Patent Application
20250181030
The present invention relates to holography and methods of generating holographic images.
Display systems capable of showing images with a continuous range of depths are collectively known as light field displays. Such displays may broadly employ a Computer Generated Holography (CGH) technique. A well-known problem in CGH is that the technique typically yields displays with a rather small eyebox. As used herein, an “eyebox” defines pupil positions in which an image can be viewed; the volume in which a viewer's pupil can be positioned to view an image from an image source. In order to view the image, the viewer's pupil must be located within the eyebox, which may be not much larger than the pupil itself. This presents a challenge to align the eyebox with the viewer's pupil.
Some display systems include mechanical adjustment to physically move the eyebox and align it with the viewer's pupil, for example adjusting an Interpupillary Distance (IPD) on a head-mounted display or mechanically adjusting position of a heads-up display so that it can be seen by a viewer. Other displays are custom made for a particular user; the Focals 1.0 commercially available by North® are designed to align the eyebox of the display system with the viewer's pupil following a custom fitting procedure. Such hardware methods are typically not scalable or require significant effort on the part of the viewer in order to correctly align the eyebox with the pupil. Use of the display system by more than one user also requires time consuming re-adjustment or is simply not possible.
To address the alignment problem outlined above, it may be more appropriate to expand the size of the eyebox. One approach is to enlarge the eyebox using an image-replicating combiner, also known as a waveguide combiner. This expands the size of the eyebox provided by an image source by generating multiple spatially separated replications of the input image. The viewer's pupil can then be located in a larger area and still view a complete image. However, image-replicating combiners suffer from reduced image quality due to problems such as focus spread.
Another approach for expanding the size of the eyebox involves using a modulator having a suitably high modulation speed to display light fields at different positions in quick succession so that the viewer perceives one larger image due to persistence of vision. Examples of such modulators are digital micromirror devices (DMDs) and liquid crystal on silicon (LCoS) devices. However, in practice, these types of displays cannot achieve the perfect full-complex modulation required to generate a perfect holographic image because they only have a very limited number of values they can display. For example, these displays may only be capable of modulating one of amplitude or phase. The resolution may also be limited, perhaps to 5 bits of resolution (giving 32 possible displayed values or fewer), even only 2 values in the case of a binary display technology.
As a result, pixels of a full-complex holographic image are quantised for display, to a value that can be reproduced by the display. For example, in the extreme case of a binary display (such as a DMD) each pixel in the display can only be in one of two states. All points on the full-complex Argand diagram need to be mapped to one of the two states. The process of quantisation for display therefore reduces the image quality, visible in the perceived image as reduced contrast and/or noise.
It would be desirable to be able to expand the field-of-view possible with such CGH displays while also improving the image quality of the generated holographic images.
According to a first aspect of the present invention, there is provided a spatial filter for positioning in a Fourier plane of a holographic display system. The spatial filter delimits a set of apertures, wherein each aperture in the set of apertures is switchable between a substantially transmissive and a substantially non-transmissive state. The set of apertures comprises a plurality of subsets of apertures, each subset comprising at least one aperture, and each of the subsets of apertures corresponds to a Fourier transform of a target light field, F(H), wherein F(H) substantially does not overlap a Fourier transform of a complex conjugate of the corresponding target light field, F(H*), in the Fourier plane. The union of the set of apertures forms a shape which is at least one of simply connected and substantially space filling. “Simply connected” is used in its mathematical sense to mean a shape which is free of holes, gaps or other discontinuities; a simply connected shape is one in which any simple closed curve can be shrunk to a point continuously in the shape. A “simple closed curve” is used in its mathematical sense to mean a connected curve that does not cross itself and ends at the same point it begins. Furthermore, despite the name “curve”, a simple closed curve does not have to curve and can incorporate, or be formed entirely of, straight sections. A “substantially space filling” shape generally does not have holes, gaps or apertures within its perimeter. A substantially space filling shape may fill greater than 90%, greater than 95%, greater than 98% or greater than 99% of an area inside a perimeter of the shape. It is understood that a subset of apertures may include one or more apertures.
The effective area in which the hologram can be viewed can be increased using such a spatial filter because the union of apertures forming a space-filling or simply connected shape allows for an increase in the eyebox coverage. The continuity of the shape reduces the chance of a path between two eye-pupil positions in the eyebox being interrupted by a gap in the shape. Furthermore, as will be explained in more detail later, the inventors have realised that noise introduced by quantisation for display results in additional components in the Fourier plane that are approximated by a series expansion. By considering the F(H*) term of the series expansion and ensuring that it does not overlap with F(H) so that F(H*) is blocked by the spatial filter, higher image quality can be obtained. By F(H) it is meant the part of the Fourier transform which has non-zero values.
