtual image point within the first area component and a second sub-hologram component of the virtual image point within the second area component. The method also includes superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point. The method only considers light rays from the virtual image that can pass through the entrance pupil of an observation system (e.g., an observer's eye) at a specific location within the extended exit pupil. Thus, when computing the hologram, only light rays that contribute to the "primary image" (and not ghost images) are considered. Therefore, the aforementioned CGH method automatically avoids the formation of unwanted ghost images. Furthermore, because the method only propagates wavelets / rays from the virtual image, which can pass through the observer's entrance pupil at the relevant eye location, computational complexity is reduced. This reduces the speed of computing point cloud holograms and the consumption of computing resources. Furthermore, the method automatically accounts for depth differences between replicas in the replica array.

[0051] The method further includes applying a local phase ramp function to at least one of the first regional component and the second regional component. The applied local phase ramp function advantageously improves image quality by eliminating or reducing elongation of image points formed by light encoded with the computed hologram. In particular, the elongation of the image points relative to the virtual image points for which the hologram was computed can be eliminated or reduced.

[0052] The inventors have deduced that the elongation of the image point is similar to the diffraction effect caused by the amplitude aberration effect. Such diffraction may cause the light of the light cone (or composite light field) propagating from the display device to be displaced or offset. The light at the boundaries of the replicas produced by the waveguide may be displaced to the greatest extent. This effect may be referred to as amplitude distortion. The amplitude aberration disclosed herein is similar to coma, but as will be understood by those skilled in the art, coma is a pure phase aberration rather than an amplitude aberration. The light cone may include multiple point spread functions. Diffraction may cause the main lobe of one or more point spread functions emanating from an area of the display device at or towards the edge of the replica to be deformed or offset.

[0053] This amplitude aberration is particularly problematic when the sub-holograms for a virtual image point include a first sub-hologram component, representing the virtual image point on a first virtual replica, and a second sub-hologram component, representing the virtual image point on a second virtual replica, representing the virtual image point on a second virtual replica. In this case, the image point reconstructed from the hologram is formed from the first and second sub-hologram components (which are superimposed to form the sub-hologram). Ideally, the light from the first and second sub-hologram components would be aligned, combined, and superimposed to form a single (typically circular) image point that appears identical to the virtual image point of the computational sub-hologram. In other words, the light from the first and second sub-hologram components would ideally appear to overlap and / or potentially appear to be formed from a single point spread function. In this case, the light can be referred to as "co-localized." However, the inventors have discovered errors similar to diffraction-induced amplitude aberrations. Amplitude aberrations can cause light from one or both of the first and second sub-hologram components to be misaligned. Specifically, the point spread function associated with the first sub-hologram component may be misaligned relative to the point spread function associated with the second sub-hologram component, and / or the point spread function associated with the second sub-hologram component may be misaligned relative to the point spread function associated with the second sub-hologram component. The misalignment of the point spread function mentioned here is relative to the corresponding main lobe of the point spread function.

[0054] Misalignment of the point spread functions may mean that the point spread functions from the first and second sub-hologram components are not correctly combined / superimposed / overlapped / co-located. Such errors caused by aberration-type effects are detrimental to the image quality of the formed image points. In particular, the formed image points may appear elongated (relative to the expected shape of the virtual image points).

[0055] The discovered error is specific to computational holography methods that involve propagating light waves from an image point, such as point cloud holography, for use in optical systems that include waveguides for pupil expansion. The inventors unexpectedly encountered this problem while testing the robustness of this method. Through simulations and experiments, the inventors have discovered that appropriately applying a local phase ramp function to the first and / or second area components can advantageously compensate for the error, thereby reducing or eliminating the elongation of the corresponding image point. Specifically, the local phase ramp can be selected to steer the point spread function associated with the corresponding sub-hologram component to reduce the induced error. Thus, after applying the local phase ramp function, the light from the first and second sub-hologram components can be combined / superimposed / overlapped / co-localized. As explained in more detail below, the local phase ramp can be superimposed on the first and / or second sub-hologram components of the virtual image point.

[0056] A phase ramp (or grating function) applied to a regional component (e.g., the first and / or second regional component) can displace the light of the corresponding sub-hologram component to which the phase ramp has been applied by a predetermined amount in a first direction at the exit pupil. In particular, when illuminated, the point spread function formed by the corresponding sub-hologram component can be displaced by a predetermined amount in the first direction. The predetermined displacement amount can be the displacement amount at the exit pupil. The phase ramp (or grating function) can be calculated to provide a high-precision displacement range. The gradient of the phase ramp can be similar to the grating angle of the grating function. The displacement can be a linear displacement in the first direction. The first direction can be the x-direction. The local phase ramp can be combined with the corresponding sub-hologram component by addition or superposition. Therefore, the step of applying a local phase ramp function to at least one of the first regional component and the second regional component can include adding or superimposing the local phase ramp function to the corresponding first sub-hologram component or the second sub-hologram component. In an embodiment, the phase delay profile is displayed on a display device, which may be a phase modulation device such as a liquid crystal on silicon spatial light modulator, and the phase ramp is added to the hologram by wrapping (modulo 2p) phase addition. Two perpendicular local phase ramps can be added to the sub-hologram components and modified separately to fine-tune the position of the light encoded in the corresponding sub-hologram component.

[0057] Throughout this disclosure, "phase ramps" (or "grating functions") are referred to only by way of example of functions that provide a linear translation of light at the exit pupil. That is, an array of light modulation values, when added to a hologram, linearly shifts the replay field with a defined amplitude and direction. The displacement can be measured in pixels, millimeters or degrees. A phase ramp may also be referred to as a phase wedge. The phase values of a phase ramp may be wrapped (e.g. modulo 2). A wrapped phase ramp may be considered a phase grating. However, the present disclosure is not limited to pure phase modulation, and the terms "grating function", "software grating" and "blazed grating" may be used as examples of beam steering functions, such as a wrapped modulation ramp. A phase ramp may be characterized by its phase gradient. The term "grating function" is preferred in this disclosure because the associated grating angle is a key component of the disclosed method.

[0058] As used herein, a "local phase ramp function" means a phase ramp function that is applied only to a specific regional component / sub-hologram component to steer the point spread function formed by the light incident on that sub-hologram component. The spatial extent (i.e., size) of the local phase ramp function may be the same as the spatial extent of the corresponding sub-hologram component. In other words, the phase ramp function is restricted to the same sub-region of the display device (e.g., a spatial light modulator) as the corresponding sub-hologram component. Thus, typically, the local phase ramp function steers a portion of the light propagating from the display device, rather than all of the light. The word "local" is used here to reflect that the phase ramp component does not extend (in pixel space) beyond the first regional component and / or the second phase ramp component. That is, outside the region of the first / second regional component, the local phase ramp function is not applied. In other words, the local phase ramp is not applied to pixels of the display device outside the region of the first / second regional component. The local phase ramp function is restricted or limited to the pixel region / area of the first / second regional component. Different local phase ramp functions can be applied to different sub-hologram components, so that different steering amounts in one or more directions are applied to different sub-hologram components. In this way, the sub-hologram formed by superimposing the first sub-hologram component and the second sub-hologram component can include multiple different local phase ramp functions, which are selected to address amplitude aberration errors.

[0059] The displacement associated with the local phase ramp function can align the point spread functions formed by the corresponding sub-hologram components when illuminated. As described above, the phase ramp function can shift the point spread function by a predetermined amount at the exit pupil. This displacement can be relative to the position of the point spread function without the application of the local phase ramp function. As described above, aligning the point spread function can include, for example, overlapping, superimposing, or co-locating the point spread functions of the first and second sub-hologram components.

[0060] The method may include applying a first local phase ramp function to the first area component and applying a second local phase ramp function to the second area component. The first local phase ramp function and the second local phase ramp function may be different. The first direction corresponding to the first local phase ramp function may be opposite to the second direction corresponding to the second local phase ramp function. The gradient of the first local phase ramp function (grating function) may be different from the gradient of the second local phase ramp function. In this way, the shift or displacement of the first point spread function formed by the first sub-hologram component and the second point spread function formed by the second sub-hologram component may be asymmetric or opposite or complementary. One or both of the amplitude and polarity of the gradient of the first and second local phase ramp functions may be different.

[0061] There may be a point spread function associated with each illuminated sub-hologram component. To align the point spread functions, the amount of displacement of the first point spread function of the first sub-hologram component can depend on the amount of displacement of the second point spread function of the second sub-hologram component. Therefore, a local phase ramp function can be applied to shift the first and second point spread functions by different amounts and in different directions. For example, as a result of amplitude aberration, the first point spread function associated with the first sub-hologram component can be shifted by a first amount in the second direction. The second point spread function associated with the second sub-hologram component can be shifted by a second amount in the first direction, which is opposite to the second direction. To correct for amplitude aberration, a first local phase ramp function can be applied to the first sub-hologram to shift the first point spread function by a first amount in the first direction. A second local phase ramp function can be applied to the second sub-hologram to shift the second point spread function by a second amount in the second direction. In some examples, the first amount can be the same as (and opposite in direction to) the second amount, making the shifts of the first and second point spread functions symmetrical. In other examples, the first amount can be different from (and opposite in direction to) the second amount, making the shifts of the first and second point spread functions asymmetrical.

