Patent Publication Number: US-2020301143-A1

Title: Holographic Projector

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority of United Kingdom Patent Application no. 1903934.6, filed Mar. 22, 2019, which is hereby incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates to a projector. More specifically, the present disclosure relates to a holographic projector or a holographic projection system. Some aspects relate to a head-up display and a head-mounted display. Some aspects relate to a method of improving the quality of the holographic image formed by a holographic projector. 
     BACKGROUND AND INTRODUCTION 
     Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well-known interference techniques to form a holographic recording, or “hologram”, comprising interference fringes. The hologram may be reconstructed by illumination with suitable light to form a two-dimensional or three-dimensional holographic reconstruction, or replay image, representative of the original object. 
     Computer-generated holography may numerically simulate the interference process. A computer-generated hologram, “CGH”, may be calculated by a technique based on a mathematical transformation such as a Fresnel transform or Fourier transform. These types of holograms may be referred to as Fresnel or Fourier holograms. A Fourier hologram may be considered as a Fourier domain representation of the object or a frequency domain representation of the object. A CGH may also be calculated by coherent ray tracing or a point cloud technique, for example. 
     A CGH may be displayed, represented, or otherwise encoded on a spatial light modulator, “SLM”, arranged to modulate the amplitude and/or phase of incident light. Light modulation may be achieved using electrically-addressable liquid crystals, optically-addressable liquid crystals or micro-mirrors, for example. 
     The SLM may comprise a plurality of individually-addressable pixels which may also be referred to as cells or elements. The light modulation scheme may be binary, multilevel or continuous. Alternatively, the device may be continuous (i.e. not comprised of pixels) and light modulation may therefore be continuous across the device. The SLM may be reflective, meaning that modulated light is output from the SLM in reflection. The SLM may equally be transmissive, meaning that modulated light is output from the SLM is transmission. 
     A holographic projector for imaging may be provided using the described technology. Such projectors have found application in head-up displays, “HUD”, and head-mounted displays, “HMD”, including near-eye devices, for example. 
     The projector forms an image on a replay plane. More specifically, an image is holographically-reconstructed on a replay plane which is downstream of the display device. The holographically formed image is made up of a plurality of light spots. The light spots have some irregularity and unevenness which can affect the overall quality of the image perceived by the viewer. 
     Speckle is the consequence of using highly coherent light sources to form an image. In particular, speckle is the result of interference of many waves having the same frequency but different phases (and in some cases different amplitudes). The different phases cause the waves to interfere to give a resultant wave whose amplitude, and therefore intensity, varies randomly. It is desirable to reduce such speckle, since speckle degrades the quality of the image. 
     The present disclosure describes an approach with increases the sharpness of the light spots which are holographically formed on the replay plane and reduces laser speckle. 
     SUMMARY 
     Aspects of the present disclosure are defined in the appended independent claims. 
     There is provided a holographic projector comprising: a spatial light modulator arranged to display a hologram; a light source arranged to illuminate at least one region of the spatial light modulator with first light such that the first light is spatially modulated by the spatial light modulator in accordance with the hologram to form second light, wherein the second light forms a holographic reconstruction on a light receiving surface spatially separated from the spatial light modulator; and a controller-driven assembly arranged to move at least one of the first light and the spatial light modulator relative to the other, optionally, whilst the holographic reconstruction remains formed on the light-receiving surface. 
     There is provided a method of improving a holographic image, comprising: displaying a hologram on a spatial light modulator; illuminating at least one region of the spatial light modulator with first light; spatially modulating the first light in accordance with the hologram to form second light, wherein the second light forms a holographic reconstruction on a light receiving surface spatially separated from the spatial light modulator; and moving at least one of the first light and the spatial light modulator relative to the other, optionally, whilst the holographic reconstruction remains formed on the light-receiving surface. 
     There is provided a holographic projector comprising: a spatial light modulator arranged to display a hologram; a light source arranged to illuminate at least one region of the spatial light modulator with an input beam such that the input beam is spatially modulated by the spatial light modulator in accordance with the hologram to form a holographic reconstruction; and an assembly arranged to move at least one of the input beam and the spatial light modulator relative to the other. 
     In accordance with the holographic projector and method, the holographic reconstruction is formed on a replay plane and is projected to form the holographic image. Moving the input beam relative to the SLM (or vice versa) has the effect of averaging the phase and brightness of the illuminating beam. This improves the light spots that are holographically-formed on the replay plane. More specifically, the shape of each light spot becomes more regular and the brightness profile of each light spot becomes more uniform. It may be said that the light spots are less blurred. This means that they are smaller. Smaller light spots represent an increase in the resolution of the display system. In summary, in accordance with embodiments, the light spots which make up the holographic image are smaller and sharper. This makes for a better display device. 
     The holographic projector also improves the image quality of a holographic reconstruction by reducing speckle. Moving at least one of the input beam and the spatial light modulator relative to the other can exploit any inherent non-uniformities in the light source and/or SLM to introduce a randomness in the resulting holographic reconstruction. This randomness manifests itself in different speckle patterns. Therefore, moving the input beam or SLM multiple times can average out the speckle patterns and improve the quality of the holographic reconstruction. In particular, moving the input beam to be incident at a plurality of different positions on the spatial light modulator whilst forming the holographic reconstruction can improve the appearance of the holographic image, since the human eye averages out the speckle patterns. It has been suggested that presenting in the order of 20 statistically independent speckle patterns within the integration time of the human eye (15-300 milliseconds, or ms, more typically 30-100 ms) enables a good smoothing out of any speckle pattern by the human eye. 
     In some embodiments, the assembly comprises an optical element arranged to receive the input beam on a first optical path and output the input beam on a second optical path. Optionally, the second optical path is substantially parallel to but spatially off-set from the first optical path. Alternatively, the second optical path can be angled relative to the first optical path. The first optical path is that followed by the input beam prior to movement or displacement thereof by the assembly. Optical elements such as lenses or mirrors can be used to translate or displace the optical path of the input beam. In other embodiments, the optical element is a parallel-face plate (otherwise known as a parallel-face window or parallel-face optical window). A parallel-face plate is a transparent optical plate formed with parallel faces to ensure minimal angular deviation. Preferably, the parallel-face plate is inclined with respect to an axis parallel to the first optical axis of the input beam—this inclination acts to produce a translation or other deviation in the beam position. 
     In some embodiments, the assembly may be arranged to rotate the optical element (the parallel-face plate or other optical element such as a lens or a mirror) in order to rotate the second optical path around an axis parallel to the first optical axis. Optionally, the axis parallel to the first optical axis is collinear with the first optical axis. Since the input beam has a spatial light profile, translating or rotating the light beam in this way acts to translate or rotate the profile of the light beam illuminating the SLM such that a different spatial profile illuminates a region of the SLM with each movement. 
     The assembly may be arranged to move the input beam and/or the spatial light modulator in a direction perpendicular to the first optical path of the input beam of light. For example, the light beam can be moved in a circular motion relative to the first optical path or in a linear direction along an axis which intersects the first optical path. The assembly may be arranged to move at least one of the input beam and the spatial light modulator along an axis perpendicular to the first optical path of the input beam. The linear direction in which the input beam and/or the spatial light modulator are moved can be horizontal and/or vertical relative to the first optical path. This relative movement displaces the input beam from the first optical path to a second optical path which is spatially displaced relative to the first optical path, but optionally which remains parallel to the first optical path. In other embodiments, the assembly is arranged to tilt the input beam and/or the spatial light modulator relative to a normal of the first optical path of the input beam. 
     In other embodiments, the assembly may be arranged to move the input beam relative to the spatial light modulator by electrical signals rather than mechanically (e.g. by rotation). For example, the assembly may comprise an acousto-optic deflector (AOD) arranged to receive the input beam on a first optical path and output the input beam on a second optical path. This is achieved by diffraction of the input beam as it travels through a light propagation medium carrying an acoustic wave (typically travelling across the path of the input beam. The direction of the second output path can be changed by changing an electrically controlled acoustic drive signal applied to the light propagation medium to generate the acoustic wave. The change in direction of the second output path moves the input beam relative to the SLM (e.g. to a different position on the SLM). For example, the input beam may be moved in response to a change in the frequency of an oscillating radio-frequency (RF) drive signal applied to a piezo-electric transducer attached to the light propagation medium. The changes in RF drive signal leads to change in the diffraction angle of the light beam. Thus, changes in the applied frequency of the RF drive signal may change the output angle of the light beam exiting the AOD so as to displace the input beam relative to the spatial light modulator. 
     In other embodiments, the input beam can be moved by any other suitable means. Moreover, the assembly can move the input beam continuously, or in a discrete manner. Alternatively, the assembly can comprise an optical element which is moved continuously, or in a discrete manner, to move the input beam. Such movement up and down, or such tilting or rotating can be achieved by movement of an optical element of the assembly, or by movement of the light source emitting the input beam. The SLM can additionally, or alternatively, be moved relative to the input beam. Varying the portion of the input beam which illuminates the SLM improves quality of a holographically-projected image. 