Determining a target light field, H, satisfying this non-overlapping condition is computationally simpler than prior iterative methods, such as Gerchberg Saxton, reducing requirements for processing resources. This can allow higher quality holographic displays having larger addressable eyeboxes with reduced processing and/or power requirements, allowing displays to be one or more of: lower-cost, more portable, and for battery-powered devices, increased battery life. This lower processing and or power requirement can enable a plurality of target light fields to be generated in a time-sequence at high frequency. Each of the time sequence of F(H) may correspond to a respective one of the plurality of subsets of apertures of the spatial filter, in substantial synchrony with a respective one of the plurality of subsets of apertures of the spatial filter being in a substantially transmissive state. As discussed above, through persistence of vision, this means that the viewer effectively views an image covering a larger area and thus, the effective size of eyebox is increased while at the same time improving image quality of the image.
The shape may be a simple polygon. That is, the shape may be a polygon that does not intersect itself and has no holes. In some cases, the shape is one that can be substantially tessellated. The shape may be a shape that periodically tessellates to a two-dimensional plane. When the shape can be substantially tessellated the spatial filter may delimit a plurality of such sets of apertures. Each set may then be arranged on the spatial filter such that at least a portion of the spatial filter is tessellated by the shapes, allowing an even greater expansion of the addressable eyebox.
The shape may be substantially tessellated on a rhombic grid. This provides a particular advantage when a holographic light field is transmitted via an image replicating combiner that is configured to generate replications of the light field on a rhombic grid because the image replicating combiner can replicate the shape to provide near-continuous coverage over an expanded phase volume, thereby increasing the coverage of the addressable eyebox of the display system.
In some examples, the shape is dodecagonal. The shape may have a two-fold symmetry, such as a two-fold rotational symmetry or a two-fold axis of symmetry. The shape may substantially have the form of an “I” or “H”. The “I” or “H” shape might be dodecagonal, such as corresponding to an “I” in a serif font and an “H” in a sans serif font. At least one of the apertures of the set of apertures may be a quadrilateral.
In some examples, at least one of the subsets of apertures corresponds to a Fourier transform of a first target light field, F(H) and further does not substantially overlap (i) a Fourier transform of the first target light field multiplied by the complex conjugate of the target light field, F(HH*), (ii) a Fourier transform of a square of the target light field, F(H2), and (iii) a Fourier transform of a square of the complex conjugate of the light field F(H*2). The energy in the series expansion tends to be concentrated in lower order terms, so ensuring no overlap with at least F(H*) is useful, but the next higher order terms such as F(HH*), F(H2) and F(H*2) also contain reasonable amounts of energy so that blocking these is also useful. A union of apertures, wherein all of the subsets of apertures satisfy this additional non-overlapping condition, cannot also satisfy the simply connected criterion (that the union has no holes or apertures). However, a spatial filter delimiting a combination of subsets of apertures satisfying both the weaker and stronger non-overlapping conditions can also satisfy the simply connected criterion. This can allow a good balance of image quality and coverage.
A subset of apertures may have an area approximately ⅙th of an area of a square on the grid formed by integer diffraction orders of light having a predetermined wavelength incident on a modulator. A ⅙th area is understood to set a limit on the maximum size of the aperture (or subset of apertures) which can meet the stronger non-overlapping constraint whereby F(H) does not overlap with first and second order terms of its Fourier expansion: F(H*), F(HH*), F(H2) and F(H*2).
According to a second aspect of the invention, there is provided a holographic display system. The holographic display system comprises a light source configured to emit at least partially coherent light, a modulator arranged to be illuminated by the at least partially coherent light and to generate a time sequence of light fields, wherein each of the light fields is a quantised representation of a target light field. The holographic display system further comprises a spatial filter according to the first aspect, in a Fourier plane.
The modulator may be a digital micromirror device (DMD). DMDs have certain advantages for displaying holograms such as allowing an improved (darker) black level. In particular, they feature high modulation speeds, typically much higher than 1000 binary patterns per second. Such high modulation speeds allow the time sequence of light fields to be generated fast enough that a viewer will perceive such a series of rapidly displayed light fields as a single hologram, through persistence of vision. In other examples, the spatial light modulator is a Liquid Crystal on Silicon, LCoS, device. Although LCoS devices may have more quantisation states than a DMD, useful increases in image quality are also achieved using the methods described herein.
As mentioned above, generating a time sequence of light fields in substantial synchrony with a respective one of the plurality of subsets of apertures of the spatial filter being in a substantially transmissive state can increase the size of the eyebox of the display system.
The spatial filter may be positioned so that the union of the set of apertures substantially aligns with a peak diffraction efficiency of the modulator. This may increase the amount of light that can be transmitted by the spatial filter. The light source may be configured to emit at least partially coherent light at a plurality of wavelengths selected so that the peak diffraction efficiency of the modulator approximately aligns in at least one direction with an integer diffraction order for each of the plurality of wavelengths. The plurality of wavelengths may comprise red, green and blue light, and the peak diffraction efficiency for each of red, green and blue light may be aligned with a different integer diffraction order. In some examples, the DMD is configured such that the landed edge of an “on-state” mirror is horizontal i.e. parallel to the long side of the DMD. In this case, the peak diffraction efficiency may be approximately aligned with the 5th, 6th and 7th vertical diffraction orders for red, green and blue respectively. Red may have a wavelength between 620 nm-750 nm such as 635 nm. Blue light may have a wavelength around 450 nm-495 nm, for example, 450 nm. Green light may have a wavelength in the range of 495-570 nm or in the range of 520-560 nm, such as around 520 nm.