[0062] A virtual surface or so-called extended modulator may comprise a one-dimensional or two-dimensional array of a display device and virtual replicas. The optical path length of each replica may be different. This may be because the optical paths of different replicas may have different path lengths through the waveguide, for example bouncing with a different number of "bounces" between the surfaces of a first and an optional second waveguide. Thus, the expanded path length of each replica may be different, and thus the array of replicas of the virtual surface or extended modulator may be offset from each other. In other words, the multiple replicas may be "staggered". Due to the different path lengths in the waveguide associated with each replica, each replica of the display device may be at a different vertical distance from the display device. For an optical system comprising a first waveguide and a second waveguide, an expansion modulator can be defined as comprising: (i) a first offset between replicas produced in the first waveguide (e.g., an elongated waveguide), defined by an angle (in space) and a corresponding pupil expansion direction, (ii) a second offset between replicas produced in the second waveguide (e.g., a planar waveguide), defined by an angle (in space) and a corresponding pupil expansion direction; (iii) any skew between the directions of the first offset and the second offset—producing a roughly parallelogram if the original display device is rectangular, and / or (iv) the optical path length (difference) between the display device replica and the eye position.

[0063] An area of the virtual surface may be associated with each virtual image point of the virtual image. The area may be depicted, for example, by a straight line path (e.g., representing a spherical wave or wavelet) propagating from each virtual image point through the virtual surface to an entrance pupil of an observer. At least some virtual image points of the virtual image may have an associated area spanning multiple replicas. For example, a first area component of an area associated with a first virtual image point may be on a first virtual replica, and a second area component of an area component associated with the first virtual image point may be on a second virtual replica. The first and second virtual replicas may be adjacent to each other. A method of calculating a first sub-hologram of a first virtual image point may include determining a first sub-hologram component of the virtual image point within the first area component and a second sub-hologram component of the virtual image point within the second area component. The method may further include superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point.

[0064] The step of applying a local phase ramp function can include selecting a phase ramp function for at least one of the first and second regional components based on a parameter of the corresponding regional component and / or the associated sub-hologram component. The parameter can be or relate to at least one of: a distance from a center of at least a portion of the corresponding regional component to an edge of the corresponding replica; a size of the corresponding regional component; a size of the corresponding sub-hologram component; a ratio of the size of the regional component for which the phase ramp is selected to the other of the first or second regional components; and / or a ratio of the size of the sub-hologram component for which the phase ramp is selected to the other of the first or second sub-hologram components. The amount of shift in the point spread function formed by the sub-hologram components can depend on the relative sizes of the sub-hologram components / regional components. Thus, each parameter can serve as a proxy for the desired amount of shift in the point spread function.

[0065] Typically, the phase ramp function selected for the first regional component can have an opposite polarity to the phase ramp function selected for the second regional component. In some examples, the first regional component differs in size and distance from the edge of the corresponding region to the second regional component. Thus, the phase ramp function selected for the first regional component can have a different gradient magnitude than the phase ramp function selected for the second regional component. In other words, the phase ramp functions applied to the first and second regional components can be asymmetric.

[0066] The step of selecting a phase ramp function for at least one of the first and second regional components may include searching for parameters of the corresponding sub-hologram component in a lookup table or database. The lookup table or database may include data pairs or key-value pairs. The data pairs or key-value pairs may associate parameter values with appropriate phase ramp functions. The lookup table or database may include gradient values of the phase ramp function. The step of selecting a phase ramp function for at least one of the first and second regional components may include inputting the parameters into the lookup table or database. A local phase ramp function may then be output. The method may include selecting and outputting the local phase ramp function for the corresponding first or second regional component.

[0067] The method may include calibrating the phase ramp function output by the lookup table or database. The calibration may include applying a calibration factor. The calibration factor may take into account parameters of the optical system. For example, the parameters of the optical system may include the dimensions of the display device, the angle of incidence of light injected into a waveguide of the optical system, the wavelength of the incident light, and the optical path length in the system. In this way, the same lookup table or database may be used in conjunction with various different embodiments of the optical system. Alternatively, the values stored in the lookup table or database may already be calibrated.

[0068] The method may include identifying a virtual surface between the virtual image and the waveguide. The virtual surface may include a display device and multiple virtual copies of the display device formed by the waveguide. The method may also include identifying an area on the virtual surface.

[0069] The virtual surface includes a first virtual replica adjacent to a second virtual replica. The first sub-hologram component of the first virtual replica may be adjacent to the second sub-hologram component of the second virtual replica. In such an embodiment, the amplitude aberration may cause the first sub-hologram component to be shifted in a direction opposite to the second sub-hologram component.

[0070] In an embodiment, each sub-hologram is a point cloud hologram, which is determined by propagating a light wave from a corresponding virtual image point toward an observer and determining a composite light field arriving at the corresponding position in the region, wherein the light wave is optionally a spherical light wave. As will be understood by those skilled in the art, this can be computationally performed by simulating the propagation of the light wave to form a wavefront / composite light field.

[0071] In embodiments, each virtual replica of a display device formed by the waveguide is positioned at a different vertical distance from the display device, thereby forming a staggered virtual surface of virtual replicas of the display device. In an example, each virtual replica of the display device corresponds to a corresponding replica of a hologram formed by the waveguide. The method may include 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. Each virtual replica of the display device corresponds to a corresponding replica of the hologram formed by the waveguide.

[0072] The method of calculating sub-holograms of a virtual image point of the first aspect has been described with respect to such a method: the area bounded by a straight line path from the virtual image point includes a first area component on a first replica and a second area component on a second replica and the first and second sub-hologram components are calculated. However, the method of the first aspect is not limited to this arrangement. The area may include additional area components on additional replicas (e.g., a third area component on a third replica and a fourth area component on a fourth replica). More sub-hologram components may be calculated. For example, a third sub-hologram component within the third area component may be calculated. A fourth sub-hologram component within the fourth area component may be calculated. The step of forming a sub-hologram of the virtual image point may include superimposing the first sub-hologram component, the second sub-hologram component, and additional (e.g., third and fourth) sub-hologram components. The method may include applying a local phase ramp function to the additional sub-hologram components.

[0073] According to a second aspect, a method for computing a hologram is provided. A hologram is a virtual image and is used in an optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram. A corresponding sub-hologram is computed for each of a plurality of virtual image points of the virtual image.

[0074] Each sub-hologram is calculated according to the method described in the first aspect. For example, each sub-hologram is calculated by determining an area bounded by a straight line path from a virtual image point to the periphery of an observer's entrance pupil, wherein the area includes a first area component on a first virtual replica of the display device and a second area component on a second virtual replica of the display device; determining a first sub-hologram component of the virtual image point within the first area component and a second sub-hologram component of the virtual image point within the second area component; superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point; and applying a local phase ramp function to at least one of the first area component and the second area component. As defined in the second aspect, any other features described with respect to the method of the first aspect may be applied to the step of calculating the corresponding sub-hologram of the virtual image point.

[0075] The method may further include superimposing the corresponding sub-hologram for each of the plurality of virtual image points to form a hologram of the virtual image.

[0076] In another aspect, a method for computing a hologram is provided. The hologram is a virtual image of an optical system, the optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram. The method comprises determining a sub-hologram for each virtual image point of the virtual image. Each sub-hologram is determined by: propagating a light wave from the corresponding virtual image point toward an observer; defining an intersection region of the propagated light wave on a virtual surface between the virtual image and the observer, wherein the virtual surface comprises the display device and multiple virtual replicas of the display device formed by the waveguide, wherein the defined region is bounded by a straight line path from the corresponding virtual image point to a periphery of an entrance pupil of an observer's eye; and identifying one or more sub-regions of the defined region of a composite light field, wherein each sub-region intersects the virtual surface at a location corresponding to a different one of the display device and the multiple virtual replicas. Each of the one or more sub-regions of the composite light field forms a respective component of the sub-hologram.

[0077] In another aspect, a method for computing a sub-hologram of a virtual image point of an optical system is provided, the optical system comprising a display device configured to display the sub-hologram and a waveguide configured to replicate the sub-hologram. The method comprises propagating a light wave from a corresponding virtual image point toward an observer. The method further comprises defining an intersection region of the propagated light wave on a virtual surface between the virtual image and the observer. The virtual surface comprises the display device and at least a first virtual replica of the display device and a second virtual replica of the display device. Each virtual replica is formed by a waveguide. The defined region is bounded by a straight line path from the corresponding virtual image point to a periphery of an entrance pupil of an observer's eye. The method further comprises identifying at least a first regional component of a defined region of the light wave on the first virtual replica of the display device and a second regional component of a defined region of the light wave on the second virtual replica of the display device; wherein each regional component of the light wave forms a corresponding component of the sub-hologram. The method further comprises applying a local phase ramp function to at least one of the first regional component and the second regional component.

[0078] In an embodiment, a virtual surface comprising a display device and a plurality of virtual replicas is "staggered." Specifically, each replica of the display device is positioned at a different vertical distance from the display device due to different path lengths in the waveguide associated with each replica. Consequently, a portion of the virtual surface associated with each replica (e.g., in the x,y dimensions) is offset vertically (e.g., in the z dimension) from the display device.