     Optionally, the hologram displayed by the SLM comprises two or more tiles, each representative of at least a part of an input hologram. The term “tile” is used herein to refer to a continuous set of pixels of a hologram (whole tile) or subset of pixels of a hologram (part tile). The input hologram is a hologram representative of the image to be reconstructed by the spatially modulated input beam (i.e. the holographic image to be projected by the holographic projector). The hologram displayed on the SLM is thus formed of different combinations of complete sets (whole tile) or subsets (part tiles) of pixels of the input hologram. 
     Optionally, at least one tile is a whole tile representative of a whole of the input hologram. Optionally, the whole tile displayed on the SLM remains illuminated by the input beam. This arrangement confers the below described benefits of tiling, which improves image quality, whilst further improving image quality through the relative movement of the input beam and the spatial light modulator. Optionally, the holographic projector is part of a system comprising a processor arranged to receive or generate the input hologram and form the hologram to be displayed by the SLM from the input hologram by tiling. The processor can be further arranged to transmit the hologram to the spatial light modulator for display. 
     In some embodiments, when the hologram displayed on the SLM is tiled, i.e. is comprised of whole and/or part tiles (representative of a whole or a part of an input hologram to be reconstructed on the light-receiving surface by the spatially modulated light), only part of the SLM may be illuminated by the input beam. In other words, a size of the at least one region of the SLM illuminated is smaller than the overall size of the display area of the SLM, i.e. a cross-sectional area of the input beam is smaller than the display area of the SLM and the SLM is “underfilled”. Preferably, but not necessarily, the region or part of the SLM to be illuminated is the region comprising a whole tile. Thus, in some embodiments, the input beam is moved to a plurality of different positions in which a whole tile displayed on the SLM is illuminated thereby. 
     In other embodiments, the light source is arranged to illuminate all of the SLM and an area surrounding the SLM. In other words, the light source is arranged such that not only is all of the SLM illuminated, but the areas surrounding the SLM are also illuminated. In this way, the SLM is “overfilled” by the light incident upon it. This overfill ensures that all of the SLM pixels are illuminated at all times. The input beam can be moved in any desired manner to a plurality of different positions in which the SLM remains overfilled, such that the portion of the input beam incident on the SLM varies and any non-uniformities or variations in the input beam are exploited without a risk that a region of the SLM will not be illuminated with the input beam. As such, this overfill can remove constraints on the movement of the input beam or the SLM, since there is a greater degree of freedom in the relative movement of the input beam and the SLM. Where the SLM is fully illuminated, as well as some of the surrounding space, the hologram displayed on the SLM can be a tiled hologram, or can be an un-tiled hologram representative of the image to be reconstructed. 
     Optionally, the holographic reconstruction remains formed during the relative movement of the input beam and the spatial light modulator. In other words, the relative movement is such that the input beam is incident at a plurality of different positions on the SLM and either the whole of the SLM or at least one whole tile is illuminated at all times. When the SLM is overfilled, the holographic reconstruction does not move during the relative movement of the input beam and the spatial light modulator (providing angle of incidence is preserved). Optionally, the holographic reconstruction may be formed at a replay field in a replay plane. In this embodiment, there is no physical light-receiving surface (for example there is no screen or diffuser), but only a plane in space comprising an area at which the holographic reconstruction is formed. This arrangement can provide flexibility as to the projection of the holographic reconstruction. The replay plane can be spatially remote from the spatial light modulator or the projector. Optionally, the holographic reconstruction may be formed at a light receiving surface. Optionally, the light receiving surface is at the replay plane such that the holographic reconstruction is in focus on the light receiving surface. Optionally, the light receiving surface is spatially separated from the spatial light modulator or projector. Optionally, the holographic reconstruction remains formed on the light receiving surface whilst at least one of the input beam and the spatial light modulator are moved relative to the other. 
     Optionally, the light-receiving surface is a diffuser or a screen. When the holographic projector is implemented in a head-up display (HUD) for a vehicle, the light-receiving surface may be the windshield or windscreen, or it may be a separate diffuser on which the holographic reconstruction is formed, for example before projection onto the windscreen. 
     Optionally, the light source emits spatially coherent light and/or emits monochromatic light. Optionally, the light source is a laser. 
     Optionally, the spatial light modulator is a liquid crystal on silicon spatial light modulator. Optionally, the spatial light modulator is an optically addressed SLM. In embodiments, the spatial light modulator comprises a plurality of independently addressable pixels. Preferably, the SLM is arranged to spatially-modulate the phase and/or the amplitude of the light of the input beam. Optionally, the holographic reconstruction is formed by interference of the spatially modulated light; optionally, the holographic reconstruction is formed by interference of the spatially modulated light at the light receiving surface. 
     In some embodiments, the hologram displayed or represented on the SLM is a computer generated hologram. In other words, the hologram has been computed, rather than merely displayed or represented on the SLM. Optionally, when the hologram is a computer generated hologram, the computer generated hologram is a mathematical transformation of the holographic reconstruction. Optionally, the computer generated hologram is a Fourier transformation or a Fresnel transformation of the holographic reconstruction. Optionally, the computer generated hologram is a Fourier hologram or a Fresnel hologram. Optionally, the computer generated hologram is generated by a point cloud method. 
     In some embodiments, the holographic projector further comprises a controller arranged to drive the assembly. Alternatively, the holographic projector is part of a system comprising a controller arranged to drive the assembly. The controller can be arranged to drive the assembly to move at least one of the input beam and the spatial light modulator relative to the other. For example, the controller can be arranged to drive the assembly to drive motion of an optical element and thus move the position of the input beam relative to the SLM. Alternatively, the controller can be arranged to drive the assembly without moving an optical element thereof. For example, the controller can provide a drive signal to a piezo-electric transducer of an acousto-optic deflector or the like arranged to deflect the input beam, travelling through an optical element thereof, in different directions according to characteristics of the drive signal. Thus, by changing the drive signal, the position of the input beam can be moved relative to the SLM. Optionally, the controller can be arranged to drive the assembly to actuate the light source and/or spatial light modulator in a suitable manner to move at least one of the input beam and the spatial light modulator relative to the other. 
     It has been recognised that it is advantageous to introduce additional components early on in the holographic projector, or optical system, since the beam size is still small and thus the necessary mechanisms can be compact. For example, it can be better to move the SLM or input beam (by adjusting the optical path, moving the light source or SLM, or otherwise) relative to each other than to move downstream components, since this would be more difficult. 
     There is provided a method of improving a holographic reconstruction, comprising: displaying a hologram on a spatial light modulator; illuminating at least one region of the spatial light modulator with an input beam; spatially modulating the input beam in accordance with the hologram to form a holographic reconstruction; and moving at least one of the input beam and the spatial light modulator relative to the other. 
     Optionally, the holographic reconstruction remains formed whilst at least one of the input beam and the spatial light modulator are moving relative to the other. It may be said that the input beam may be moved to a plurality of different positions relative to the SLM whilst the holographic reconstruction remains formed, typically for a time period within the integration time of the human eye. In some embodiments, the holographic reconstruction is formed on a light receiving surface spatially separated from the spatial light modulator and, optionally, remains formed on the light receiving surface during the relative movement of the input beam and SLM. 
     The method may comprise inserting an optical element into a first optical path of the input beam to output the input beam on a second optical path. The second optical path may be substantially parallel to, but spatially off-set from, the first optical path and, optionally, the method further comprises rotating the optical element in order to rotate the second optical path around an axis parallel to the first optical axis. 
     Optionally, the movement of the at least one of the input beam and the spatial light modulator relative to the other is facilitated by an assembly. The assembly may be controller driven. The movement may be translation, rotation, or tilting and may be achieved by mechanical or non-mechanical means. Optionally, the assembly comprises the optical element. The optical element may be the above described parallel-face plate (otherwise known in the art as a parallel-face window), or another optical element such as a mirror or a lens. The assembly is in some embodiments arranged to rotate the optical element in order to rotate the second optical path around an axis parallel to the first optical axis. The axis parallel to the first optical axis is optionally collinear with the first optical axis. In other embodiments, the assembly is arranged to translate or otherwise displace the optical element in order to shift the input beam from a first optical path to a second optical path. The second optical path is not necessarily parallel to the first optical path. In other embodiments, the assembly is arranged to deflect the input beam travelling through an optical element using electrical signals, rather than mechanically, for example by means of an acousto-optic deflector (AOD) as described below. In embodiments, changing the deflection of the input beam travelling through the optical element changes the angle of the second optical path in order to move (displace or translate) the input beam across the plane of the SLM. 
     The method may further comprise tiling an input hologram to be reconstructed to form the hologram displayed on the spatial light modulator (SLM). Tiling comprising forming the hologram displayed by the SLM of two or more tiles, each tile representative of at least a part of the input hologram to be reconstructed. Optionally, at least one tile is a whole tile representative of a whole of the input hologram to be reconstructed. The tiling can be performed by a processor, for example, and the hologram to be displayed can be provided to the SLM for display. 
     Optionally, when the hologram is tiled using at least one whole tile (and one or more other whole tiles and/or part tiles), the method further comprises illuminating the at least one region of the SLM such that the at least one whole tile remains illuminated by the input beam during the relative movement of the input beam and/or spatial light modulator. Optionally, a size of the at least one region of the SLM is smaller than a size of the SLM. Alternatively, illuminating the at least one region of the SLM comprising illuminating all regions of the SLM and an area surrounding the SLM. 