The holographic display system may further comprise an image replicating combiner positioned in an optical path after the spatial filter and a processing system coupled to the modulator. The processing system may be configured to: determine a light field to be displayed at a viewing location (for example the location of the eye pupil within the addressable eyebox of the image replicating combiner); determine a transfer function describing the propagation of light through the image-replicating combiner between the viewing location and the Fourier plane which may be near to an input surface of the image-replicating combiner; determine an input light field by applying the determined transfer function to the light field at the viewing location, wherein the input light field corresponds to the union of the set of apertures, determine the plurality of F(H) corresponding to each of the subsets of apertures to be displayed at the Fourier plane, and cause the modulator to generate each of the plurality of F(H) at the input location. Image replicating combiners are known to provide a large addressable eyebox by generating a plurality of replications of an input light field. This larger addressable eyebox can be utilised with a spatial filter according to the first aspect to improve the eyebox coverage available from the display system. Furthermore, the transfer functions allow images to be precisely targeted at a particular viewing position, reducing common problems associated with image replicating combiners for holographic images, such as focus spread. The input surface of the image-replicating combiner may be substantially in the Fourier plane, within a short distance of the Fourier plane such as 1 mm and 2 mm, or positioned right up against the spatial filter.
The union of apertures in the Fourier plane is essentially the exit pupil of the holographic display system. With the addition of an image replicating combiner, the exit pupil can be replicated to further increase the addressable eyebox of the holographic display system. The plurality of replications may approximately tesselate in a plane when viewed from at least one viewing position. In some examples, a “viewing position” may mean any viewing position within the addressable eyebox of the display system. This is particularly advantageous when the union of the set of apertures of the spatial filter forms a shape which tessellates. A plurality of such sets, replicated by the image-replicating combiner, provide near-continuous coverage over an expanded phase volume, thereby increasing the coverage of the addressable eyebox, meaning that a larger range of eye positions may be addressed. The tessellation may be approximately exact for a single viewing angle.
The holographic display system may further comprise an eye-tracking system arranged to provide data indicative of a viewing position to the processing system. The data may be used by the processor to generate light fields which can be displayed at the determined viewing position(s). Furthermore, due to the expanded size of eyebox of the holographic display system, the holographic display system may not require mechanical adjustment to accommodate a plurality of users having a range of interpupillary distances.
The light source may be configured to emit at least partially coherent light at a plurality of wavelengths, including green light, and the subset of apertures correspond to positions of respective F(H) for green light. Such subsets of apertures will approximately correspond to positions of respective F(H) for blue and red light, but the overall error across all colours is reduced compared to aligning the apertures with F(H) for blue or red light.
The holographic display system may comprise a controller configured to cause the modulator to display a time sequence of quantised target light fields, each of the time sequence of quantised target light fields corresponding to a respective one of the plurality of subsets of apertures, in substantial synchrony with the respective one of the plurality of subsets of apertures of the spatial filter being in a substantially transmissive state. This allows a viewing eyebox to be expanded by time-multiplexing multiple apertures of spatial filter.
According to a third aspect of the invention, there is provided a method of displaying a holographic image. The method comprises: determining a first light field, H1, for quantisation, the first light field having a Fourier transform, F(H1), such that it does not overlap a Fourier transform of its complex conjugate, F(H1*); determining a second light field, H2, for quantisation, the second light field having a Fourier transform, F(H2), such that it does not overlap a Fourier transform of its complex conjugate, F(H2*); at a first time, displaying a quantised version of the first light field using the holographic display system according to the second aspect, wherein a first subset of apertures corresponds to an extent of F(H1) in a Fourier plane such that components corresponding to F(H1*) resulting from quantisation are substantially blocked by the spatial filter; and at a second time, displaying a quantised version of the second light field using the holographic display system according to the second aspect, wherein a second subset of apertures corresponds to an extent of F(H2) in a Fourier plane such that components corresponding to F(H2*) resulting from quantisation are substantially blocked by the spatial filter, wherein at the first time, the first subset of apertures allows light to pass and the second subset of apertures prevents (blocks) light from passing, and at the second time, the first subset of apertures prevents (blocks) light from passing, and the second subset of apertures is allowing light to pass. The first and second light fields can be target light fields as described above in that they are the light fields in the plane of a modulator used to generate the light fields. For example, a target light field may be a desired light field before quantisation.
According to a fourth aspect of the invention, there is provided a computer-readable medium comprising instructions, that, when executed by a processor, cause the holographic display system according to the second aspect to display a holographic image according to the fourth aspect.
Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, which is made with reference to the accompanying drawings.
Holographic images are images with depth information that give the perception to a viewer of depth and can be generated by exploiting the electromagnetic wave nature of light. The term images as used herein is understood to include static images as well as moving holographic images comprising a sequence of holographic frames displayed in rapid succession. Furthermore, the present disclosure is relevant to both 2-dimensional and 3-dimensional holograms.