[0079] A method for computing a point cloud hologram is provided. A point cloud hologram is a hologram of a virtual image of an optical system, the optical system comprising a display device arranged to display the hologram and a waveguide arranged to replicate the hologram. The method comprises forming a point cloud sub-hologram at a location corresponding to a location of the display device. The method further comprises forming a point cloud sub-hologram at each location corresponding to a corresponding virtual replica of the display device formed by the waveguide. Each point cloud sub-hologram is formed using only light from the virtual image, which light can pass through an observer's entrance pupil.

[0080] In an embodiment, the method comprises determining the position of each replica of the display device by unfolding a respective optical path within the waveguide from the display device to the hologram replica.

[0081] As used herein, the term "virtual image" refers to an image or holographic reconstruction formed upstream of a display device. That is, the display device is positioned between the virtual image and the observer. In other words, the distance from the virtual image to the observer is greater than the distance from the display device to the observer. Those skilled in the art of optics will understand that the observer effectively sees the virtual image through the display device. The virtual image may be perceived several meters behind the display device. Therefore, those skilled in the art will understand how it is possible to account for the path of light rays from the virtual image through the display device, or an extended surface containing the display device, to the observer on the other side of the display device.

[0082] The prefix "sub" associated with each hologram and its replicas in the multiple holograms formed on the display device is used only to distinguish them from the final / combined hologram of the entire virtual image and reflects that each is a component of a hologram. A hologram can be a point cloud hologram. Therefore, a sub-hologram and a sub-hologram component can also be a point cloud sub-hologram or a point cloud sub-hologram component, respectively.

[0083] As described herein, the waveguide effectively forms an array of replicas (also referred to herein as "virtual replicas") of the display device, wherein each display device replica corresponds to a corresponding replica of the hologram. The array of replica display devices is referred to here as an "interlaced surface". The "surface" is not continuous because the replicas are spatially separated in a direction orthogonal to the display device surface, for example in the z direction. The surface is referred to as "interlaced" to reflect the separation of this variation of different display device replicas in the z direction. Typically, the display device replicas are on different x, y planes that are spatially offset (without any skew) in the z direction. In the case of using a waveguide for one-dimensional replication, the interlaced surface can be similar to a series of independent steps with no vertical faces of the steps. In the case of using two orthogonal waveguides to replicate in two orthogonal directions, as is known in the field of pupil expansion, the interlaced surface is effectively interlaced in two directions, for example x and y, but has no surface component in the z direction. The terms "virtual surface", "interlaced expansion modulator" and "expanded surface" may also be used herein to refer to an array of replicas of the display device formed by the waveguide. This disclosure describes how each sub-hologram can be confined / limited to an area of the display device that spatially corresponds to the area of the interlace or virtual surface defined by the straight line path from the corresponding virtual image point to the periphery of the entrance pupil of the viewing system. The area of the interlace or virtual surface effectively defines the "contribution area" of the display device for the sub-hologram.

[0084] The process of "unfolding" the optical path within the waveguide is described by extrapolating light rays exiting the waveguide through its output port (i.e., the light rays of the replica) back to the virtual surface with no internal reflection within the waveguide. By extrapolating all the light rays of the replica back to the virtual surface, the position or orientation of the corresponding virtual replica of the display device is identified. Each virtual replica of the display device is at a different distance from the observer because the optical path length within the waveguide associated with each replica is different.

[0085] This disclosure describes the process of "superimposing" sub-holograms and components of sub-holograms with reference to the process of combining holograms, which preserves positional or spatial information on a display device, for example, in the xy plane.

[0086] The determination of a sub-hologram or sub-hologram component at various "positions" mentioned herein is made with reference to a position in a direction orthogonal to the display device surface, which direction may also be referred to herein as the propagation axis or projection axis. As is well known to those skilled in the art of optics, the propagation axis is typically defined as the z-axis. The display device and its virtual replica are typically defined in the xy plane. In some embodiments, a point cloud hologram is determined by propagating a light wave to the described "position" or plane.

[0087] Reference is made here to confining each sub-hologram to (or defining each sub-hologram within) one or more regions defined / bounded / delineated by a straight line. Each region is a region of the display device defined by an area of the virtual surface or corresponding to an area of the virtual surface. For example, if the straight line defines an area in the middle of a single virtual replica, then the sub-hologram is confined / defined within the middle area of the display device. Similarly, if the straight line intersects two or more virtual replicas, then each area of the virtual replica (or a "sub-area" of the delineated area of the virtual surface) effectively defines a corresponding area (or "sub-area") of the display device. In some embodiments, overlapping areas are defined on different virtual replicas, and according to further improvements disclosed herein, these areas may be treated differently.

[0088] For the avoidance of doubt, the image formed or perceived is a holographic reconstruction of the target image. The holographic reconstruction is formed from a hologram based on the target image. In some embodiments, the hologram is determined (e.g., calculated) from the target image.

[0089] The method disclosed herein identifies contributing light paths for virtual image points used to form a master image. Contributing light paths are light paths from the virtual image that pass through the observer's entrance pupil and thus contribute to the image. Therefore, the method does not consider light paths that result in duplicates or "ghost" versions of the master image. Consequently, all "sub-holograms" of a computational hologram actively contribute to the "master" target image.

[0090] In this disclosure, the term "replica" is used solely to reflect that spatially modulated light is split, resulting in a composite light field being directed along multiple distinct optical paths. The term "replica" is used to refer to each occurrence or instance of the composite light field following a replication event—such as the partial reflection-transmission of a pupil expander. Each replica propagates along a different optical path. Some embodiments of the present disclosure relate to the propagation of light encoded with a hologram rather than an image—that is, light spatially modulated with a hologram of an image rather than the image itself. Those skilled in the art of holography will understand that the composite light field associated with the propagation of light encoded with a hologram will vary with propagation distance. The term "replica" as used herein is independent of propagation distance, so two light branches or paths associated with a replication event are still referred to as "replicas" of each other, even if the branches have different lengths, causing the composite light field to evolve differently along each path. That is, according to this disclosure, even if two composite light fields are associated with different propagation distances, they are still considered "replicas"—assuming they originate from the same replication event or series of replication events.

[0091] According to the present disclosure, a "diffraction light field" is a light field formed by diffraction. The diffraction light field can be formed by illuminating a corresponding diffraction pattern. According to the present disclosure, an example of a diffraction pattern is a hologram, and an example of a diffraction light field is a holographic light field or a light field of a holographic reconstruction that forms an image. The holographic light field forms a (holographic) reconstruction of the image on a playback plane. The holographic light field propagating from the hologram to the playback plane can be said to include light encoded with / through the hologram or light in the holographic domain. The diffraction light field is characterized by a diffraction angle determined by the minimum characteristic size of the diffraction structure and the wavelength of the light (of the diffraction light field). According to the present disclosure, it can also be said that the "diffraction light field" is a reconstructed light field formed on a plane that is spatially separated from the corresponding diffraction structure. Disclosed herein is an optical system for propagating a diffraction light field from a diffraction structure to an observer (for example, from a display device to an observation system). The diffraction light field can form an image.

[0092] The term "hologram" is used to refer to a record that contains amplitude information or phase information, or some combination thereof, about an object. The term "holographic reconstruction" is used to refer to the optical reconstruction of an object formed by illuminating a hologram. The system disclosed herein is described as a "holographic projector" because the holographic reconstruction is a real image and is spatially separated from the hologram. The term "replay field" is used to refer to the 2D region within which the holographic reconstruction is formed and is perfectly focused. If the hologram is displayed on a spatial light modulator comprising pixels, the replay field will be repeated in the form of multiple diffraction orders, where each diffraction order is a replica of the zeroth order replay field. The zeroth order replay field typically corresponds to the preferred or primary replay field because it is the brightest replay field. Unless otherwise explicitly stated, the term "replay field" should be taken to refer to the zeroth order replay field. The term "replay plane" is used to refer to the plane in space that contains all replay fields. The terms "image," "replay image," and "image area" refer to the area of the replay field that is illuminated by the light of the holographic reconstruction. In some embodiments, an "image" may comprise discrete points, which may be referred to as "image points," or, for convenience only, as "image pixels."

[0093] The terms "encoding," "writing," and "addressing" are used to describe the process of providing a plurality of control values, each of which determines the modulation level of each pixel, to a plurality of pixels of the SLM. It can be said that the pixels of the SLM are configured to "display" a light modulation profile in response to receiving the plurality of control values. Thus, the SLM can be said to "display" a hologram, and a hologram can be considered an array of light modulation values or levels.

[0094] It has been discovered that holographic reconstructions of acceptable quality can be formed from "holograms" containing only phase information related to the Fourier transform of the original object. Such holographic recordings may be referred to as phase-only holograms. The embodiments relate to phase-only holograms, but the disclosure is equally applicable to amplitude-only holography. The embodiments relate to the computation of point cloud holograms, i.e., holograms constructed using point cloud methods.

[0095] The present disclosure is also applicable to forming a holographic reconstruction using amplitude and phase information associated with the Fourier transform of the original object. In some embodiments, this is achieved by using complex modulation of a so-called full complex hologram that contains amplitude and phase information related to the original object. Because the value (gray level) assigned to each pixel of the hologram has both amplitude and phase components, such a hologram can be referred to as a full complex hologram. The value (gray level) assigned to each pixel can be represented as a complex number having both amplitude and phase components. In some embodiments, a full complex computer-generated hologram is calculated.