     The method may further comprise a method of implementing any of the above described features of the holographic projector, as well as the alternative embodiments described herein. Any of the above described optional embodiments can be combined in any suitable combination. 
     The term “hologram” is used to refer to the recording which contains amplitude and/or phase information about the object. The term “holographic reconstruction” is used to refer to the optical reconstruction of the object which is formed by illuminating the hologram. The term “replay plane” is used herein to refer to the plane in space where the holographic reconstruction is fully formed. The term “replay field” is used herein to refer to the sub-area of the replay plane which can receive spatially-modulated light from the spatial light modulator. The terms “image” and “image region” refer to areas of the replay field illuminated by light forming the holographic reconstruction. Again, the “image” comprises discrete spots which may be referred to as “image spots” or “image pixels”. 
     The terms “encoding”, “writing” or “addressing” are used to describe the process of providing the plurality of pixels of the SLM with a respect plurality of control values which respectively determine the modulation level of each pixel. It may be said that the pixels of the SLM are configured to “display” or “represent” a light modulation distribution in response to receiving the plurality of control values. 
     It has been found that a holographic reconstruction of acceptable quality can be formed from a “hologram” containing only phase information related to the original object. Such a holographic recording may be referred to as a phase-only hologram. Embodiments relate to a phase-only hologram but the present disclosure is equally applicable to amplitude-only holography. 
     The present disclosure is also equally applicable to forming a holographic reconstruction using amplitude and phase information related to the original object. In some embodiments, this is achieved by complex modulation using a so-called fully complex hologram which contains both amplitude and phase information related to the original object. Such a hologram may be referred to as a fully-complex hologram because the value (modulation level) assigned to each pixel of the hologram has an amplitude and phase component. The value (modulation level) assigned to each pixel may be represented as a complex number having both amplitude and phase components. In some embodiments, a fully-complex computer-generated hologram is calculated. 
     Reference may be made to the phase value, phase component, phase information or, simply, phase of pixels of the computer-generated hologram or the spatial light modulator as shorthand for “phase-delay”. That is, any phase value described is, in fact, a number (e.g. in the range 0 to 2Π) which represents the amount of phase retardation provided by that pixel. For example, a pixel of the spatial light modulator described as having a phase value of Π2 will change the phase of received light by Π/2 radians. In some embodiments, each pixel of the spatial light modulator is operable in one of a plurality of possible modulation values (e.g. phase delay values). The term “grey level” may be used to refer to the plurality of available modulation levels. For example, the term “grey level” may be used for convenience to refer to the plurality of available phase levels in a phase-only modulator even though different phase levels do not provide different shades of grey. The term “grey level” may also be used for convenience to refer to the plurality of available complex modulation levels in a complex modulator. 
     Reference is made throughout this disclosure to a parallel-face plate (or parallel-face window) optical element by way of example only. The present disclosure is not limited to such an optical element, and extends to other optical elements such as mirrors or lenses, or any other means of shifting an input beam from a first optical path to a second optical path different to the first optical path in order to realise the above described advantages of moving at least one of the input beam and SLM relative to the other. 
     Although different embodiments and groups of embodiments may be disclosed separately in the detailed description which follows, any feature of any embodiment or group of embodiments may be combined with any other feature or combination of features of any embodiment or group of embodiments. That is, all possible combinations and permutations of features disclosed in the present disclosure are envisaged. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Specific embodiments are described by way of example only with reference to the following figures: 
         FIG. 1  is a schematic showing a reflective SLM producing a holographic reconstruction on a screen; 
         FIG. 2A  illustrates a first iteration of an example Gerchberg-Saxton type algorithm; 
         FIG. 2B  illustrates the second and subsequent iterations of the example Gerchberg-Saxton type algorithm; 
         FIG. 2C  illustrates alternative second and subsequent iterations of the example Gerchberg-Saxton type algorithm; 
         FIG. 3  is a schematic of a reflective LCOS SLM; 
         FIG. 4  shows a schematic of a holographic projector in accordance with embodiments; 
         FIGS. 5A-5E  shows a moving input beam and overfilled SLM in accordance with embodiments; 
         FIGS. 6A-6E  shows a moving input beam and an underfilled SLM in accordance with embodiments; 
         FIG. 7  shows another example of a moving input beam and an underfilled SLM; 
         FIG. 8  shows an assembly in accordance with embodiments; 
         FIGS. 9A-9C  shows an optical element in accordance with embodiments; 
         FIG. 10  shows an alternative assembly in accordance with other embodiments; 
         FIG. 11  shows the arrangement for the acousto-optic deflector of the assembly of  FIG. 10 ; 
         FIG. 12  is a schematic showing an arrangement for implementing the assembly of  FIGS. 10 and 11 ; and 
         FIG. 13  shows a moving input beam in accordance with embodiments. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The present invention is not restricted to the embodiments described in the following but extends to the full scope of the appended claims. That is, the present invention may be embodied in different forms and should not be construed as limited to the described embodiments, which are set out for the purpose of illustration. 
     Terms of a singular form may include plural forms unless specified otherwise. 
     A structure described as being formed at an upper portion/lower portion of another structure or on/under the other structure should be construed as including a case where the structures contact each other and, moreover, a case where a third structure is disposed there between. 
     In describing a time relationship—for example, when the temporal order of events is described as “after”, “subsequent”, “next”, “before” or suchlike—the present disclosure should be taken to include continuous and non-continuous events unless otherwise specified. For example, the description should be taken to include a case which is not continuous unless wording such as “just”, “immediate” or “direct” is used. 
     Although the terms “first”, “second”, etc. may be used herein to describe various elements, these elements are not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the appended claims. 
     Features of different embodiments may be partially or overall coupled to or combined with each other, and may be variously inter-operated with each other. Some embodiments may be carried out independently from each other, or may be carried out together in co-dependent relationship. 
     Optical Configuration 
       FIG. 1  shows an embodiment in which a computer-generated hologram is encoded on a single spatial light modulator. The computer-generated hologram is a Fourier transform of the object for reconstruction. It may therefore be said that the hologram is a Fourier domain or frequency domain or spectral domain representation of the object. In this embodiment, the spatial light modulator is a reflective liquid crystal on silicon, “LCOS”, device. The hologram is encoded on the spatial light modulator and a holographic reconstruction is formed at a replay field, for example, a light receiving surface such as a screen or diffuser. 
     A light source  110 , for example a laser or laser diode, is disposed to illuminate the SLM  140  via a collimating lens  111 . The collimating lens causes a generally planar wavefront of light to be incident on the SLM. In  FIG. 1 , the direction of the wavefront is off-normal (e.g. two or three degrees away from being truly orthogonal to the plane of the transparent layer). However, in other embodiments, the generally planar wavefront is provided at normal incidence and a beam splitter arrangement is used to separate the input and output optical paths. In the embodiment shown in  FIG. 1 , the arrangement is such that light from the light source is reflected off a mirrored rear surface of the SLM and interacts with a light-modulating layer to form an exit wavefront  112 . The exit wavefront  112  is applied to optics including a Fourier transform lens  120 , having its focus at a screen  125 . More specifically, the Fourier transform lens  120  receives a beam of modulated light from the SLM  140  and performs a frequency-space transformation to produce a holographic reconstruction at the screen  125 . 
     Notably, in this type of holography, each pixel of the hologram contributes to the whole reconstruction. There is not a one-to-one correlation between specific points (or image pixels) on the replay field and specific light-modulating elements (or hologram pixels). In other words, modulated light exiting the light-modulating layer is distributed across the replay field. 
     In these embodiments, the position of the holographic reconstruction in space is determined by the dioptric (focusing) power of the Fourier transform lens. In the embodiment shown in  FIG. 1 , the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens and the Fourier transform is performed optically. Any lens can act as a Fourier transform lens but the performance of the lens will limit the accuracy of the Fourier transform it performs. The skilled person understands how to use a lens to perform an optical Fourier transform. 
     Hologram Calculation 
     In some embodiments, the computer-generated hologram is a Fourier transform hologram, or simply a Fourier hologram or Fourier-based hologram, in which an image is reconstructed in the far field by utilising the Fourier transforming properties of a positive lens. The Fourier hologram is calculated by Fourier transforming the desired light field in the replay plane back to the lens plane. Computer-generated Fourier holograms may be calculated using Fourier transforms. 
     A Fourier transform hologram may be calculated using an algorithm such as the Gerchberg-Saxton algorithm. Furthermore, the Gerchberg-Saxton algorithm may be used to calculate a hologram in the Fourier domain (i.e. a Fourier transform hologram) from amplitude-only information in the spatial domain (such as a photograph). The phase information related to the object is effectively “retrieved” from the amplitude-only information in the spatial domain. In some embodiments, a computer-generated hologram is calculated from amplitude-only information using the Gerchberg-Saxton algorithm or a variation thereof. 