2-dimensional holograms are those which occupy substantially a single image plane but where the image plane can be positioned at a perceived depth from the user. This can allow more comfortable focussing for a viewer's eye especially in augmented reality situations; the hologram can be given a depth matching a point of interest. 3-dimensional holograms give the appearance of a 3-dimensional scene or object with appropriate depth cues for a viewer's eye.
As will be explained in more detail below, by applying constraints on the position of a desired full-complex hologram, H, so that F(H) occupies a particular position in the Fourier plane where it does not overlap with at least F(H*), spatial filtering in a Fourier plane can be used to reduce quantisation noise. This technique may be applied together with time-multiplexing of a plurality of quantised full-complex holograms targeted to different areas of the Fourier plane to expand an eyebox of a display system. Some examples further expand the eyebox using an image replicating combiner. These may also apply a transfer function to account for a viewing position amongst the replications and reduce problems, such as focus spread, that can be associated with image-replicating combiners when holograms are displayed.
In CGH, a hologram for display is typically first calculated as a “full-complex” hologram which comprises an array of values corresponding to each element (pixel) on the surface of a display device. Each value is a complex number with respective phase and amplitude. However, many display systems used for CGH images, such as DMD and LCoS spatial light modulators, have a finite range of values that they can reproduce. To display the hologram, each pixel in the full-complex modulated holographic image needs to be mapped, or quantised, to a value that can be reproduced by the display. In one example, the display device is a binary display, capable of generating images comprising pixels taking one of two possible amplitude or phase values. An example binary amplitude display device is a digital micromirror device (DMD) comprising an array of microscopic actuating mirrors. When illuminated by a light source, each mirror can either direct light to the next component in the optical system, representing a pixel “on” state, or direct light elsewhere, such as towards a heat sink, representing an “off” state. Each mirror can be actuated between the two states as required to generate the desired hologram. Similarly, in a binary phase display device, each pixel is capable of emitting light at one of two discrete phases.
Mapping the continuum of full-complex modulated values to quantised amplitude and/or phase values requires a particular quantisation method to be used. A simple example of a binary amplitude quantisation scheme is as follows. If the value has a negative or zero real part (the point is in the second or third quadrant on the Argand diagram), the point is mapped to (0,0) on the Argand diagram. If the value has a positive real component, the point is mapped to the point (0,1) on the Argand diagram. The person skilled in the art will be aware that many alternative quantisation methods can be used and the present disclosure is not limited to any particular quantisation method. However, this example highlights the loss in phase and amplitude information that results from quantising points for display on a DMD. While other display technologies may offer more values, the number of finite states available is still low, perhaps 5 bits (32 values). It is clear that any quantisation will result in a loss of amplitude and phase information, reducing image quality.
The inventors have shown that the noise introduced by quantisation can be reduced by selectively filtering out unwanted noise in the quantised hologram using a physical filter in the display apparatus while also expanding the size of the eyebox of such a display system. By approximating a quantised representation, HQ, of a target light field as a series expansion, a quantised field can be determined in which one or more additional unwanted components introduced by the quantisation can be filtered out in the Fourier domain/Fourier plane, allowing a much improved approximation of the full-complex target field to be displayed despite the quantisation that has taken place in the display system. The display system and method discussed may provide a computationally inexpensive technique for achieving full-complex modulation using conventional display devices, especially compared to prior iterative software-based techniques, such as Gerchberg Saxton.
Equation 1 above is an expansion of the quantised target light field, HQ. In addition to the desired component H, additional components, H*, H2, H*2, HH*, . . . are introduced by the quantisation. a, b, c, d, e and f are scalar coefficients whose values depend on the particular quantisation scheme employed. They can be determined numerically but, for the methods described herein, their determination is not essential. It will be appreciated that, as only the H component is desired, the extent to which the rest of the expansion is considered may vary. For example, only the terms in the expansion with the greatest impact (largest coefficient) may be considered. Some examples may consider further components than those in equation 1, such as a H3 term and so on. Other examples may include fewer components than those in equation 1, such as only the H* term.
The quantised Hologram, HQ, is displayed by quantising the initial full-complex hologram, calculated or determined with known techniques, for display. Any suitable display device can be used, including a Spatial light modulator (SLM). The SLM may be, for example, a DMD, an LCD, an Amplitude LCoS, or a phase LCoS. Alight source is configured to generate at least partially coherent light, which is modulated by the SLM and may be, for example, a laser or a light emitting diode (LED).
The SLM generates a light field which, when observed by a viewer through an optical system, recreates the light field so the image is perceived. Conventional holographic display systems include a lens that creates a Fourier transform of the image displayed on the SLM, with the eye of a viewer causing an inverse Fourier transform to take place. Without applying further steps, such as iterative techniques to account for the quantised values reproducible by the SLM, image quality is low because of the errors introduced by quantisation.