[0096] Reference may be made to the phase value, phase component, phase information, or simply phase of a pixel of a computer-generated hologram or spatial light modulator as shorthand for "phase delay". That is, any phase value described is actually a number (e.g., in the range of 0 to 2π) that represents the amount of phase delay provided by that pixel. For example, a pixel of a spatial light modulator described as having a phase value of π / 2 will delay the phase of received light by π / 2 radians. In some embodiments, each pixel of the spatial light modulator can operate at one of a plurality of possible modulation values (e.g., phase delay values). The term "grayscale" may be used to refer to a plurality of available modulation levels. For example, the term "grayscale" may be used for convenience to refer to a plurality of available phase levels in a phase modulator alone, even though the different phase levels do not provide different shades of gray. For convenience, the term "grayscale" may also be used to refer to a plurality of available complex modulation levels in a complex modulator.

[0097] Thus, a hologram comprises an array of gray levels, i.e. an array of light modulation values, such as phase delay values or an array of complex modulation values. A hologram is also considered a diffraction pattern, since it is a pattern that causes diffraction when displayed on a spatial light modulator and illuminated with light of a wavelength relative to (usually less than) the pixel pitch of the spatial light modulator. Reference is made herein to combining a hologram with other diffraction patterns, such as diffraction patterns used as lenses or gratings. For example, a diffraction pattern used as a grating can be combined with a hologram to shift the replay field on the replay plane, or a diffraction pattern used as a lens can be combined with a hologram to focus the holographic reconstruction on the replay plane in the near field.

[0098] Although different embodiments and groups of embodiments may be disclosed separately in the detailed description below, 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 the features disclosed in this disclosure are contemplated. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Certain embodiments are described, by way of example only, with reference to the following drawings:

[0100] Figure 1 is a schematic diagram showing a reflective SLM producing a holographic reconstruction on a screen;

[0101] Figure 2 shows an image comprising a plurality of image regions (bottom) and a corresponding hologram comprising a plurality of hologram components (top);

[0102] Figure 3 A hologram is shown wherein holographically encoded light is routed or directed into a plurality of discrete hologram channels;

[0103] Figure 4A system is shown, which is arranged to transmit Figure 3 The light content of each hologram channel is routed to the eye;

[0104] Figure 5 showing a perspective view of a pair of stacked image replicators arranged to expand a light beam in two dimensions;

[0105] Figure 6 shows an example visualization of an "extended modulator" or "virtual surface" comprising a 3D array including a display device and multiple replicas of the display device formed by waveguides;

[0106] Figure 7 An apparatus for computing a point cloud hologram using an expansion modulator is shown, showing the paths of waves propagating from first and second example image points of a desired virtual image to be holographically reconstructed by the hologram;

[0107] Figure 8 Shown Figure 7 calculation of a sub-hologram for a first example image point of the device;

[0108] Figure 9 Shown Figure 7 calculation of a sub-hologram for a second example image point of the device;

[0109] Figures 10A to 10C relates to actual image points formed when light is encoded with a sub-hologram comprising a single sub-hologram component, such as the second example image point;

[0110] Figures 11A to 11C relates to an actual image point formed when light is encoded with a sub-hologram comprising a plurality of sub-hologram components formed in an area spanning a plurality of replicas, such as a first example image point;

[0111] Figure 12 is a flow chart of a method for calculating a sub-hologram of an image point according to the present disclosure; and

[0112] Figure 13 The elimination of elongation errors in the formed image points is shown.

[0113] The same reference numbers will be used throughout the drawings to refer to the same or like parts. DETAILED DESCRIPTION

[0114] The present invention is not limited to the embodiments described below, but extends to the full scope of the appended claims. That is, the present invention can be embodied in different forms and should not be construed as limited to the described embodiments, which are set forth for illustrative purposes.

[0115] Unless otherwise stated, terms in the singular may include plural forms.

[0116] A structure described as being formed on / under or above / below another structure should be construed to include a case where the structures are in contact with each other and, further, a case where a third structure is provided therebetween.

[0117] When describing a temporal relationship, for example, when the temporal order of events is described as "after," "followed," "next," "before," etc., the present disclosure should be considered to include both consecutive and non-consecutive events unless otherwise specified. For example, unless terms such as "just," "immediately," or "directly" are used, the description should be considered to include non-consecutive situations.

[0118] Although the terms "first," "second," etc. may be used herein to describe various elements, these elements are not limited by these terms. These terms are only used to distinguish between the various elements. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the appended claims.

[0119] The features of different embodiments may be coupled or combined with each other in part or in whole, and may interoperate with each other in different ways. Some embodiments may be performed independently of each other, or may be performed together in a mutually dependent relationship.

[0120] Optical configuration

[0121] Figure 1 An embodiment is shown 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 being reconstructed. Thus, the hologram can be said to be a Fourier, frequency, 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, such as a light-receiving surface like a screen or diffuser.

[0122] A light source 110, such as a laser or laser diode, is arranged to illuminate the SLM 140 via a collimating lens 111. The collimating lens causes a substantially planar wavefront of light to be incident on the SLM. Figure 1 In embodiments, the direction of the wavefront is off-normal (e.g., two or three degrees from a plane that is truly normal to the transparent layer). However, in other embodiments, a substantially planar wavefront is provided at normal incidence, and a beam splitter arrangement is used to separate the input and output optical paths. Figure 1In the embodiment shown, the arrangement is such that light from the light source reflects from the mirrored back surface of the SLM and interacts with the light modulating layer to form an exit wavefront 112. The exit wavefront 112 is applied to an optical device including a Fourier transform lens 120, the focus of which is located at a screen 125. More specifically, the Fourier transform lens 120 receives the modulated light beam from the SLM 140 and performs a frequency-to-space transform to produce a holographic reconstruction at the screen 125.

[0123] It's important to note that in this type of hologram, every pixel of the hologram contributes to the entire reconstruction. There is no one-to-one correlation between a specific point on the replay field (or image pixel) and a specific light modulation element (or hologram pixel). In other words, the modulated light leaving the light modulation layer is distributed across the entire replay field.

[0124] In these embodiments, the position of the holographic reconstruction in space is determined by the power (focus) of the Fourier transform lens. Figure 1 In the illustrated embodiment, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens and optically performs a Fourier transform. Any lens can function as a Fourier transform lens, but the accuracy of the Fourier transform it performs will be limited by the lens's performance. Those skilled in the art understand how to use lenses to perform an optical Fourier transform.

[0125] Hologram computing

[0126] In some embodiments, the computer generated hologram is a Fourier transform hologram, or simply a Fourier hologram or a Fourier-based hologram, where the image is reconstructed in the far field by exploiting the Fourier transform properties of a positive lens. The Fourier hologram is computed by Fourier transforming the desired light field in the replay plane back to the lens plane. The computer generated Fourier hologram can be computed using the Fourier transform. By way of example only, the embodiments relate to Fourier holography and Gerchberg-Saxton type algorithms. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms that can be computed by similar methods. In some embodiments, the hologram is a phase or pure phase hologram. However, the embodiments relate to holograms computed based on point cloud methods. UK patent application GB2112213.0 filed on August 26, 2021 discloses an example hologram computation method that can be combined with the present disclosure, and the patent application is incorporated herein by reference. In particular, this earlier patent application describes a method for computing a (special) type of hologram, which will be referenced below Figure 2 and Figure 3 Described, it performs angular division / channelization of image content.

[0127] In some embodiments, a real-time engine is provided that uses an algorithm to receive image data and calculate holograms in real time. 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 the SLM. That is, in some embodiments, a repository of pre-determined holograms is provided.

[0128] Optical Modulation

[0129] The display system includes a display device that defines an exit pupil of the display system. The display device is a spatial light modulator. The spatial light modulation can be a phase modulator. The display device can be a liquid crystal on silicon "LCOS" spatial light modulator as is known in the art. The LCOS SLM includes a plurality of pixels, such as a quadrilateral LC pixel array. The pixels can be addressed or encoded with a diffraction pattern that includes a hologram. The LCOS SLM can be said to be arranged to "display" the hologram. The LCOS SLM is arranged to be illuminated with light and output spatially modulated light in accordance with the hologram. The spatially modulated light output by the LCOS SLM includes a diffracted or holographic light field as described herein.

[0130] Optical Channel

[0131] The optical systems disclosed herein are applicable to pupil expansion with any diffracted light field. In some embodiments, the diffracted light field is a holographic light field—that is, a composite light field that is spatially modulated according to a hologram of an image rather than the image itself. In some embodiments, the hologram is a special type of hologram that angularly divides / directs the image content. This type of hologram is further described herein merely as an example of a diffracted light field compatible with the present disclosure. Other types of holograms can be used in conjunction with the display systems and light engines disclosed herein.