     The Gerchberg Saxton algorithm considers the situation when intensity cross-sections of a light beam, I A (x, y) and I B (x, y), in the planes A and B respectively, are known and I A (x, y) and I B (x, y) are related by a single Fourier transform. Wth the given intensity cross-sections, an approximation to the phase distribution in the planes A and B, ψ A (x, y) and ψ B (x, y) respectively, is found. The Gerchberg-Saxton algorithm finds solutions to this problem by following an iterative process. More specifically, the Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeatedly transferring a data set (amplitude and phase), representative of I A (x, y) and I B (x, y), between the spatial domain and the Fourier (spectral or frequency) domain. The corresponding computer-generated hologram in the spectral domain is obtained through at least one iteration of the algorithm. The algorithm is convergent and arranged to produce a hologram representing an input image. The hologram may be an amplitude-only hologram, a phase-only hologram or a fully complex hologram. 
     In some embodiments, a phase-only hologram is calculated using an algorithm based on the Gerchberg-Saxton algorithm such as described in British patent 2,498,170 or 2,501,112 which are hereby incorporated in their entirety by reference. However, embodiments disclosed herein describe calculating a phase-only hologram by way of example only. In these embodiments, the Gerchberg-Saxton algorithm retrieves the phase information ψ[u, v] of the Fourier transform of the data set which gives rise to a known amplitude information T[x, y], wherein the amplitude information T[x, y] is representative of a target image (e.g. a photograph). Since the magnitude and phase are intrinsically combined in the Fourier transform, the transformed magnitude and phase contain useful information about the accuracy of the calculated data set. Thus, the algorithm may be used iteratively with feedback on both the amplitude and the phase information. However, in these embodiments, only the phase information ψ[u, v] is used as the hologram to form a holographic representative of the target image at an image plane. The hologram is a data set (e.g. 2D array) of phase values. 
     In other embodiments, an algorithm based on the Gerchberg-Saxton algorithm is used to calculate a fully-complex hologram. A fully-complex hologram is a hologram having a magnitude component and a phase component. The hologram is a data set (e.g. 2D array) comprising an array of complex data values wherein each complex data value comprises a magnitude component and a phase component. 
     In some embodiments, the algorithm processes complex data and the Fourier transforms are complex Fourier transforms. Complex data may be considered as comprising (i) a real component and an imaginary component or (ii) a magnitude component and a phase component. In some embodiments, the two components of the complex data are processed differently at various stages of the algorithm. 
       FIG. 2A  illustrates the first iteration of an algorithm in accordance with some embodiments for calculating a phase-only hologram. The input to the algorithm is an input image  210  comprising a 2D array of pixels or data values, wherein each pixel or data value is a magnitude, or amplitude, value. That is, each pixel or data value of the input image  210  does not have a phase component. The input image  210  may therefore be considered a magnitude-only or amplitude-only or intensity-only distribution. An example of such an input image  210  is a photograph or one frame of video comprising a temporal sequence of frames. The first iteration of the algorithm starts with a data forming step  202 A comprising assigning a random phase value to each pixel of the input image, using a random phase distribution (or random phase seed)  230 , to form a starting complex data set wherein each data element of the set comprising magnitude and phase. It may be said that the starting complex data set is representative of the input image in the spatial domain. 
     First processing block  250  receives the starting complex data set and performs a complex Fourier transform to form a Fourier transformed complex data set. Second processing block  253  receives the Fourier transformed complex data set and extracts the set of phase values. The second processing block  253  quantises each phase value to form hologram  280 A. Each phase value is quantised in accordance with the phase-levels which may be represented on the pixels of the spatial light modulator which will be used to “display” the hologram. For example, if each pixel of the spatial light modulator provides 256 different phase levels, each phase value of the hologram is quantised into one phase level of the 256 possible phase levels. Hologram  280 A is a phase-only Fourier hologram which is representative of an input image. It may be said that hologram  280 A is representative of the input image in the spectral or Fourier or frequency domain. In some embodiments, the algorithm stops at this point. 
     However, in other embodiments, the algorithm continues as represented by the dotted arrow in  FIG. 2A . In other words, the steps which follow the dotted arrow in  FIG. 2A  are optional (i.e. not essential to all embodiments). If the algorithm continues, second processing block  253  additionally replaces the magnitude values of the Fourier transformed complex data set with new magnitude values. The new magnitude values are a distribution of values representative of the magnitude distribution of the light pattern which will be used to illuminate the spatial light modulator. In some embodiments, each new magnitude value is unity. In other embodiments, second processing block  253  processes the magnitude values of the second complex data set—for example, performs a mathematical operation or series of mathematical operations on each magnitude value—to form the new magnitude values. Second processing block  253  outputs a complex data set comprising the quantised phase values and the new magnitude values. 
     Third processing block  256  receives the complex data set output by the second processing block  253  and performs an inverse Fourier transform to form an inverse Fourier transformed complex data set. It may be said that the inverse Fourier transformed complex data set is representative of the input image in the spatial domain. 
     Fourth processing block  259  receives the inverse Fourier transformed complex data set and assesses the distribution of magnitude values  211 A. Specifically, the fourth processing block  259  compares the distribution of magnitude values  211 A of the inverse Fourier transformed complex data set with the input image  510  which is itself, of course, a distribution of magnitude values. If the difference between the distribution of magnitude values  211 A and the input image  210  is sufficiently small, the fourth processing block  259  determines that the hologram  280 A is acceptable. That is, if the difference between the distribution of magnitude values  211 A and the input image  210  is sufficiently small, the fourth processing block  259  determines that the hologram  280 A is a sufficiently-accurate representative of the input image  210 . In some embodiments, the distribution of phase values  213 A of the inverse Fourier transformed complex data set is ignored for the purpose of the comparison. 
     It will be appreciated that any number of different methods for comparing the distribution of magnitude values  211 A and the input image  210  may be employed and the present disclosure is not limited to any particular method. In some embodiments, a mean square difference is calculated and if the mean square difference is less than a threshold value, the hologram  280 A is deemed acceptable. If the fourth processing block  259  determines that the hologram  280 A is not acceptable, a further iteration of the algorithm is performed. 
       FIG. 2B  represents a second iteration of the algorithm and any further iterations of the algorithm. The distribution of phase values  213 A of the preceding iteration is fed-back through the processing blocks of the algorithm. The distribution of magnitude values  211 A is rejected in favour of the distribution of magnitude values of the input image  210 . In the first iteration, the data forming step  202 A formed the first complex data set by combining distribution of magnitude values of the input image  210  with a random phase distribution  230 . However, in the second and subsequent iterations, the data forming step  202 B comprises forming a complex data set by combining (i) the distribution of phase values  213 A from the previous iteration of the algorithm with (ii) the distribution of magnitude values of the input image  210 . 
     The complex data set formed by the data forming step  202 B of  FIG. 2B  is then processed in the same way described with reference to  FIG. 2A  to form second iteration hologram  280 B. The explanation of the process is not therefore repeated here. The algorithm may stop when the second iteration hologram  280 B has been calculated. However, any number of further iterations of the algorithm may be performed. It will be understood that the third processing block  256  is only required if the fourth processing block  259  is required or a further iteration is required. The output hologram  280 B generally gets better with each iteration. However, in practice, a point is usually reached at which no measurable improvement is observed or the positive benefit of performing a further iteration is out-weighted by the negative effect of additional processing time. Hence, the algorithm is described as iterative and convergent. 
       FIG. 2C  represents an alternative embodiment of the second and subsequent iterations. The distribution of phase values  213 A of the preceding iteration is fed-back through the processing blocks of the algorithm. The distribution of magnitude values  211 A is rejected in favour of an alternative distribution of magnitude values. In this alternative embodiment, the alternative distribution of magnitude values is derived from the distribution of magnitude values  211  of the previous iteration. Specifically, processing block  258  subtracts the distribution of magnitude values of the input image  210  from the distribution of magnitude values  211  of the previous iteration, scales that difference by a gain factor a and subtracts the scaled difference from the input image  210 . This is expressed mathematically by the following equations, wherein the subscript text and numbers indicate the iteration number: 
         R   n+1 [ x,y ]= F′{exp ( iΨ   n [ u,v ])} 
       Ψ n [ u,v ]=∠ F{η·exp ( i∠R   n [ x,y ])}
 
       η= T [ x,y ]−α(| R   n [ x,y ]|− T [ x,y ]|− T [ x,y ])
 
     where: 
     F′ is the inverse Fourier transform;
 
F is the forward Fourier transform;
 
R[x, y] is the complex data set output by the third processing block  256 ;
 
T[x, y] is the input or target image;
 
∠ is the phase component;
 
ψ is the phase-only hologram  280 B;
 
η is the new distribution of magnitude values  211 B; and
 
α is the gain factor.
 
     The gain factor α may be fixed or variable. In some embodiments, the gain factor a is determined based on the size and rate of the incoming target image data. In some embodiments, the gain factor a is dependent on the iteration number. In some embodiments, the gain factor α is solely function of the iteration number. The embodiment of  FIG. 2C  is the same as that of  FIG. 2A  and  FIG. 2B  in all other respects. It may be said that the phase-only hologram ψ(u, v) comprises a phase distribution in the frequency or Fourier domain. 