However, the present disclosure makes use of the observation that if a lens having a focal length, f, is positioned one focal length in front of the SLM, such that light modulated by the SLM is incident on the lens, then the Fourier transform of HQ, F(HQ), will be produced one focal length behind the lens. This position is referred to as a Fourier plane of the SLM. This is the plane where the complex amplitude is described by a Fourier transform of the complex amplitude at the SLM, potentially modulo scaling or including a multiplicative spherical phase term. In the present case, the Fourier transform of HQ can be written in terms of the Fourier transform of the series expansion of equation 1 above. Using linearity of the Fourier transform and equation 1, F(Hg) can be expressed as equation 2 below:
The components F(H*), F(H2), F(H*2) and F(HH*) will be referred to herein as noise components because they relate to unwanted components generated by quantising the target field, H. It will be understood that the effect of these components could be visible as classical “noise” but could also be a reduction in image contrast and will generally result in reduced image quality.
The Fourier transform of a function of space (the target light field, H, is a function of space, H≡H(x,y), for example) decomposes that function into its respective frequency components, kx and ky. The Fourier transform of the constant, a, in Eq 1 is a delta function, multiplied by a, and centred at kx=ky=0, as represented by the term aF(1) in Eq 2, and sometimes known as the zero-order diffraction peak. The locations of each of the components on the right-hand side of Eq. 2 in the Fourier plane can be determined from knowledge of the location of F(H) as will now be explained with reference to
An example of F(H) 102 targeted at an arbitrary area in the Fourier plane is illustrated in
Similar spatial plots in the Fourier plane can be made for the higher order components of the expansion.
It will be appreciated how varying the area occupied by F(H) affects the area occupied by each of the noise components. For example, enlarging the area of F(H) in the Fourier plane causes the noise components to grow correspondingly. Once F(H) reaches a sufficient extent, it will begin to overlap with one or more of the noise components. Further, translating and/or rotating F(H) relative to the origin in the Fourier plane will cause a corresponding translation and/or rotation of the noise components.
As can be seen from
In an example, the filtering takes place by positioning a spatial filter delimiting an aperture corresponding to the region in the Fourier plane to which F(H) has been targeted. A spatial filter located in the Fourier plane of a lens (for example, where a lens is one focal length from the SLM, the lens's Fourier plane is one focal length at the opposite side), the spatial filter can therefore block one or more of the noise components physically. The aperture allows light corresponding to F(H) to pass through the filter and thus reach a target plane where the hologram can be viewed. Selecting the position of F(H) such that there is no overlap of F(H) with at least one of the considered noise components ensures that light corresponding to F(H) reaches the target plane while blocking the at least one noise components.
As discussed above, once the location of F(H) in the Fourier plane is determined, the locations of the noise components can also be determined, using the method of
Some example filters will now be discussed.
The filters 200, 210 are shown as unit squares with relative side lengths of 1 for illustration purposes, but in reality will have lengths equal to λf/p.
It will be understood that a reflection of filter 200 about a vertical line extending through a centre of the filter, a reflection about a horizontal line extending through a centre of the filter, rotations of 90° about the centre of the filter, reflections about the axes extending through the origin of the Fourier plane, and rotations of 90° about the origin are also possible and also satisfy the constraint of non-overlapping noise components. For example, as shown in
It will be understood that because components on the Fourier plane repeat in a periodic pattern, the region covered by the filter can be translated on the Fourier plane to produce another filter where aperture 212 could appear on the right of 214. This can be visualised for example by taking the left half of
It will be appreciated that these are just examples of the shapes of apertures that can satisfy the requirement that F(H) does not overlap with at least one other component of its series expansion in the Fourier plane and the disclosure is not limited to any particular form. For example, although all the filters described above have straight sides, which can be useful to maximise useable area, other examples may use curved sides, or may choose not to maximise useable area of the filter.
While the discussion above has considered maximising the area of the aperture such that all the unwanted components are blocked, some examples may use a still larger aperture. In general, the higher order noise components are not evenly distributed within the Fourier plane and will tend to have a lower power and/or amplitude at their periphery than in the centre. The size of the aperture may therefore be increased slightly beyond the ⅙ criterion described above without introducing too much noise. For example, the aperture may have an area of between ⅕ and ⅙ of a unit square in the Fourier plane and still exhibit improved performance with a hologram targeting the aperture, compared to not targeting the hologram and having no aperture.
The discussion so far has considered apertures that are static, in that their position within the filters does not change in time. In these examples, the maximum area of the filter delimiting the aperture is ⅙th of the total area. While this has the advantages discussed above in terms of improved image quality, it does mean that the area in which the hologram can be viewed is reduced. The inventors have found that an effective viewable area in which the hologram can be perceived (sometimes referred to as an “eyebox”) can be increased by using a plurality of portions which are selectively controlled to either allow light to pass or to block light from reaching a viewer. The aperture then comprises the portions of the filter that allow light to pass. The portions may be configured to allow at least two of the sets of apertures {202}, {212, 214}, {302, 304} shown in
While One Step Phase Retrieval (OSPR) algorithms also exploit the persistence of vision, the methods of the present disclosure can give higher quality results with lower use of computational resources. In OSPR, many holograms using the entire Fourier plane, but with different random phase patterns, are displayed in rapid temporal succession and the viewer's eye combines them to perceive a single hologram with overall reduced noise (the noise averages out). The concept here uses the same persistence of vision effect, but rather than average out the effect of noise, the averaging is used to increase the portion of the Fourier plane which is used and thus the viewable area. Furthermore, rather than calculate multiple holograms with different random phase patterns, as in OSPR, the method here can simply mask a hologram with the same random phase pattern, which is computationally less intensive. Nevertheless, other examples may use different random phase patterns for each displayed hologram, effectively applying the apertures disclosed herein to OSPR.