[0132] A display system and method are described below that include a waveguide pupil expander. As will be familiar to the skilled reader, a waveguide can be configured as a "pupil expander" in that it can be used to increase the area over which light emitted by a relatively small light emitter (such as a relatively small SLM or other pixelated display device used in the apparatus described herein) can be viewed by a human observer or other viewing system 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 through which light is output to the observer. As a result, the light can be seen from multiple different observer positions, for example, the observer can move their head, and thereby their line of sight, while still being able to see the light from the light emitter. Thus, it can be said that by using a waveguide pupil expander, the observer's "eye box" or "eye box" is enlarged. This has many useful applications, such as, but not limited to, heads-up displays, such as, but not limited to, automotive heads-up displays.

[0133] The display systems described herein can be configured to direct light, such as a diffracted light field, through a waveguide pupil expander so as to provide pupil expansion in at least one dimension, for example, in two dimensions. The diffracted light field may include light output by a spatial light modulator (SLM), such as an LCOS SLM. For example, the diffracted light field may include light encoded by a hologram displayed by the SLM. For example, the diffracted light field may include light of a holographic reconstructed image corresponding to the hologram displayed by the SLM. The hologram may include 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 a "diffraction structure" or a "modulation pattern". The SLM or other display device may be arranged to display a diffraction pattern (or modulation pattern) in a manner familiar to the skilled reader, comprising a hologram and one or more other elements, such as a soft lens or a diffraction grating.

[0134] The hologram can be calculated to provide guidance of the diffracted light field. This is described in detail in GB2101666.2, GB2101667.0 and GB2112213.0, all of which are incorporated herein by reference. In general, the hologram can be calculated to correspond to the image to be holographically reconstructed. The image to which the hologram corresponds can be referred to as the "input image" or "target image". The hologram can be calculated so that when it is displayed on the SLM and appropriately illuminated, it forms a light field (output by the SLM) comprising a spatially modulated light cone. In some embodiments, the light cone comprises a plurality of continuous light channels of spatially modulated light corresponding to corresponding continuous regions of the image. However, the present disclosure is not limited to this type of hologram.

[0135] Although we refer to them here as "holograms" or "computer-generated holograms (CGHs)", it should be understood that the SLM can be configured to dynamically display multiple different holograms continuously or according to a sequence. The systems and methods described herein are applicable to the dynamic display of multiple different holograms.

[0136] Figure 2 and 3 An example of the type of hologram that can be displayed on a display device, such as an SLM, that can be used in conjunction with the pupil expander disclosed herein is shown. However, this example should not be viewed as limiting the present disclosure.

[0137] Figure 2 An image 252 is shown for projection, comprising eight image regions / components V1 to V8. By way of example only, Figure 2 Eight image components are shown, and image 252 may be separated into any number of components. Figure 2Also shown is a coded light pattern 254 (i.e., a hologram) that can reconstruct image 252—for example, when transformed by a lens of a suitable viewing system. The coded light pattern 454 includes first through eighth sub-holograms or components H1 through H8, corresponding to first through eighth image components / regions V1 through V8. Figure 2 It further shows how a hologram decomposes the image content by angle. Therefore, a hologram is characterized by its guidance of light. Figure 3 Specifically, the hologram in this example directs light into multiple discrete regions. In the example shown, the discrete regions are disks, but other shapes are also contemplated. After propagation through the waveguide, the optimal disk size and shape can be related to the size and shape of the observation system's entrance pupil.

[0138] Figure 4 A system 400 is shown, including a display such as Figure 2 and 3 A display device for a computed hologram is shown.

[0139] System 400 includes a display device that, in this arrangement, includes an LCOS 402. LCOS 402 is arranged to display a modulation pattern (or "diffraction pattern") comprising a hologram and projects holographically encoded light into an eye 405, which includes a pupil serving as an aperture 404, a lens 409, and a retina (not shown) serving as an observation plane. There is a light source (not shown) arranged to illuminate LCOS 402. The lens 409 of eye 405 performs the conversion of the hologram into an image. The light source can be of any suitable type. For example, it can include a laser source.

[0140] The viewing system 400 also includes a waveguide 408 located 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 408 acts as a pupil expander in a well-known manner and will therefore only be briefly described here.

[0141] in short, Figure 4The illustrated waveguide 408 comprises a generally elongated structure. In this example, waveguide 408 comprises an optical plate of refractive material, but other types of waveguides are well known and may be used. Waveguide 408 is positioned to intersect the light cone (i.e., the diffracted light field) projected from LCOS 402, for example, at an oblique angle. In this example, the size, position, and orientation of waveguide 408 are configured to ensure that light from each of the eight light beams within the light cone enters waveguide 408. Light from the light cone enters waveguide 408 via a first planar surface of waveguide 408 (located closest to LCOS 402) and is guided at least partially along the length of waveguide 408 before being emitted via a second planar surface of waveguide 408, substantially opposite the first surface (located closest to the eye). As will be readily appreciated, the second planar surface is partially reflective and partially transmissive. In other words, as each light ray propagates within waveguide 408 from the first planar surface and strikes the second planar surface, some light will be transmitted through waveguide 408, and some light will be reflected by the second planar surface back toward the first planar surface. The first planar surface is reflective so that all light striking it from within the waveguide 408 will be reflected back toward the second planar surface. Thus, some light may simply be refracted between the two planar surfaces of the waveguide 408 before being transmitted, while other light may be reflected and, therefore, may experience one or more reflections (or "bounces") between the planar surfaces of the waveguide 408 before being transmitted.

[0142] Figure 4 A total of nine "bounce" points B0 to B8 are shown along the length of waveguide 408. Figure 2 As shown, light associated with all points of the image (V1-V8) is transmitted out of the waveguide at each "bounce" from the second planar surface of the waveguide 408, but only light from one angular portion of the image (e.g., light from one of V1 to V8) has a trajectory that enables it to reach the eye 405 from each corresponding "bounce" point B0 to B8. In addition, light from a different angular portion of the image (V1 to V8) reaches the eye 405 from each corresponding "bounce" point. Therefore, Figure 4 In the example shown, each angular channel of coded light reaches the eye only once from waveguide 408.

[0143] The above methods and apparatus can be implemented in a variety of different applications and viewing systems. For example, they can be implemented in a head-up display (HUD) or in a head or helmet mounted device (HMD) such as an augmented reality (AR) HMD.

[0144] Although virtual images have been discussed generally herein, which require the eye to convert received modulated light to form a perceived image, the methods and apparatus described herein can be applied to real images.

[0145] 2D pupil expansion

[0146] Although Figure 5 The arrangement shown includes a single waveguide that provides pupil expansion in one dimension, but pupil expansion can be provided in more than one dimension, for example in two dimensions. Figure 4 The examples in use a hologram that has been calculated to create channels of light, each corresponding to a different portion of an image, but the present disclosure and the systems described below are not limited to this type of hologram.

[0147] Figure 5 A perspective view of a system 500 is shown, comprising two replicators 504, 506 arranged to expand a light beam 502 in two dimensions.

[0148] exist Figure 5 In the system 500, the first replicator 504 includes a first pair of surfaces stacked parallel to each other, arranged in a manner similar to Figure 4 The first pair of surfaces are similar in size and shape to each other (in some cases identical) and are substantially elongated in one direction. The light beam 502 is directed to the input of the first replicator 504. Due to internal reflection processes between the two surfaces, as well as from one of the surfaces (the upper surface, such as Figure 5 As will be familiar to the skilled reader, light from beam 502 is replicated in a first direction along the length of first replicator 504 by partial transmission of light from each of a plurality of output points on a first replicator 504. Thus, a first plurality of replica light beams 508 are emitted from first replicator 504 toward second replicator 506.

[0149] The second replicator 506 includes a second pair of surfaces stacked parallel to one another, arranged to receive each collimated beam of the first plurality of light beams 508, and further arranged to provide replication or pupil expansion by expanding each of these beams in a second direction that is substantially orthogonal to the first direction. The first pair of surfaces are similar in size and shape to one another (in some cases identical), and are substantially rectangular. The rectangular shape is implemented for the second replicator so that it has a length along the first direction so as to receive the first plurality of light beams 508, and a length along the second orthogonal direction so as to provide replication in the second direction. Due to internal reflection processes between the two surfaces, as well as from one of the surfaces (such as Figure 5 The light of each beam in the first plurality of light beams 508 is replicated in the second direction by partial transmission of light from each of the plurality of output points on the upper surface (as shown in FIG. 1 ). Thus, a second plurality of light beams 510 is emitted from the second replicator 506, wherein the second plurality of light beams 510 includes a replica of the input light beam 502 along each of the first and second directions. Thus, the second plurality of light beams 510 can be viewed as a two-dimensional grid or array including replicated light beams.

[0150] Therefore, it can be said that Figure 5 The first and second replicators 504, 505 are combined to provide a two-dimensional replicator (or "two-dimensional pupil expander").

[0151] A virtual replica of a display device formed by one or more waveguides

[0152] Figure 6 An example visualization of an "extended modulator" or "virtual surface" comprising a 3D array including a hologram formed on a display device and multiple replicas of the hologram formed by a waveguide is shown.

