Patent Application
20240160152
The present invention relates to holography and methods of generating holographic images.
Computer Generated Holography, CGH, is known. A holographic light field is determined for display using coherent or at least partially coherent light and is defined in terms of an amplitude and phase of each element (pixel) of a display. This combination results in a light field perceived with depth information by a viewer. An ideal holographic display for such a light field is capable of full-complex modulation where the amplitude and phase values at each pixel of the hologram can be varied to very closely resemble the determined amplitude and phase of the light field. In other words, an ideal holographic display is capable of displaying all possible combinations of phase and amplitude.
In practice, displays used for CGH cannot achieve perfect full-complex modulation. Typical displays used for CGH may only have a very limited number of values they can display. For example, the 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 Digital Micromirror Device, 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 reduces the image quality, visible in the perceived image as reduced contrast and/or noise.
It is known to improve the quality of quantised holograms for display through iterative methods such as the Gerchberg Saxton algorithm. However, these methods require many iterations (perhaps 100 or more) and so require significant processing resources and/or power. This is especially apparent for moving holograms, where such iterative methods may reduce a frame rate and/or introduce a lag.
It would be desirable to improve the image quality of CGH displays with reduced requirements for processing resources and/or power.
According to a first aspect of the present invention, there is provided a holographic display system comprising: 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 a spatial filter delimiting an aperture in a Fourier plane. A Fourier transform of the target light field, F(H), substantially does not overlap (i) a Fourier transform of a complex conjugate of the target light field, F(H*), (ii) a Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH*), (iii) a Fourier transform of a square of the target light field, F(H2), and (iv) a Fourier transform of a square of the complex conjugate of the light field F(H*2); and the aperture substantially corresponds to F(H) in the Fourier plane.
Such a construction can improve an image quality of displayed holograms by the combination of limitation on an extent of the target light field in the Fourier plane (by defining that it cannot overlap the Fourier transform of its complex conjugate and the higher order terms) and the positioning of the aperture to correspond to F(H) in the Fourier plane. By F(H) it is meant the part of the Fourier plane which has non-zero values. It has been found that this arrangement prevents additional components in the Fourier plane that are introduced by quantisation for display. Furthermore, determining H in this way is computationally simpler than prior iterative methods, such as Gerchberg Saxton, reducing requirements for processing resources. This can allow higher quality holographic displays with reduced processing and/or power requirements, allowing displays to be one or more of lower-cost, more portable, and for battery-powered devices, of increased battery life.
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 additional terms of the series expansion and ensuring those do not overlap with F(H) so that the additional components are blocked by the filter, additional image quality can be obtained. The energy in series expansion tends to be concentrated in lower order terms, so ensuring no overlap with at least F(H*) is useful, the next higher order terms such as F(HH*), F(H2) and F(H*2) are also useful but there comes a point where the impact of each term is small and imposing further constraints has little observable impact on image quality.
The light source may be, for example a laser or other coherent or semi-coherent light source. It may comprise a single emitter or multiple emitters and may emit light having a single wavelength or multiple wavelengths.
The modulator can be any modulator or modulation means suitable for modulating an amplitude and/or phase of coherent or semi-coherent light. This includes Liquid Crystal on Silicon (LCoS) devices, Digital Micromirror Devices (DMD) and Liquid Crystals. In one example, the modulator is a spatial light modulator.
The spatial filter can be any suitable means of forming a Fourier plane and a means for spatially filtering light in that plane. In one example, the spatial filter comprises: a lens having a focal length; and a filter delimiting the aperture. The filter and the modulator are positioned on opposite sides of the lens, at a distance of one focal length from the lens. The lens is preferably a Fourier lens and may be formed from multiple elements. In some examples the lens may be a lens array, where the lenses comprising the array extend over an imaging area.
The modulator, lens and filter may be substantially coaxial in some examples. Other arrangements are also possible, for example a folded optical path with mirror and/or prism elements in the optical path, possibly to allow a more compact arrangement.
The filter delimits an aperture through which light can pass and generally blocks or otherwise prevents light from passing outside the aperture (for example the filter may be configured to absorb light outside the aperture, or to reflect it elsewhere, outside of an optical path).
Further constraints can be placed on F(H) in some examples.