Some examples may combine OSPR with the aperture described herein. In that case the OSPR may make use of a lower bit depth because of the noise reduction provided by the aperture. The OSPR becomes less computationally intensive and/or can process frames more quickly to maximise the benefit of the time-averaging effect to reduce noise in OSPR.
The portions can be arranged contiguously within each unit cell of the filter, i.e. the portion of the filter with dimensions λf/p, so that multiple portions exist per unit cell. The SLM may then be configured to generate the holographic light field, H, so that F(H) is targeted at one or more portions of the filter activated to be transmissive. Synchronising the activated portions of the filter with the holographic light field generated by the SLM targeting those portions allows an increase in the effective area of the hologram generated at a target plane. If the portions of the filter are activated and deactivated at sufficient speed, such as greater than or equal to 100 Hz, 200 Hz or more, a viewer may not perceive the switches. This allows a further effective increase in the size of the eyebox.
The size of eyebox achievable by the display can be increased by providing a filter comprising a set of apertures, the set of apertures comprising a plurality of subsets of apertures, and each subset comprising at least one aperture, wherein the union of the set of apertures forms a shape which is simply connected, or bounded by a simple closed curve. A simple closed curve is a closed curve without intersections. It is understood that “curve” is construed in the broadest mathematical sense of the term and can include any combination of straight lines, curved edges and vertices. A shape is simply connected if any simple closed curve can be shrunk to a point continuously in the shape. A simply connected shape may be said to be space-filling. Such a shape may also be described as lacking self-intersections of the perimeter or holes in the interior of the shape. The union of apertures forming a simply connected shape allows more of an image plane to be targeted, and thus the size of the eyebox of a display system to be increased. The simply connected criterion also improves tessellation of the set of apertures. The union of apertures in the Fourier plane is essentially the exit pupil of an image generating unit of a display system incorporating the spatial filter. Therefore, the enlarged and simply connected region covered by the union of the apertures corresponds to an enlarged exit pupil in real/physical space.
A subset of apertures in this respect is understood to correspond to one or more apertures that correspond to a single F(H), so an example of a subset of apertures would be the apertures 212 and 214. A set of apertures compliant with this simply connected criterion cannot be achieved when all of the subsets of apertures correspond to an F(H) which does not overlap with all of the noise terms up to second order. Instead, to comply with the simply connected criterion, at least one of the subsets of apertures may satisfy the weaker non-overlapping condition wherein the corresponding F(H) does not overlap F(H*), but does have some overlap of the second order F(H2), F(H*2) and F(HH*) terms. Such a combination of subsets of apertures can still provide improved image quality over a filter that is arranged not to block any of the noise components, while providing a potential large increase in the eyebox size. An example of apertures that fulfil this weaker non-overlapping condition are shown in the filter 300 of
The shape formed by the union of the set of apertures may be a simple polygon. The upshot of this is that the shape can be selected such that it can be substantially tessellated. The shape may periodically tessellate to a two-dimensional plane, such as in the example shown in
From equation 2 above, the quantised hologram in the Fourier plane includes a delta function (sometimes referred to as the zero order). This is a diffraction peak and is not desirable to retain, so is ideally blocked by the spatial filter.
The “X”s indicate locations of a diffraction peak for light of a given wavelength, so that it is understood that the filter 400 delimiting the portions 402 to 416 extends beyond a single unit square defined by successive horizontal and vertical diffraction orders. In fact, the filter 400 extends over 6 unit squares covering four horizontal diffraction orders and three vertical diffraction orders. As described above, the filter 400 may be positioned in the Fourier plane such that the centre of the union of the portions substantially aligns with a peak diffraction efficiency of the modulator being used to display H. In the example of
At any one time, a single one of the portions 402 to 416 is in a state to allow light to pass, while all other portions are in a state where light does not pass. Correspondingly, a holographic light field, H, may be targeted so that F(H) corresponds to the portion that allows light to pass. In use, a controller may supply a suitable hologram to the SLM and control the filter 400 so the relevant portion allows light to pass. Some SLMs may be operated quickly enough that all eight portions 402 to 416 can be displayed in a single frame period. Any sequence of operation can be used, including incrementing from portions 402 to 416 as labelled and decrementing from portions 416 to 402 as labelled.
The union of all of the portions 402 to 416 forms an irregular dodecagon that substantially takes the form of an “I”. It is understood using the rules of reflection and translation that an equivalent spatial filter can be produced by providing the portions 402 to 416 rotated 90 degrees in the plane. In this case, the union of the portions 402 to 416 forms an irregular dodecagon that substantially takes the form of an “H”.