[0153] As above reference Figure 4 As described above, the one-dimensional waveguide 408 can be arranged to expand the exit pupil of the display system. The display system includes a display device 402 that displays a hologram, which is output at a "bounce" point B0 of the waveguide 408. In addition, the waveguide forms multiple copies of the hologram at corresponding "bounce" points B1 to B8 along its length, corresponding to the direction of pupil expansion. Figure 4 As shown, the multiple replicas can be extrapolated linearly back to the corresponding multiple replicas or virtual display device 402'. This process corresponds to the step of "unfolding" the light path within the waveguide, so that the light rays of the replicas are extrapolated back to the "virtual surface" without internal reflection within the waveguide. Therefore, the light of the expanded exit pupil can be considered to originate from the virtual surface (also referred to herein as the "expanded modulator") comprising display device 402 and replica display device 402'.

[0154] The proposed method for CGH defines a so-called "extended modulator" where a display device (e.g. LCOSSLM) is "extended" by an array of its virtual replicas, which would be formed by one or more waveguide pupil expanders to form an "extended modulator" or "virtual surface" (e.g. Figure 4 For example, a display device (e.g., an LCOS SLM) may be located Figure 6 The position of the expansion modulator is shown as (0,0), and the (virtual) replica formed by the two one-dimensional pupil expanders (i.e., the replica display device) is located at a position extending to (0,2) in a first direction of pupil expansion and to (4,0) in a second direction of pupil expansion. The direction of the light path is shown by arrow 601, which is perpendicular to the first and second directions of pupil expansion.

[0155] Thus, an expanding modulator is defined as comprising: (i) a first offset between replicas produced in a first waveguide pupil expander (e.g., an elongated waveguide) defined by an angle (in space) and a corresponding pupil expansion direction, (ii) a second offset between replicas produced in a second waveguide pupil expander (e.g., a planar waveguide) defined by an angle (in space) and a corresponding pupil expansion direction; and (iii) any skew between the directions of the first and second offsets—producing Figure 6 and (iv) the optical path length (difference) between the display device replica and the eye position—in Figure 6 In the direction 601 shown.

[0156] Figure 7 The invention shows the use of a spreading modulator (e.g. Figure 6 Device for calculating point cloud holograms) using the extended modulator shown.

[0157] The apparatus comprises a virtual image 700 at a desired virtual image position in space, and an observation system comprising an eye 720 having a pupil forming an entrance aperture 730 of the observation system. The apparatus shows one position of the eye 720 within an eye box. Thus, the point cloud hologram is associated with a specific eye box position. In addition, the apparatus comprises an expansion modulator (or virtual surface) 710 located between the virtual image 700 and the eye 720. A person skilled in the art will appreciate that in Figure 7 In the waveguide, the light path is effectively "unfolded" within the waveguide.

[0158] According to conventional techniques known in the art for computing point holograms, spherical waves (or "wavelets") are propagated along a path from each virtual image point to the display device plane. A point cloud hologram is determined based on (e.g., by combining / superimposing) a composite light pattern (i.e., a composite light field having an amplitude and phase distribution) formed by the wavelets propagating from each virtual image point at its corresponding region of intersection with the display device plane. The composite light pattern of the wavelets associated with each virtual image point is, so to speak, "captured" at the corresponding region of intersection with the display device plane.

[0159] However, according to the present disclosure, a point cloud hologram is determined based on (e.g., by combining / superimposing) a composite light pattern (i.e., amplitude and / or phase distribution) formed by wavelets propagating from each virtual image point at its corresponding intersection area with the expansion modulator or virtual surface. Furthermore, only the portion of the wavelet propagating from the virtual image point that reaches the observer's eye is considered.

[0160] Figure 7First and second example virtual image points 701 and 702 of a virtual image 700 are shown, located at a desired distance from an observer's eye 720. As indicated by the dashed lines, a (spread) spherical wave or wavelet propagates from each example virtual image point 701 and 702 through a spreading modulator 710 to an entrance aperture 730 of the observer's eye 720. A first pair of straight lines 711 extends from the first virtual image point 701 to opposite extremes of the entrance aperture 730 (i.e., the left-hand and right-hand sides in the figure), representing the edges / perimeter of (the relevant portion of) the associated wavelet. Similarly, a second pair of straight lines 721 extends from the second virtual image point 702 to opposite extremes / edges of the entrance aperture 730 (i.e., the left-hand and right-hand sides in the figure), representing the edges / perimeter of (the relevant portion of) the associated wavelet. The first and second pairs of straight lines 711 and 721 have regions 800 and 900, respectively, where they intersect the spreading modulator 710 (or virtual surface). Thus, in accordance with the present disclosure, the first and second pairs of straight lines 711, 721 "delineate" (i.e., form boundaries around) (a portion of) a desired wavelet in relation to first and second virtual image points 701, 702, respectively, which may pass through the entrance aperture 730 (i.e., pupil) of the observer's eye 720 at a particular eyebox location. In the following description, references to a "wavelet" propagating from a virtual image point relate to the portion of the propagating wave delineated by the straight lines, as described above.

[0161] Because the spreading modulator is "interleaved," as described herein, the intersection regions of the wavelets propagating from each virtual image point are at different perpendicular distances (to the plane of the display device)—or different distances in the direction of propagation. In particular, wavelets propagating from different virtual image points pass through different "replicas" (of the display device) of the spreading modulator 710. Some wavelets—such as the wavelet associated with virtual image point 701—may intersect with multiple replicas, while other wavelets—such as the wavelet associated with virtual image point 702—intersect with only a single replica, as described further below. For example, Figure 7 A first region 800 is shown that intersects the spreading modulator 710 of the first wavelet, depicted / bounded by a first pair of lines 711, propagating from the first virtual image point 701 to the eye 720. Similarly, Figure 7 A second region 900 is shown that intersects the extended modulator 710 of the second wavelet, depicted / bounded by a second pair of lines 721, propagating from the second virtual image point 702 to the eye 720. Figure 8 and 9 Describe these intersection areas.

[0162] Figure 8A first region 800 intersecting the extended modulator 710 of the first wavelet is shown in more detail, depicted by a first pair of lines 711, propagating from a first virtual image point 701. In particular, the first wavelet intersects in a region comprising two adjacent virtual copies of the extended modulator 710 - these virtual copies being at Figure 7 Shown as a horizontal line, Figure 8 , shown as vertical lines in FIG. As described above, different virtual replicas of the stretched modulator are located in different planes at different vertical distances. Therefore, the composite light pattern at the region intersecting each virtual replica of the stretched modulator is determined separately. This is necessary because the wavelet portions intersecting two adjacent virtual replicas will propagate different distances from virtual image point 791 and therefore have different composite light patterns or wavefronts upon reaching the stretched modulator.

[0163] The term "composite light pattern" hereafter refers to the spatial distribution of amplitude and phase value pairs representing the light field arriving at the spreading modulator from each virtual image point. In other words, the "composite light pattern" corresponds to the wavefront of the wavelet at one or more points where it intersects the spreading modulator. In embodiments, the "composite light pattern" is an array of amplitude and phase value pairs. In some embodiments, the display device is a phase modulator, in which case the amplitude values may ultimately be ignored or discarded. The "composite light pattern" may also be referred to as the "composite light field."

[0164] therefore, Figure 8 A first composite light pattern 810' is shown formed by the wavelet at the intersection with the first virtual replica (shown at the top of the figure) of the spreading modulator 710. The first composite light pattern 810' is "trapped" on the plane of the first virtual replica and forms a first sub-hologram component 810 associated with the first virtual image point 701. In addition, Figure 8 A second composite light pattern 811' formed by the wavelet at its intersection with a second virtual replica of the stretch modulator 710 (shown at the bottom of the figure) is shown. The second composite light pattern 811' is "trapped" in the plane of the second virtual replica and forms a second sub-hologram component 811 associated with the first virtual image point 701. Notably, the intersection region of each of the first and second virtual replicas of the stretch modulator 710 is shown as (a portion of) a circle or ellipse. This corresponds to the "primary contributing region" because it corresponds to light rays that pass through the entrance pupil of the observation system. In some cases, this ensures that the observation system forms a primary image (rather than a "ghost image"). In some embodiments, the shape of the primary contributing region corresponds to the shape of the entrance pupil of the observation system (e.g., having the same overall shape, but not necessarily the same size). Because the composite light patterns 810', 811' formed by the wavelets are located at the edges of their respective virtual replicas, the primary contributing regions are located at the top and bottom edges of the sub-hologram 820 for the virtual image point 701.

[0165] Figure 8 The first sub-hologram component 810 and the second sub-hologram component 811 are shown combined, in particular superimposed, to form a sub-hologram 820 associated with the first virtual image point 701. In particular, the spatial information associated with each composite light pattern 810', 811' (on the display device) is preserved during the superposition step. That is, the first composite light pattern 810' is formed at a location corresponding to the lower region of the display device and thus appears in the corresponding lower region of the final sub-hologram 820 for the virtual image point 701. Similarly, the second composite light pattern 811' is formed at a location corresponding to the upper region of the display device and thus appears in the corresponding upper region of the final sub-hologram 820 for the virtual image point 701.