     In some embodiments, the Fourier transform is performed computationally by including lensing data in the holographic data. That is, the hologram includes data representative of a lens as well as data representing the object. In these embodiments, the physical Fourier transform lens  120  of  FIG. 1  is omitted. It is known in the field of computer-generated hologram how to calculate holographic data representative of a lens. The holographic data representative of a lens may be referred to as a software lens. For example, a phase-only holographic lens may be formed by calculating the phase delay caused by each point of the lens owing to its refractive index and spatially-variant optical path length. For example, the optical path length at the centre of a convex lens is greater than the optical path length at the edges of the lens. An amplitude-only holographic lens may be formed by a Fresnel zone plate. It is also known in the art of computer-generated hologram how to combine holographic data representative of a lens with holographic data representative of the object so that a Fourier transform can be performed without the need for a physical Fourier lens. In some embodiments, lensing data is combined with the holographic data by simple vector addition. In some embodiments, a physical lens is used in conjunction with a software lens to perform the Fourier transform. Alternatively, in other embodiments, the Fourier transform lens is omitted altogether such that the holographic reconstruction takes place in the far-field. In further embodiments, the hologram may include grating data—that is, data arranged to perform the function of a grating such as beam steering. 
     Again, It is known in the field of computer-generated hologram how to calculate such holographic data and combine it with holographic data representative of the object. For example, a phase-only holographic grating may be formed by modelling the phase delay caused by each point on the surface of a blazed grating. An amplitude-only holographic grating may be simply superimposed on an amplitude-only hologram representative of an object to provide angular steering of an amplitude-only hologram. 
     In some embodiments, there is provided a real-time engine arranged to receive image data and calculate holograms in real-time using the algorithm. In some embodiments, the image data is a video comprising a sequence of image frames. In other embodiments, the holograms are pre-calculated, stored in computer memory and recalled as needed for display on a SLM. That is, in some embodiments, there is provided a repository of predetermined holograms. 
     Embodiments relate to Fourier holography and Gerchberg-Saxton type algorithms by way of example only. The present disclosure is equally applicable to Fresnel holography and holograms calculated by other techniques such as those based on point cloud methods. 
     Light Modulation 
     A spatial light modulator may be used to display the computer-generated hologram. If the hologram is a phase-only hologram, a spatial light modulator which modulates phase is required. If the hologram is a fully-complex hologram, a spatial light modulator which modulates phase and amplitude may be used or a first spatial light modulator which modulates phase and a second spatial light modulator which modulates amplitude may be used. 
     In some embodiments, the light-modulating elements (i.e. the pixels) of the spatial light modulator are cells containing liquid crystal. That is, in some embodiments, the spatial light modulator is a liquid crystal device in which the optically-active component is the liquid crystal. Each liquid crystal cell is configured to selectively-provide a plurality of light modulation levels. That is, each liquid crystal cell is configured at any one time to operate at one light modulation level selected from a plurality of possible light modulation levels. Each liquid crystal cell is dynamically-reconfigurable to a different light modulation level from the plurality of light modulation levels. In some embodiments, the spatial light modulator is a reflective liquid crystal on silicon (LCOS) spatial light modulator but the present disclosure is not restricted to this type of spatial light modulator. 
     A LCOS device provides a dense array of light modulating elements, or pixels, within a small aperture (e.g. a few centimeters in width). The pixels are typically approximately 10 microns or less which results in a diffraction angle of a few degrees meaning that the optical system can be compact. It is easier to adequately illuminate the small aperture of a LCOS SLM than it is the larger aperture of other liquid crystal devices. An LCOS device is typically reflective which means that the circuitry which drives the pixels of a LCOS SLM can be buried under the reflective surface. The results in a higher aperture ratio. In other words, the pixels are closely packed meaning there is very little dead space between the pixels. This is advantageous because it reduces the optical noise in the replay field. A LCOS SLM uses a silicon backplane which has the advantage that the pixels are optically flat. This is particularly important for a phase modulating device. 
     A suitable LCOS SLM is described below, by way of example only, with reference to  FIG. 3 . An LCOS device is formed using a single crystal silicon substrate  302 . It has a 2D array of square planar aluminium electrodes  301 , spaced apart by a gap  301   a,  arranged on the upper surface of the substrate. Each of the electrodes  301  can be addressed via circuitry  302   a  buried in the substrate  302 . Each of the electrodes forms a respective planar mirror. An alignment layer  303  is disposed on the array of electrodes, and a liquid crystal layer  304  is disposed on the alignment layer  303 . A second alignment layer  305  is disposed on the liquid crystal layer  304  and a planar transparent layer  306 , e.g. of glass, is disposed on the second alignment layer  305 . A single transparent electrode  307  e.g. of ITO is disposed between the transparent layer  306  and the second alignment layer  305 . 
     Each of the square electrodes  301  defines, together with the overlying region of the transparent electrode  307  and the intervening liquid crystal material, a controllable phase-modulating element  308 , often referred to as a pixel. The effective pixel area, or fill factor, is the percentage of the total pixel which is optically active, taking into account the space between pixels  301   a.  By control of the voltage applied to each electrode  301  with respect to the transparent electrode  307 , the properties of the liquid crystal material of the respective phase modulating element may be varied, thereby to provide a variable delay to light incident thereon. The effect is to provide phase-only modulation to the wavefront, i.e. no amplitude effect occurs. 
     The described LCOS SLM outputs spatially modulated light in reflection. Reflective LCOS SLMs have the advantage that the signal lines, gate lines and transistors are below the mirrored surface, which results in high fill factors (typically greater than 90%) and high resolutions. Another advantage of using a reflective LCOS spatial light modulator is that the liquid crystal layer can be half the thickness than would be necessary if a transmissive device were used. This greatly improves the switching speed of the liquid crystal (a key advantage for the projection of moving video images). However, the teachings of the present disclosure may equally be implemented using a transmissive LCOS SLM. 
     Holographic Projector 
     One embodiment of the present holographic projector is described with reference to  FIG. 4 . A spatial light modulator, or SLM,  410  is arranged to be illuminated with an input beam from a light source  420 . An assembly  430  is arranged to move at least one of the input beam and the spatial light modulator relative to the other. A controller  440  is arranged to drive the assembly. In some embodiments, the controller  440  is electrically connected  450  to the assembly  430  to drive the assembly. In some embodiments, the assembly  430  is electrically connected to one or both of the SLM  410  and light source  420  in order to produce the relative movement. Additionally or alternatively, the assembly  430  is arranged to produce the relative movement of the input beam and the SLM without moving the SLM  410  or light source  420 ; in this embodiment, the assembly need not be electrically connected to the SLM  410  or light source  420 . 
     An embodiment of the present holographic projector is described with reference to  FIG. 5 . The spatial light modulator, or SLM,  510  is illuminated with an input beam  500  from the light source. The assembly is arranged to move at least one of the input beam and the spatial light modulator relative to the other. In particular, the assembly is arranged to move at least one of the input beam  500  and the SLM  510  so that the light is incident on the spatial light modulator  510  at a plurality of different positions. In the illustrated arrangement, the light spot formed by the input beam  500  in the plane of the SLM  510  is substantially circular. Thus, the area illuminated by the input beam  500  is substantially circular. As the skilled person will appreciate, the shape and size of the area illuminated corresponds to the shape and size of the cross section through the input beam  500  in the plane of the SLM  510 . Thus, the light spot may be elliptical when the angle of incidence of the input beam is off-normal (i.e. with tilt). Although not illustrated in  FIG. 5 , the intensity (and phase?) profile of the light spot of the input beam  500  is generally non-uniform. Typically, the spatial intensity profile is such that the intensity (brightness) is higher at the centre that the periphery of a light beam. For example, the ideal spatial intensity profile of a laser beam has a gaussian distribution in a plane orthogonal to its axis. The phase profile of the light may also vary across a light beam. 
     As shown in  FIGS. 5A to 5E , in this embodiment the SLM  510  remains stationary and the position of the input beam  500  is moved with respect to the SLM  510  by the assembly by any suitable means. The light source is arranged such that the input beam  500  illuminating the SLM illuminates the entire surface of the SLM, as well as the area surrounding the SLM. This is termed overfill. Such overfill ensures that the SLM is always illuminated, regardless of the exact position of the input beam  500  during the movement by the assembly. This overfill can also be advantageous since the larger cross section of the input beam applied to the SLM  510  can facilitate greater variations in the illuminating light pattern between each successive image. As the portion or cross-section of the input beam which illuminates the SLM is varied as a result of the relative movement, non-uniformities in the light beam are effectively smoothed out resulting in improvements to the holographic reconstruction. 