The total area covered by the union of the portions 402 to 416 is 4/3 of the area of a grid square defined by neighbouring diffraction orders. Therefore, the filter 400 can address a larger phase volume than would be possible for a typical CGH display with a fixed aperture.
The controllable portions of
In the previous discussion of
Example Display System for Use with Techniques Described Herein
The filter 908 is positioned one focal length from the lens 906, on the opposite side of the lens 906 from the SLM 904. An example of a suitable filter is shown in
The SLM 904 is arranged to be illuminated by the at least partially coherent light and to generate a time sequence of light fields, wherein each of the light fields is a quantised representation of a target light field. Each of the time sequence of quantised target light fields corresponds to a respective one of the plurality of subsets of apertures of the filter 908, in substantial synchrony with a respective one of the plurality of subsets of apertures of the filter 908 being in a substantially transmissive state.
The arrangement of the holographic optical system 900 is such that the Fourier transform of the light fields, F(H), is formed at a plane coinciding with the position of the filter 908. This plane is the Fourier plane of the SLM 904 as formed by the lens 906. The target light fields are determined such that the Fourier transform of the target light fields, F(H), do not overlap at least the Fourier transform of the complex conjugate of the corresponding target light field, F(H*), in the Fourier plane of the SLM 904. Further, each subset of apertures in the filter 908 corresponds to an F(H) in the Fourier plane, such that portions of the target light fields outside of F(H) are blocked.
The light source 902 may, for example, comprise a laser module or an LED. The light source 902 is configured to generate at least partially coherent light at one wavelength, or a plurality of wavelengths (corresponding to red, green and blue, for example).
The SLM 904 may be configured to modulate at least one of the phase, amplitude, binary phase and binary amplitude of the light. The SLM 904 may be, for example, a DMD, an LCD, an amplitude LCoS or a phase LCoS.
The display system 900 may comprise a controller configured to cause the SLM 904 to display the time sequence of quantised target light fields.
As shown, the SLM 904, lens 906 and filter 908 are coaxial. Other configurations may also be used, such as a folded light path that may allow a more compact display.
Image-replicating combiners can be used to increase the addressable size of the eyebox of a display system. When the holographic optical system 900 further comprises an image replicating combiner, positioned in an optical path after the filter 908, the larger addressable eyebox can be coupled with the properties of the filter 908 to increase the eyebox coverage.
In general, image-replicating combiners comprise an input surface, also known as an in-coupler or an entrance pupil, to receive light rays corresponding to an input image. The notion of an entrance pupil corresponds to the limiting aperture in an input of the image-replicating combiner. The input surface is a coupling feature that couples light waves, propagating externally, to the inside of the image-replicating combiner. The coupling feature may be, for example, an array of mirrors, an array of prisms, a diffraction grating or a hologram. Further possible coupling features include embedded mirrors, micro-prisms, a surface relief slanted grating, a surface relief blazed grating, a surface relief binary grating, a multilevel surface relief grating, a thin volume hologram, a thin photopolymer hologram, a Holographic Polymer Dispersed Liquid Crystal (H-PDLC) volume holographic coupler, a thick photopolymer hologram, a resonant waveguide grating, a metasurface coupler and embedded half-tone mirrors. An image-replicating combiner further comprises an output surface, also called an out-coupler, to output light corresponding to the input image. The output surface is a further coupling feature, which may use the same technology as the input surface. Image-replicating combiners may be manufactured from materials with high-refractive indices that support total internal reflection over a wide range of internal incidence angles. Lanthanum dense flint glass, for example N-LASF46 manufactured by Schott™, has a critical angle of θc=310 at wavelength λ=530 nm. An image-replicating combiner will propagate waves by total internal reflection at all internal angles above the critical angle.
In an example, an image-replicating combiner takes the form of a substantially planar sheet. The planar sheet may be constructed from a transparent material, such as glass. In this case, one arrangement for the input and output surfaces is to position them on the same side of the planar sheet, such that light enters and exits at the same side of the planar sheet. In another arrangement, the input and output surfaces may be positioned on opposite sides of the planar sheet. The particular arrangement may be selected based on a function of the image-replicating combiner. In other examples, a combiner takes the form of a non-planar sheet. Such combiners may find use as a lens in a pair of spectacles, for example. In non-planar combiners, the input and output surfaces of the combiner may be on the same or opposite sides of the sheet depending on the function of the combiner, as described above.
PCT patent application publication no. WO2023/057543, having priority date 6 Oct. 2021, which is hereby incorporated by reference for all purposes, describes a method of displaying a target light field using an image-replicating combiner. The method comprises determining a target light field to be displayed at a viewing location; determining a transfer function describing the propagation of light through the image-replicating combiner between the viewing location and an input location near to an input surface of the image-replicating combiner; determining an input light field by applying the determined transfer function to the target light field; and displaying the input light field at the input location. Using this method, it is possible to generate a desired light field at a desired location.