[0166] Figure 9 The intersection region 900 of the extended modulator 710 with the second wavelet is shown in more detail, depicted by the second pair of lines 721, propagating from the second virtual image point 702. Specifically, the wavelet intersects in the region of a single virtual replica of the extended modulator 710 - the virtual replica at Figure 7 Shown as a horizontal line, Figure 9 , shown as a vertical line. Thus, a composite light pattern 920′ at the intersection region at the (single) plane of the virtual replica of the extended modulator 710 is captured and forms a sub-hologram 920 associated with the second virtual image point 702. Again, the intersection region at the virtual replica of the extended modulator 710 is shown as a circle or ellipse. This corresponds to the “primary contribution region” for the second virtual image point 702. Because the composite light pattern formed by the wavelet is located at the center of the virtual replica, the primary contribution region for this virtual image point 702 is located at the center of the sub-hologram 920.

[0167] By combining / superimposing (eg by vector addition) the sub-holograms, eg 820 , 920 , associated with each virtual image point, eg 701 , 702 , of the virtual image 700 , a point cloud hologram is determined for the entire virtual image 700 .

[0168] As described above, because the improved method for computing point cloud holograms uses an expanded modulator, it automatically takes into account the following differences: (i) a first offset between replicas in a first dimension, (ii) a second offset between replicas in a second dimension, and (iii) any skew between replicas generated by one or more waveguide pupil expanders, and (iv) differences in optical path lengths between replicas to the eye position.

[0169] In addition, the improved method for calculating point cloud holograms only considers wavelets / rays from virtual images that can pass through the entrance pupil of the observer's eye at the relevant eye position. Therefore, only rays that contribute to the "main image" (not the ghost image) are considered, that is, the main contribution area where the wavelet intersects with the expansion modulator. As a result, as described above, the improved method automatically avoids the formation of undesirable "ghosts". In addition, since the method only propagates wavelets / rays from virtual images that can pass through the entrance pupil of the observer's eye at the relevant eye position, the computational complexity is reduced. This reduces the speed of calculating point cloud holograms and also reduces the consumption of computing resources.

[0170] Correction of elongated virtual image points

[0171] Thus far, a method for computing a hologram of virtual image points of an optical system comprising a waveguide has been described. After testing the quality and clarity of images formed by holograms computed according to the method, the inventors unexpectedly discovered that, even after accounting for offsets and skews between replicas, when light is encoded with the computed hologram, the image points actually formed appear to be elongated relative to the original virtual image points on which the computed sub-holograms are based. This is the case for image points formed by sub-holograms comprising more than one sub-hologram component, and having intersections that span multiple replicas. Elongated image points have an adverse effect on the quality and clarity of images formed by holograms computed according to the method described above. About Figures 10A to 10C 11A to 11C describe the elongation of the actual image point in more detail.

[0172] Figures 10A to 10C The actual image point 1002 is formed when light is encoded with a sub-hologram including the sub-hologram component 920 (as described above). When light from a display device displaying the sub-hologram 920 is encoded with the hologram and passes through the waveguide, multiple copies of the hologram are generated, i.e., a similar image point is formed. Figure 6 and 7 The "expanded modulator" shown. The corresponding composite light field 1006 forming the image point 1002 falls within a single replica 1004 of the display device. In other words, Figures 10A to 10C Shown is the corresponding Figure 7 The actual image point 1002 of the virtual image point 702. Figure 10A A composite light field 1006 within a single replica 1004 is shown. Figure 10B The main lobe 1008 of the point spread function associated with the composite light field 1006 is shown. Figure 10CShown is an actual image point 1002 resulting from a point spread function 1008. A single point spread function comprising a single main lobe 1008 contributes to the actual image point 1002. The actual image point 1002 appears circular (i.e., not elongated) and thus has the same shape as the virtual image point 702, which is also circular.

[0173] Figures 11A to 11C Referring to an actual image point 1102 formed when light is encoded with a sub-hologram 820 comprising first and second sub-hologram components 810, 811 (as described above), the actual image point 1102 comprises first and second composite light fields 1106, 1107. These first and second composite light fields 1106, 1107 are formed within respective adjacent first and second virtual replicas 1104, 1105. Figure 11A The composite light field 1106 within the first replica 1104 and the composite light field 1107 within the second replica 1105 are shown. Figure 11A Only two replicas are shown in , but in some examples, the extended modulator includes more than two replicas, which, as described above, can form a one-dimensional or two-dimensional array, and the composite light field can intersect more than two replicas. Figure 11A Only the first and second composite light fields 1106 and 1107 are shown. Figure 11A Parts of the first and second copies 1104 and 1105. Figures 11A to 11C represents the actual image point 1102 observed by the inventor, which corresponds to Figure 7 The reconstructed image point 1102 is elongated, while the virtual image point 702 is circular.

[0174] Figure 11B The main lobe 1108 of the first point spread function (solid line) corresponding to the composite light field 1106 and the main lobe 1109 of the second point spread function (dashed line) corresponding to the composite light field 1107 are shown. The main lobes 1108, 1109 of the first and second point spread functions partially overlap, but the peaks are spatially separated. In other words, the two main lobes 1108, 1109 are not co-localized, and as a result, the combined composite light field forming the reconstructed image point 1102 includes two non-co-localized point spread functions. This is different from Figure 10B Single petal 1008, Figure 10B A single point spread function with a single peak / main lobe 1008 is included. Figure 11C Shown from Figure 11B The actual image point 1102 is obtained by using two point spread functions of . Because the two main lobes 1108 and 1109 are not spatially co-located, the resulting actual image point 1102 has an elongated circular shape (i.e., an ellipse). The elongation of the actual image point has the effect of reducing the quality and clarity of the entire image formed, including the actual image point 1102.

[0175] The inventors surprisingly found that the reconstructed image point 1102 has an elongated shape relative to the virtual image point used for the calculation of the sub-hologram. Figures 6 to 9 The described method takes into account the offset between replicas, the skew of the replicas and the optical path length differences of the replicas, so the expected Figure 11A The combined composite light fields 1106, 1107 will be equivalent to and equivalent to Figure 10A A single composite light field 1006 is expected to (effectively) produce a single point spread function with a single main lobe. However, simulations and experiments by the inventors show that this is not the case (e.g. Figure 11B and 11C ). The inventors have found that the spatial separation of the main lobes 1108, 1109 is caused by diffraction-type effects at the boundaries between the replicas forming the extended modulator / virtual surface. This diffraction results in a displacement / shift of the main lobes 1108, 1109. In particular, the main lobe 1108 of the first point spread function is shifted in the negative x-direction and the main lobe 1109 of the second point spread function is shifted in the positive x-direction. The inventors have found that by applying an appropriate local phase ramp function to at least one of the first area component and the second area component, the shift of the first and second point spread functions can be compensated so that the main lobes 1108, 1109 are aligned. Aligning the main lobes 1108, 1109 means that the main lobes 1108, 1109 become co-located so that the combined first and second point spread functions resemble Figure 10B In other words, the actual image point formed by the combined main lobes 1108, 1109 is essentially circular, rather than elongated, and therefore has the same shape as the associated virtual image point formed by the hologram calculation. This adversely affects the quality of the resulting hologram / image. Furthermore, it reduces the resolution of the display, as fewer pixels can be displayed per unit area, which is undesirable.

[0176] Figure 12 A flow chart representing a method according to the present invention for calculating a sub-hologram of a virtual image point (eg, virtual image point 701 ) is shown, wherein elongation of the virtual image point is substantially eliminated.

[0177] Step 1202 of the method includes determining an area bounded by a straight line path from a virtual image point to the periphery of an entrance pupil of an observer, wherein the area includes a first area component on a first virtual copy of the display device and a second area component on a second virtual copy of the display device. In the case of the first area component of FIG. 11 , step 1204 of the method includes determining a first sub-hologram component of the virtual image point within the first area component and a second sub-hologram component of the virtual image point within the second area component. Step 1206 of the method includes superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point. Steps 1202 to 1206 correspond to the method described above with respect to the virtual image point 701 (see Figure 7 and 8 ).

[0178] Step 1208 of the method includes applying a first local phase ramp function to the first regional component and applying a second local phase ramp function to the second regional component. Each phase ramp function can be referred to as a grating function. Applying the first local phase ramp step includes superimposing (e.g., adding) the first local phase ramp function to the calculated first sub-hologram component. Applying the second local phase ramp step includes superimposing (e.g., adding) the second local phase ramp function to the calculated second sub-hologram component.

[0179] By superimposing local phase ramp functions onto the sub-hologram components, light encoded with the corresponding sub-hologram component (and phase ramp function) can be steered in a direction opposite to the displacement caused by diffraction at the boundaries between replicas. By applying different phase ramp functions in different local regions (specifically, on different sub-hologram components), light encoded with different sub-hologram components can be steered in different directions. Knowing / estimating the displacement of light caused by diffraction effects allows the selection of appropriate local phase ramp functions to align / co-locate the point spread functions emitted from different sub-hologram components. Therefore, steering using at least one local phase ramp function described herein can be advantageously used to substantially eliminate stretching effects.

[0180] Now it will Figure 8 The sub-hologram shown and Figure 11B Step 1208 is described in the context of the point spread function shown.