     Each of  FIGS. 5A to 5E  represents the position of the input beam  500  at a particular point in time. In particular, each of  FIGS. 5A to 5E  shows the position of the light spot formed by the input beam  500  relative to the SLM  510  (in the plane of the SLM  510 ) at a different point in time.  FIG. 5A  shows a first position of the input beam  500  incident on the SLM  510  a first point in time,  FIG. 5B  shows a second position of the input beam  500  incident on the SLM  510  at a second point in time,  FIG. 5C  shows a third position of the input beam  500  incident on the SLM  500  at a third point in time,  FIG. 5D  shows a fourth position of the input beam  500  incident on the SLM  510  at a first fourth in time and  FIG. 5E  shows a fifth position of the input beam  500  incident on the SLM  510  at a fifth point in time. In some embodiments, the input beam  500  is moved continuously between the different positions, i.e. between the first position of the input beam  500  in  FIG. 5A  and the second position of the input beam  500  in  FIG. 5B  and so on. In other embodiments, the input beam  500  is moved periodically between the different positions, i.e. the first position of the input beam  500  shown in  FIG. 5A  is held for a predetermined period of time, and then the assembly acts to switch or move the input beam  500  to the second position shown in  FIG. 5B  and so on. Optionally, between 15 to 25 positions of the input beam relative to the SLM  510  are provided in a time period within the integration time of the human eye. Optionally, 20 positions of the input beam  500  are provided within the integration time of the human eye. The integration time of the human eye is typically 15-300 ms, more typically 30-100 ms. When the SLM displays a hologram representative of a frame of a video, there are preferably 15 to 25 different positions, more preferably 20 positions, of the input beam adopted within the time of a single frame (i.e. within 1/24 second for a 24 frame per second video). In some embodiments, the number of different positions required decreases with the distance between successive positions. 
     In some embodiments, such as those described above with reference to  FIG. 5 , the size (number of pixels in each direction) of the hologram to be reconstructed is equal to the size of the spatial light modulator so that the hologram fills the spatial light modulator. That is, the hologram uses all the pixels of the spatial light modulator. In other embodiments, such as that described below with reference to  FIGS. 6 and 7 , the size of the hologram to be reconstructed, or input hologram, is less than the size of the spatial light modulator. Therefore, to fill the SLM, part of the input hologram (that is, a continuous subset of the pixels of the hologram) is repeated in the unused pixels. This technique may be referred to as tiling, wherein the surface area of the spatial light modulator is divided up into a number of tiles, each of which represents at least a subset of the hologram. Each tile is therefore of a smaller size than the spatial light modulator. Thus, in embodiments in which the SLM comprises a plurality of light modulating elements or pixels, tiling may be used when the number of pixels of the hologram to be reconstructed, or input hologram, is less than the number of pixels of the SLM. As previously noted, each tile comprises a continuous set or subset of pixels of the input hologram. 
     It is usually desirable to have small image pixels. It is also usual in display technology to want the maximum number of image pixels possible. However, degradation of image quality can occur if the density of image pixels in the holographic replay field is too high. There is an optimum number of image pixels or optimum range for the number of image pixels for a given size of holographic replay field. It has been found that tiling an input hologram onto an output hologram can reduce such image degradation and increase image quality by allowing the size and number of image spots to be optimised. Specifically, some embodiments implement the technique of tiling to optimise the size of the image pixels whilst maximising the amount of signal content going into the holographic reconstruction. Moving the input beam around on a tiled pattern improves the uniformity of the holographic light spots in the replay field due to averaging the phase and illumination distribution of the input beam. 
     In an embodiment described with reference to  FIG. 6 , a different arrangement to that described with reference to  FIG. 5  is provided; namely, an arrangement is shown in which the SLM is underfilled rather than overfilled. In  FIGS. 6A to 6E , a light spot of the input beam  600  is applied to the SLM to illuminate the SLM. The size of the area illuminated by the input beam  600  is less than the total size of the SLM  610 . As such, not all of the SLM  610  is illuminated. In these embodiments, an input hologram comprising fewer pixels than the spatial light modulator is used. The hologram displayed on the SLM comprises a series of complete tiles  605  of the input hologram; in other words, each tile  605  is wholly representative of the input hologram. This embodiment also helps mitigate the consequences of any non-uniformities in the SLM device. 
     In particular, an assembly is arranged to move at least one of the input beam  600  and SLM  610  relative to the other.  FIGS. 6A to 6E  represent the position of the input beam  600  at particular points in time. In particular, each of  FIGS. 6A to 6E  shows the position of the light spot formed by the input beam  600  relative to the SLM  610  (in the plane of the SLM  610 ) at a different point in time.  FIG. 6A  shows a first position of the input beam  600  incident on the SLM  600  a first point in time,  FIG. 6B  shows a second position of the input beam  600  incident on the SLM  610  at a second point in time,  FIG. 6C  shows a third position of the input beam  600  incident on the SLM  610  at a third point in time,  FIG. 6D  shows a fourth position of the input beam  500  incident on the SLM  610  at a first fourth in time and  FIG. 6E  shows a fifth position of the input beam  600  incident on the SLM  610  at a fifth point in time. In some embodiments, the input beam  600  is moved continuously between the different positions, i.e. between the first position of the input beam  600  in  FIG. 6A  and the second position of the input beam  600  in  FIG. 6B  and so on. In other embodiments, the input beam  600  is moved periodically between the different positions, i.e. the input beam  600  is held for a predetermined period of time in each position, such as the first position shown in  FIG. 6A , and then moved to the next position of the input beam  600 , such as the second position shown in  FIG. 6B  and so on. In this embodiment, the position of the input beam  600  is moved with respect to the SLM  610  by the assembly by any suitable means. In an alternative embodiment, the SLM  610  is moved with respect to the input beam by any suitable means, or both the input beam and the SLM are moved relative the other. 
       FIG. 6  shows an input beam  600  with a cross sectional area smaller than the area of the SLM  610 . The input beam  600  can have a larger cross sectional area relative to the area of the SLM than that illustrated, or a smaller cross sectional area relative to the area of the SLM than that illustrated.  FIG. 6  is provided for the purposes of illustration only. Similarly, 16 whole or complete tiles  605  are shown on the SLM in  FIG. 6  for the purposes of illustration only; there may be more or less complete tiles  605  represented or displayed on the SLM. It can be understood that in some embodiments the holographic pattern written to the spatial light modulator comprises at least one whole tile (that is, the whole tile  605  representative of the input hologram) and at least one fraction of a tile (that is, a continuous subset of pixels of the input hologram, or a subset of the whole tile  605 ). 
     The light source is arranged such that the input beam  600  illuminating the SLM illuminates only a region of the surface of the SLM  610 , and does not illuminate the area surrounding the SLM  610 . This is termed underfill. In some embodiments, such as the illustrated embodiment, this underfill is combined with tiling, in order that the resulting holographic representation formed from the spatially modulated input beam is representative of the input hologram. The light source is further preferably arranged such that a complete tile  605  displayed on the SLM  610  is always illuminated, regardless of the position of the input beam  600  on the SLM during the movement by the assembly. In the illustrated embodiment, the cross sectional area of the input beam  600  (in the plane of SLM  610 ) is equal to or greater than the area of 4 complete tiles  605  (assuming all tiles  605  are of equal size). This underfill, combined with tiling, advantageously improves the image quality. 
     An arrangement similar to that described above with reference to  FIG. 6  is described with reference to  FIG. 7 . In this embodiment, the SLM is arranged to display a complete, or whole, tile  705   a  and at least one part tile  705   b.  The at least one part tile  705   b  is a continuous subset of the pixels of the hologram represented by the whole tile  705   a.  The hologram displayed on the SLM can be any suitable combination of at least one whole tile  705   a  and at least one part tile  705   b.  Preferably, one whole, or complete, tile  705   a  is always illuminated by the input beam  700 . This ensures that the holographic representation formed by the spatially modulated input beam is representative of the hologram of the whole tile  705   a.  In this embodiment, the displacement or movement of the input beam  700  is necessarily small relative to the size of the SLM in order to maintain illumination of the whole tile  705   a.  For example, the movement may be in the order of a few pixels of the SLM, or it may be 5% to 25% of the width of the whole tile  705   a  (depending on the size of the input beam  700  relative to the size of the whole tile  705   a ). These values are merely examples, and the limits on the movement of the light  700  may be determined by routine experimentation and measurement/observation. 
     The above described embodiments combine tiling with a moving light beam that underfills the SLM. As the skilled person will appreciate, tiling may be used in embodiments providing a moving light beam that overfills the SLM. In such embodiments, since the whole of the SLM is illuminated by the moving light beam at all times, any suitable tiling scheme of the input hologram to be reconstructed can be used to form the output hologram for display on the SLM. 
     In embodiments of the above described projector, the assembly is arranged to move the input beam relative to the SLM by any suitable means. For example, the input beam (a laser beam or other input light) can be moved relative to the spatial light modulator, or vice versa, by a moving mirror, mirror mount, mirror assembly, laser, laser mount, collimating lens, other optic, spatial light modulator, or spatial light modulator fixture. Moving includes rotating, translating or tilting. Such movement may be achieved, for example, with an actuator, a vibrating element, or an oscillating element. The assembly is driven by a controller. In some embodiments, the input beam is not moved by way of mirrors or other optical elements, but rather the light source itself is physically moved. Additionally or alternatively, the SLM is physically moved. For example, the light source or SLM may be rotated, tilted or translated with an actuator or an oscillating element. 