When combining the features of the systems shown in
A feature of image-replicating combiners is that internal rays repeatedly split into reflected and transmitted rays. The etendue of the output ray ensemble is larger than that of the input ensemble. In terms of phase space, the phase volume of possible output ray positions and angles is larger than the phase volume of possible input ray positions and momenta. Typically, the maximum valid eyebox and field of view (or more specifically the phase volume) of an output light field after propagation through a typical, planar, image-replicating combiner, are no larger than the pupil and field of view (or more specifically the phase volume) of the input light field, respectively. The term “valid eyebox” here refers to an eyebox substantially without noise and/or artefacts. Typically, the phase space is 4-dimensional and comprises the two spatial dimensions and two angular dimensions. A phase space representation labels each ray through a given plane with spatial coordinates (representing the point it intersects the plane), and angular coordinates (representing the direction in which it is heading relative to the plane). A light field describes the intensity of each point in this phase space. The input light field spans some volume in phase space (a ‘phase volume’), with the output light field spanning a larger phase volume than the input due to the replication process. PCT patent application publication no. WO2023/057543 then describes that a target light field can be generated whose volume in phase space is no larger than the first volume, and which can be targeted anywhere within the second volume.
The action of the image-replicating combiner represented in
In the phase space representation, the offset in z corresponds to a shear in the (x, θ) plane, and so the replicated light fields at the output of
The above descriptions referencing
In further examples, the display system 900 may further comprise eye-tracking sensors. The eye-tracking sensors may generate live data about the current location of a viewer's pupil and relay this to a computing device. The computing device may then determine where the target light field is required to be generated such that the resulting light field at the image plane is at the current location of the centre of the viewer's pupil. In practice, the viewer may move their eyes based on a number of factors such as a change in position of an object of interest in the image that is currently being displayed, a change in brightness of the displayed image, and movement of the user themselves as they are viewing the image.
The geometry of how discrete replications appear in phase space is a property of the image replicating combiner. In order to be generally compliant with the tessellating condition described above it is clear that the image replicating combiner should be designed to provide optimal tiling of the replicated outputs in phase space. Specifically, it should be designed such that 1) A high fraction of the volume in phase space required for a target output phase volume is spanned by the combined phase volumes of the discrete replications; and 2) A low fraction of the volume in phase space required for a target output phase volume is covered by more than one overlapping discrete replication. In some examples, the combiner should be designed such that the combined phase volumes of the discrete replications span as much as 75%, 80%, 90%, 95%, and 99% of the volume in phase space required for a target output phase volume. However, a sufficiently high fraction depends on the characteristics of the light field and the pupil size of the user. In certain cases, an acceptable fraction could be as low as 5% (e.g. for a sparsely-sampled light field and highly dilated pupil). The volume in phase space covered by more than one overlapping discrete replication may be between 50-10% of the target output phase volume and could be as low as 5%, 1%, or even 0% of the target output phase volume.
The ideal situation is described above, where the majority of the target phase volume is spanned with minimal overlap. However, it may not be possible or efficient to produce an input light field with a sufficiently large phase volume, nor to produce an image-replicating combiner that does not have gaps between replications, so the preferred design may need to consider these practical limitations.
Referring to
The replication pitch 1318, and hence also the gap between replications 1320, is a function of the angle at which light enters the image replicating combiner 1304. In this picture of one-dimensional replication, perfect tessellation of the input light field requires that the gap between replications is zero. Correspondingly, a two-dimensional input light field may only be perfectly tessellated by two-dimensional image replicating combiner (with two axes of replication) for a single direction of input light rays or viewing angle. Referring to
Referring to
As discussed above, the design of a 2D image replicating combiner might be such that the replicated phase volumes tessellate on a non-rectilinear grid. For example, an image replicating combiner whose replicated phase volumes tessellate on a rhombic grid would have particular use with the filter 400 shown in
Having explained the theory and overall construction of a holographic display according to the present disclosure, its method of operation will now be explained.
At 1404, the method 1400 comprises determining a second light field, H2, for quantisation, the second light field having a Fourier transform, F(H2), such that it does not substantially overlap a Fourier transform of its complex conjugate, F(H2*).
At block 1406, and at a first time, the method 1400 comprises displaying a quantised version of the first light field using the holographic display system shown in
At block 1408, and at a second time, the method 1400 comprises displaying a quantised version of the second light field using the holographic display system, wherein a second subset of apertures corresponds to an extent of F(H2) in a Fourier plane such that components corresponding to F(H2*) resulting from quantisation are substantially blocked by the filter. The first subset of apertures is preventing (blocking) light from passing, and the second subset of apertures is allowing light to pass. It will be appreciated that method 1400 may be continued for each light field required to cover a desired area of the Fourier plane, for example corresponding to an area of a viewer's pupil, and is not limited to only two light fields. Blocks may also be executed in a different order and/or in parallel.
The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2211261.9 | Aug 2022 | GB | national |
This application is a continuation under 35 U.S.C. § 120 of International Application No. PCT/GB2023/052033, filed Aug. 1, 2023, which claims priority to GB Application No. GB2211261.9, filed Aug. 2, 2022, under 35 U.S.C. § 119(a). Each of the above-referenced patent applications is incorporated by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| Parent | PCT/GB2023/052033 | Aug 2023 | WO |
| Child | 19043199 | US |