[0181] Previously, it was described how a first composite light pattern 810' captured at the plane of a first replica forms a first sub-hologram component 810. When performing step 1208 of the method, forming the first sub-hologram component 810 also includes superimposing a first local phase ramp function with the first composite light pattern 810'. The first local phase ramp function is selected so that the light steering encoded using the first sub-hologram component causes the main lobe 1108 of the first point spread function to shift in, for example, the positive x-direction. This shift of the main lobe 1108 is designed to reverse the displacement in the negative x-direction that occurs at the interface between the replicas. Similarly, forming the second sub-hologram component 811 also includes superimposing a second local phase ramp function with the second composite light pattern 811'. The second local phase ramp function is selected so that the light steering encoded using the second sub-hologram component causes the main lobe 1109 of the second point spread function to shift in the negative x-direction. This shift of the main lobe 1109 is designed to reverse the displacement in the positive x-direction that occurs at the replica boundary. The combination of the first and second local phase ramp functions aligns the main lobes 1108, 1109. The result is Figure 11B The first and second point spread functions are turned into something similar to Figure 10B The single point spread function of φ is such that the actual image points generated by the shifted main lobes 1108, 1109 are not stretched and are better represented as virtual image points of their computational sub-holograms (ie, are spherical).

[0182] Figure 13 The effect of applying step 1208 of the method is shown. Image point 1302 is the actual image point without applying step 1208 of the method and is therefore stretched. Image 1304 is the actual image point with step 1208 of the method applied and is therefore not stretched and accurately represents the (circular) virtual image point that the hologram calculation is intended to represent.

[0183] In some embodiments, the first and second local phase ramp functions are selected based on parameters of the corresponding regional components on the corresponding replicas. In some embodiments, the parameters include at least one of: the distance of the center of at least a portion of the corresponding regional component from the edge of the corresponding replica; the size of the corresponding regional component; the size of the corresponding sub-hologram component; the ratio of the size of the regional component for which the phase ramp is selected to the other of the first or second regional components, and / or the ratio of the size of the sub-hologram component for which the phase ramp is selected to the other of the first or second sub-hologram components. Those skilled in the art will understand how to determine the parameters (e.g., gradient, shape, and / or size) of the local phase ramp function by a variety of different methods, including simple trial and error. Therefore, the present disclosure is not limited in any way to the parameters of the phase ramp function or the method of determining the parameters. The amount of shift of the point spread function formed by the sub-hologram components depends on the relative sizes of the sub-hologram components / regional components. Therefore, each parameter can be used as a proxy for the desired amount of shift of the point spread function.

[0184] In the example shown in FIG11 , the first and second regional components (and the first and second composite light fields 1106 and 1107) are of equal size. Therefore, each of the above parameters is equal for the first and second regional components. In this way, equal but opposite shifts in the main lobes 1108, 1009 cause the lobes to be co-located. In this example, the first and second local phase ramp functions can be described as symmetrical. In other examples, the first regional component can differ in size and in the distance from the edge of the corresponding region to the second regional component. Thus, the phase ramp function selected for the first regional component will differ in amplitude from the phase ramp function selected for the second regional component. In other words, the phase ramp functions applied to the first and second regional components can be described as asymmetric.

[0185] In some examples, selecting a phase ramp function for at least one of the first and second regional components includes searching a lookup table or database for parameters of the corresponding sub-hologram component. The lookup table or database includes data pairs or key-value pairs that relate parameter values to appropriate phase ramp functions. The lookup table or database includes gradient values for the phase ramp functions. Selecting a phase ramp function for the first and second regional components includes inputting the parameters into the lookup table or database. The local phase ramp function is then output. This is applied each time a sub-hologram component is calculated.

[0186] Additional Features

[0187] In embodiments, the holographic reconstruction is in color. In some embodiments, a method known as spatially separated color "SSC" is used to provide color holographic reconstruction. In other embodiments, a method known as frame sequential color "FSC" is used.

[0188] While the examples describe illuminating the SLM with visible light, those skilled in the art will appreciate that the light source and SLM can also be used to direct infrared or ultraviolet light, for example, as disclosed herein. For example, to provide information to a user, those skilled in the art will be aware of techniques for converting infrared and ultraviolet light into visible light. For example, the present disclosure extends to the use of phosphors and / or quantum dot technology for this purpose.

[0189] 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.

[0190] The methods and processes described herein may be embodied on a computer-readable medium. The term "computer-readable medium" includes media 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" should also be taken to include any medium or combination of media that can store instructions for execution by a machine, such that when the instructions are executed by one or more processors, the machine performs, in whole or in part, any one or more of the methods described herein.

[0191] 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 storage repositories (e.g., data volumes) in the example form of solid-state memory chips, optical disks, magnetic disks, or any suitable combination thereof. In some example embodiments, instructions for execution may be conveyed by a carrier medium. Examples of such carrier media include transient media (e.g., a propagated signal conveying the instructions).

[0192] 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. This disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.

Claims

1. A method of computing a sub-hologram of a virtual image point of an optical system, the optical system comprising a display device arranged to display the sub-hologram and a waveguide arranged to replicate the sub-hologram, wherein the method comprises: determining an area bounded by a straight line path from the virtual image point to a periphery of an entrance pupil of the observer, wherein the area includes a first area component on the first virtual copy of the display device and a second area component on the second virtual copy of the display device; determining a first sub-hologram component of a virtual image point within the first area component and a second sub-hologram component of a virtual image point within the second area component; superimposing the first sub-hologram component and the second sub-hologram component to form a sub-hologram of the virtual image point, wherein the method further comprises: A local phase ramp function is applied to at least one of the first and second area components, wherein a displacement associated with the local phase ramp function aligns point spread functions formed by the corresponding sub-hologram components when illuminated.

2. The method of claim 1, comprising applying a first local phase ramp function to the first regional component and applying a second local phase ramp function to the second regional component.

3. The method according to claim 2, wherein: The first local phase ramp function and the second local phase ramp function are different.

4. The method according to claim 2 or 3, wherein: A first direction corresponding to the first local phase ramp function is opposite to a second direction corresponding to the second local phase ramp function.

5. The method according to any one of claims 1 to 3, wherein The step of applying a local phase ramp function comprises selecting a phase ramp function based on parameters of the respective area component and / or the associated sub-hologram component.

6. The method according to claim 5, wherein: The parameter is at least one selected from: the distance of the center of at least a portion of the corresponding regional component from the edge of the corresponding replica; the size of the corresponding regional component; the size of the corresponding sub-hologram component; the ratio of the size of the regional component for which the phase slope is selected to the other of the first or second regional components; and / or the ratio of the size of the sub-hologram component for which the phase slope is selected to the other of the first or second sub-hologram components.

7. The method according to claim 5, wherein: The step of applying a local phase ramp function comprises looking up parameters of the corresponding sub-hologram components in a lookup table or database comprising data pairs or key-value pairs relating parameter values to different phase ramp functions.

8. The method of any one of claims 1 to 3, further comprising: identifying a virtual surface between the virtual image and the waveguide, wherein the virtual surface includes the display device and a plurality of virtual replicas of the display device formed by the waveguide; as well as Identify areas on a virtual surface.

9. The method of claim 8, wherein: The virtual surface includes a first virtual copy adjacent to a second virtual copy.

10. The method of claim 9, wherein: The first sub-hologram component of the first virtual copy is adjacent to the second sub-hologram component of the second virtual copy.

11. The method according to any one of claims 1 to 3, wherein Each sub-hologram is a point cloud hologram determined by propagating light waves from the corresponding virtual image point toward the observer and determining the composite light field of the corresponding position of the arrival area.

12. The method according to any one of claims 1 to 3, wherein Each virtual replica of the display device formed by the waveguide is at a different vertical distance from the display device, thereby forming a staggered virtual surface of virtual replicas of the display device.

13. The method according to any one of claims 1 to 3, wherein Each virtual replica of the display device corresponds to a respective replica of the hologram formed by the waveguide.

14. The method of claim 7, further comprising determining the position of each virtual replica of the display device by developing an optical path within the waveguide from the display device to a corresponding replica of the hologram formed by the waveguide.

15. The method of claim 11, wherein the light wave is a spherical light wave.

16. A method of computing a hologram of a virtual image of an optical system, the optical system comprising a display device arranged to display a sub-hologram and a waveguide arranged to replicate the sub-hologram, the method comprising computing a corresponding sub-hologram for each of a plurality of virtual image points of the virtual image, wherein each sub-hologram is computed according to the method of any one of the preceding claims.

17. The method of claim 16, further comprising superimposing respective sub-holograms to form a hologram of the virtual image.

18. A method of computing a sub-hologram of a virtual image point of an optical system, the optical system comprising a display device arranged to display the sub-hologram and a waveguide arranged to replicate the sub-hologram, wherein the method comprises: Propagation of light waves from the corresponding virtual image points toward the observer; defining an intersection region of propagating light waves at a virtual surface between the virtual image and an observer, wherein the virtual surface comprises a display device and includes at least a first virtual replica of the display device and a second virtual replica of the display device, each virtual replica being formed by a waveguide, wherein the defined region is bounded by a straight line path from a respective virtual image point to a periphery of an entrance pupil of an eye of the observer; identifying at least a first regional component of a light wave defining a region on a first virtual replica of the display device and a second regional component of a light wave defining a region on a second virtual replica of the display device; wherein each regional component of the light wave forms a respective component of a sub-hologram; and applying a local phase ramp function to at least one of the first regional component and the second regional component, Therein, a displacement associated with the local phase ramp function aligns point spread functions formed by corresponding sub-hologram components when illuminated.

Images