     One example of the assembly is described with reference to  FIGS. 8 and 9 .  FIG. 8  illustrates an example assembly  800  driven by a controller which is arranged to rotate one or more parallel-face plates (typically referred to as parallel-face windows or parallel-face optical windows) around an axis of rotation. The assembly  800  comprises a plurality of slots  850  to hold one or more parallel-face plates, the one or more slots  850  being arranged along a housing  830 . The assembly may comprise only one slot  850  of any suitable thickness to hold the desired thickness of parallel-face plate; multiple slots are shown as an example only. When the housing  830  comprises multiple slots  850 , multiple parallel-face plates may be inserted into the housing  830  to change the effective thickness of the optical element. 
     The input beam  810  from the light source travels along an optical path or axis, shown by the line in  FIG. 8  between the arrows showing the direction of the light beam  810 ,  820  (a dashed-dotted line is shown inside the assembly  800 ). The assembly  800  is positioned central to this optical axis, such that a parallel-face plate inserted into one or more of the slots  850  is placed into the input beam  810 . The input beam  810  is preferably collimated light. As can be seen from  FIG. 8 , each of the one or more slots  850  is inclined with respect to the optical axis. As such, a parallel-faced plate inserted into a slot  850  will be inclined with respect to the collimated light beam of the input beam  810 . 
     The assembly  800  comprises a base and two arms which extend from the base to support housing  830 . The arms each comprise a hole containing a bushing—the housing  830  is supported in the holes of the arms of the assembly  800 . The bushings facilitate rotation of the housing in direction of rotation  840 . Bearings may alternatively be used to facilitate rotation. A controller drives the assembly  800 . The assembly  800  may be driven by a motor (which can be any commercially available DC brushless motor, or any other form of suitable motor) connected to the housing  830  by a belt or other gearing mechanism, where the motor is controlled by the controller. Rotation of the housing  830  rotates the one (or possibly more) inclined parallel-face plate inserted into a slot  850  of the housing  830 . The axis of rotation of the parallel-face plate is parallel to the optical axis. Optionally, the axis of rotation of the parallel-face plate is collinear with the optical axis. Preferably, in this embodiment, the axis of rotation of the parallel-face plate is the optical axis. 
     The parallel-face plate acts as a decentring element. That is, it moves the light off-axis owing to refraction of the light passing through the parallel-face plate. As the parallel-face plate rotates with the housing  830  in direction  840 , the light is rotated about the axis of rotation. When the SLM is underfilled, the position of the input beam incident on the SLM is also rotated. Accordingly, the position of the input beam illuminating the SLM is continually changing and randomness is introduced to the holographic reconstruction, which reduces speckle as described above. When the SLM is overfilled, the portion of the input beam illuminating the SLM is continually changing, and the non-uniformities in the input beam introduce randomness into the holographic reconstruction. In  FIG. 8 , there is no parallel-face plate present and the input beam  810  has the same optical path as the beam  820  output from the assembly  800 . 
     It is essential that the two faces of the parallel-face plate are parallel in order for the input beam  810  and the beam  820  output from the assembly to be parallel (but spatially-offset). This effect is illustrated in  FIGS. 9A to 9C . However, in alternative embodiments a different optical element arrangement can be employed in which the faces of a plate are not parallel, in order to tilt the output beam  820  relative to the input beam  810 . Alternatively, an optical element other than an optical plate can be employed with assembly  800 , or with a different assembly arrangement. 
       FIGS. 9A to 9C  show a cross-section of the displacement  930  of the input beam  910  which is achieved with the controller-drive assembly  800  shown in  FIG. 8  and a parallel-face plate  900 . As can be seen from the three different depictions in  FIGS. 9A to 9C , as the angle of the parallel-face plate  900  changes, the displacement  930  of the output beam  920  relative to the input beam  910  changes. When the plate  900  is not inclined ( FIG. 9B ), there is no change in the position of the output beam  920  relative to the input beam  910 . However, it can be seen that the degree of tilt of the plate  900  (angle α, β of the parallel-face plate  900 ) relative to the input beam  910  changes both the extent and the direction of displacement  930 A,  930 C of the output beam  920 . 
     When α=β,  FIGS. 9A and 9C  illustrate the change in position of the output beam  920  as the assembly is driven to rotate the parallel-face plate 180 degrees around the axis of rotation. In this embodiment, the axis of rotation is the optical axis in  FIG. 8 , but alternatively the axis of rotation could be an axis parallel to the optical axis. It can be seen that the output beam  920  rotates around the optical axis of the input beam  910  as the assembly  830  rotates. 
     There are many, inter-related, variables, including the nature of the image, the viewer&#39;s pupil size, ambient light conditions etc., which determine how effective the device of  FIG. 8  is at de-speckling. In practice, the optimum parameters may be determined by experimentation and measurement/observation. However, it has been found that the following parameters applied to the assembly of  FIG. 8  improve the appearance of speckle:
         Absolute angle (α, β) of parallel-face plate relative to the optical axis=30-60 degree, optionally 40-55 degrees, further optionally 45+/−2 degree;   Thickness of plate=0.5-40 mm, optionally 2-20 mm, further optionally 4-10 mm;   Diameter of plate=5-40 mm, optionally 10-35 mm, further optionally 25+/−5 mm;   Speed of rotation=100-10,000 rpm, optionally 200-5,000 rpm.       

     Whilst the assembly of  FIGS. 8 and 9  is arranged to move the input beam relative to the SLM by mechanical means, in particular by rotating one or more parallel-face plates, it is also possible to move the input beam relative to the SLM by electrical means. One example of an assembly comprising an electrically controlled beam deflector, arranged to move the input beam relative to the SLM, is described below with reference to  FIGS. 10 to 13 . 
       FIG. 10  schematically illustrates an example assembly  1000  comprising an acousto-optic deflector (AOD)  1100  and an RF signal driver  1060 , and  FIG. 11  shows the arrangement of the AOD  1100  in more detail. The AOD  1100  is positioned in the optical path or axis of the input beam  1010  from the light source, and is arranged to receive a radio frequency (RF) drive signal from an RF signal driver  1060 .  FIG. 10  shows the optical path of the light beam by solid lines. The input beam  1010  is incident on an optical element  1050 , which is housed within the AOD  1100 , at an input angle relative to the normal of the front face thereof (corresponding to a first optical path of the light beam). The output beam  1020  is transmitted out of the optical element  1050  at one or a range of output angles relative to the normal of the rear face thereof in a first diffraction order (corresponding to a second optical path of the light beam). As described further below, when the input angle of the input beam  1010  corresponds to the Bragg angle, the output beam  1020  may be mainly diffracted in the first diffraction order at an output angle dependent on the frequency of the RF drive signal applied to the AOD  1100 .  FIG. 10  also show the optical path of the (unused) zeroth diffraction order transmitted out of the AOD  1100 , which has the same direction as the first optical path of the input beam  1010 . The output beam  1020  in the first diffraction order is deflected in a different direction, and thus at a different angle, to the input beam  1010 . Accordingly, by adopting the illustrated Bragg angle configuration and changing the frequency of the RF drive signal, it is possible to change the output angle of the output beam  1020  and thus the direction of the second optical path of the output beam  1120 . The output beam  1020  forms the input beam that is incident on the SLM. Thus, in accordance with the present disclosure, the assembly  1000  can be used to move the output beam  1020  relative to the SLM so that it is incident at a plurality of different positions on the SLM, by changing the frequency of the RF drive signal to AOD  1100  from RF signal driver  1060 .  FIG. 10  shows how AOD  1100  can move the light beam through a range of angles (as shown by double-headed arrow) to move or scan the output beam  1020  across the SLM in one dimension. As the skilled person will appreciate, an AOD  1100  that additionally provides beam displacement through a range of angles in a second dimension is possible in order to provide two-dimensional scanning of the output beam  1020  across the SLM, as described above with reference to  FIGS. 5, 6 and 7 . The AOD  1100  is shown in more detail in  FIG. 11 . 
     Referring to  FIG. 11 , the AOD  1100  includes an optical element  1150  comprising a transparent optical medium that forms a light propagation medium for the light beam  1010 ,  1020 . In particular the optical element  1150  may comprise an optically transparent material crystalline material such quartz or crystal (e.g. tellurium dioxide) or a non-crystalline materials such as glass, Optical element  1150  comprises a first side  1152 , a second side  1154  opposite the first side  1152 , a third side  1156  orthogonal to the first side  1152  and a fourth side  1158  opposite the third side  1156 . The input beam  1010  is incident on the first side  1152  and the output beam  1020  is transmitted from the second side  1154 . For ease of illustration, the beam deflection at the interface between the optical element  1150  and the ambient at the first and second sides  1152 ,  1154 , respectively, is not show in  FIG. 11 . AOD  1100  further includes a piezo-electric transducer  1170  (mechanically) attached to the third side  1156  of the optic  1150 . Piezo-electric transducer  1170  is driven by an RF signal (from RF signal driver  1060  shown in  FIG. 10 ) having a variable oscillating frequency f. When an RF signal is applied, the transducer  1170  generates acoustic (vibrational) waves  1175  according to the frequency f, as shown by dashed lines in  FIG. 11 . The acoustic waves  1175  propagate through the light propagating medium of the optical element  1050  from the third side  1156  to the fourth side  1158 , and thus across the optical path of the light beam  1010 ,  1020 . 
     As known in the art, AODs operate by virtue of a change in the refractive index of the optical material due to the photo-elastic effect of the acoustic waves generated by the piezoelectric transducer. It may be said that the light beam “interacts with” or is “diffracted off” the acoustic wavefront generated by the piezo-electric transducer according to the frequency f of the RF drive signal. Typically, the angle of incidence of the light beam  6  and the RF frequency f are chosen so that the acoustic wavelength of the acoustic waves introduces a preferential weighting for certain diffraction orders and suppresses others. In particular, the Bragg regime may be used as shown in  FIG. 11 , in which the input beam is incident at the Bragg angle θ B  and the RF frequency f is in the range of hundreds of MHz to GHz. Wth the Bragg regime, the dominant diffraction orders are the zero and a single first diffraction order. Depending on the RF power, as much as 90% of the incident beam can be directed to the single first order, to provide a distinct diffracted output beam corresponding to an incident input beam. In embodiments, the characteristics of the RF drive signal are chosen so that at least 50%, optionally at least 75%, of the incident light is diffracted to the output beam. Accordingly, modulating the RF drive frequency changes the output angle of the diffracted beam, and thus changes the deflection of the output beam. In this way, the output beam can be moved through a range of angles in a single dimension under the control of an RF drive signal, as shown in  FIG. 10 . 
     Referring to  FIG. 12 , in some embodiments, the input beam  1010  is a collimated beam of coherent light. In particular, input beam  1010  from a coherent light source (e.g. laser) is focussed by a first collimating lens  1080  to be incident on the optical element  1050  of the AOD  1100  at a first angle (e.g. Bragg angle). It may be said that collimated light of the input beam  1010  is focused to an appropriate point diameter for the AOD  1110  comprising optical element  1050 . The output beam  1020 , which corresponds to the light diffracted by optical element  1050  to the first diffraction order, is transmitted from an AOD  1100  at a second angle, which is different from the first angle. The first and second angles are measured relative to the normal of the respective surface of the optical element  1050 . The output beam  1020  has an angular deviation and so is collimated by a second collimating lens  1082  to provide a collimated beam of coherent light to illuminate the SLM.  FIG. 13  shows an example of moving the output beam  1020  from the AOD  1100  to a plurality of different positions on the SLM. In particular, the output beam  1020  is moved or scanned along a line (i.e. in one dimension) by changing the angle of the diffraction beam (e.g. in the first diffraction order), by varying the frequency of the RF drive signal to the AOD  1100 , as described herein. As described herein, light incident on the SLM at each beam position will result in the generation of an independent speckle pattern in the replay field. Thus, by scanning the output beam  1020  through a range of angles as shown in  FIG. 13 , the different speckle patterns formed in the replay field can be averaged out by the human eye. Whilst,  FIG. 13  shows a plurality of overlapping positions of the area illuminated by the light beam on the SLM, a plurality of spatially separated positions may be used and/or combinations of overlapping and non-overlapping positions. In addition, as described above, two-dimensional scanning using one or more AODs for beam displacement in two dimensions is possible. 
     Some embodiments may include the alternative assembly  1100  of  FIGS. 10 and 11  to move the input beam relative to the spatial light modulator, in particular so that the input beam is incident at a plurality of different positions on the spatial light modulator at different points in time. By continually (i.e. continuously or periodically) moving the input beam relative to the SLM, the above described effect of averaging the phase and brightness of the illuminating beam is achieved so as to improve the shape, size, uniformity and brightness profile of the light spots of the holographic reconstruction as described above. In addition, continually moving the input beam across the SLM introduces a randomness in the illumination, which can average out the speckle patterns as described above. Thus, the quality of the holographic reconstruction can be improved. In addition, the alternative assembly  1100  does not require mechanically moving parts and can be controlled accurately using electrical signals and appropriate AOD calibration techniques, which are well known in the art. 
     Additional Features 
     Embodiments refer to an optically-activated LCOS spatial light modulator by way of example only. The teachings of the present disclosure may equally be implemented on any spatial light modulator capable of displaying a computer-generated hologram in accordance with the present disclosure such as any electrically-activated SLMs, optically-activated SLM, digital micromirror device or microelectromechanical device, for example. 
     In some embodiments, the light source is a laser. In some embodiments, the light receiving surface is a screen or a diffuser. The holographic projection system of the present disclosure may be used to provide an improved head-up display (HUD) or head-mounted display. In some embodiments, there is provided a vehicle comprising the holographic projection system installed in the vehicle to provide a HUD. The vehicle may be an automotive vehicle such as a car, truck, van, lorry, motorcycle, train, airplane, boat, or ship. 
     The quality of the holographic reconstruction may be affect by the so-called zero order problem which is a consequence of the diffractive nature of using a pixelated spatial light modulator. Such zero-order light can be regarded as “noise” and includes for example specularly reflected light, and other unwanted light from the SLM. 
     In the example of Fourier holography, this “noise” is focussed at the focal point of the Fourier lens leading to a bright spot at the centre of the holographic reconstruction. The zero order light may be simply blocked out however this would mean replacing the bright spot with a dark spot. Some embodiments include an angularly selective filter to remove only the collimated rays of the zero order. Embodiments also include the method of managing the zero-order described in European patent 2,030,072, which is hereby incorporated in its entirety by reference. 
     The holographic reconstruction is created within the zeroth diffraction order of the overall window defined by the spatial light modulator. It is preferred that the first and subsequent orders are displaced far enough so as not to overlap with the image and so that they may be blocked using a spatial filter. 
     In embodiments, the holographic reconstruction is in colour. In examples disclosed herein, three different colour light sources and three corresponding SLMs are used to provide composite colour. These examples may be referred to as spatially-separated colour, “SSC”. In a variation encompassed by the present disclosure, the different holograms for each colour are displayed on different area of the same SLM and then combining to form the composite colour image. However, the skilled person will understand that at least some of the devices and methods of the present disclosure are equally applicable to other methods of providing composite colour holographic images. 
     One of these methods is known as Frame Sequential Colour, “FSC”. In an example FSC system, three lasers are used (red, green and blue) and each laser is fired in succession at a single SLM to produce each frame of the video. The colours are cycled (red, green, blue, red, green, blue, etc.) at a fast enough rate such that a human viewer sees a polychromatic image from a combination of the images formed by three lasers. Each hologram is therefore colour specific. For example, in a video at 25 frames per second, the first frame would be produced by firing the red laser for 1/75th of a second, then the green laser would be fired for 1/75th of a second, and finally the blue laser would be fired for 1/75th of a second. The next frame is then produced, starting with the red laser, and so on. 
     An advantage of FSC method is that the whole SLM is used for each colour. This means that the quality of the three colour images produced will not be compromised because all pixels on the SLM are used for each of the colour images. However, a disadvantage of the FSC method is that the overall image produced will not be as bright as a corresponding image produced by the SSC method by a factor of about 3, because each laser is only used for a third of the time. This drawback could potentially be addressed by overdriving the lasers, or by using more powerful lasers, but this would require more power to be used, would involve higher costs and would make the system less compact. 
     An advantage of the SSC method is that the image is brighter due to all three lasers being fired at the same time. However, if due to space limitations it is required to use only one SLM, the surface area of the SLM can be divided into three parts, acting in effect as three separate SLMs. The drawback of this is that the quality of each single-colour image is decreased, due to the decrease of SLM surface area available for each monochromatic image. The quality of the polychromatic image is therefore decreased accordingly. The decrease of SLM surface area available means that fewer pixels on the SLM can be used, thus reducing the quality of the image. The quality of the image is reduced because its resolution is reduced. Embodiments utilise the improved SSC technique disclosed in British patent 2,496,108 which is hereby incorporated in its entirety by reference. 
     Examples describe illuminating the SLM with visible light but the skilled person will understand that the light sources and SLM may equally be used to direct infrared or ultraviolet light, for example, as disclosed herein. For example, the skilled person will be aware of techniques for converting infrared and ultraviolet light into visible light for the purpose of providing the information to a user. For example, the present disclosure extends to using phosphors and/or quantum dot technology for this purpose. 
     Some embodiments describe 2D holographic reconstructions by way of example only. In other embodiments, the holographic reconstruction is a 3D holographic reconstruction. That is, in some embodiments, each computer-generated hologram forms a 3D holographic reconstruction. 
     The methods and processes described herein may be embodied on a computer-readable medium. The term “computer-readable medium” includes a medium arranged to store data temporarily or permanently such as random-access memory (RAM), read-only memory (ROM), buffer memory, flash memory, and cache memory. The term “computer-readable medium” shall also be taken to include any medium, or combination of multiple media, that is capable of storing instructions for execution by a machine such that the instructions, when executed by one or more processors, cause the machine to perform any one or more of the methodologies described herein, in whole or in part. 
     The term “computer-readable medium” also encompasses cloud-based storage systems. The term “computer-readable medium” includes, but is not limited to, one or more tangible and non-transitory data repositories (e.g., data volumes) in the example form of a solid-state memory chip, an optical disc, a magnetic disc, or any suitable combination thereof. In some example embodiments, the instructions for execution may be communicated by a carrier medium. Examples of such a carrier medium include a transient medium (e.g., a propagating signal that communicates instructions). 
     It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. The present disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.