Due to the presence of the filter, less than all of the Fourier plane which can be produced by an SLM is actually used. This may result in display dimming or a reduction in the size of the area in which the displayed hologram can be viewed. While there are no particular constraints on the shape of the perimeter of F(H), providing it meets the non-overlapping requirement with at least F(H*), F(H2), F(H*2) and F(HH*), an analysis of the behaviour of functions in the Fourier plane has shown that well defined areas can be defined. In some examples at least part of a perimeter of the aperture may be a straight line. This may allow a larger area for display than a curved perimeter.
The Fourier plane may be partitioned into a plurality of contiguous unit squares, wherein each unit square receives one copy of the Fourier transform of the target light field. The aperture may then have an area approximately ⅙th of a unit square. As will be explained in more detail later, the unit square is a result of taking the Fourier transform of the discrete grid of the modulator which creates a repeating pattern. A ⅙th area is understood to set a limit on the maximum size of the aperture which can meet the non-overlapping constraint.
In some examples, the perimeter of the aperture is a quadrilateral. Suitable quadrilaterals include rectangles, squares and trapeziums. Some examples use right trapeziums, other examples use isosceles trapeziums for the aperture. (Trapeziums may also be referred to as trapezoids, so a right trapezium is a right trapezoid, and an isosceles trapezium is an isosceles trapezoid.)
While some examples may have a single aperture, in other examples the filter may delimit at least two apertures. The at least two apertures may not be contiguous.
In some examples, the filter comprises a plurality of portions which can be selectively controlled to have a first state, in which light is blocked, or a second state to allow light to pass, whereby the aperture is formed by portions in the second state. This allows the position and extent of the aperture to be controlled as required. For example, with a suitably responsive display, holograms with different positions of target light field may be displayed in rapid temporal succession. This may expand the range of positions in which the displayed hologram can be viewed or to increase a perceived image quality.
As discussed above, the spatial light modulator may be a digital micromirror device (DMD). The display system and methods discussed herein can provide significant improvement to the image quality of a DMD because of its binary nature. 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. When the spatial light modulator is an amplitude-only SLM, such as a DMD, the display system and methods described herein may allow display of holograms with an improved (darker) black level.
The position and size of the aperture is determined with reference to a square with dimensions based on a wavelength of light from the light source. Some examples may use a single wavelength for a monochrome display. In other examples, the light source is configured to emit at least partially coherent light at two or more different wavelengths for a range of color, such as red, green and blue wavelengths that can be switched sequentially for a color display. In one example, the light source is configured to emit at least partially coherent light at a plurality of wavelengths, including green light, and the aperture corresponds to a position of F(H) for green light. Green light may have a wavelength in the range of 495-570 nm or in the range of 520-560 nm, such as around 530 nm. In another example, the aperture corresponds to a portion of F(H) with the at least partially coherent light at a smallest wavelength of the two different wavelengths. In that case, the aperture may only be optimised for one wavelength. Some examples may adjust the size of the aperture to correspond to the wavelength, for example using the aperture with selectively controllable portions discussed above. In other examples, the lens has optical properties configured such that the aperture corresponds to F(H) with the at least partially coherent light at both wavelengths. The optical properties include at least one of a shape and a refractive index.
The light source may be configured to emit at least partially coherent light at a plurality of wavelengths and at least one side of the aperture is angled at 45°. For example, the at least one side may be angled relative to an axis defining a unit square of the Fourier plane. This may be useful because an aperture can be positioned so that the conjugate, F(H*) does not overlap for all wavelengths.
The light source may comprise at least two emitters positioned such that a zero-order of the Fourier plane is in a different position for each of the at least two emitters, and wherein the filter delimits at least two apertures, at least one for each of the at least two emitters. This can allow a greater portion of the Fourier plane to be covered by tiling the apertures for different emitters. Each emitter may have its own respective aperture(s) delimited by the filter, independent from other aperture(s) for the other emitters. The apertures may be at least partially overlapping, such that an aperture for one emitter shares at least part of its open area with an aperture for another emitter. The at least two emitters may be operated in time sequence with their respective apertures. For example a first emitter and a first aperture is activated, followed in time by activating a second emitter and a second aperture.
The light source may comprise a first emitter with a first wavelength and a second emitter with a second wavelength, and wherein the first and second emitter are positioned such that F(H) of one the first and second emitters is contained within F(H) of the other of the first and second emitters. This can mean that the same aperture is suitable for both the emitters.
In accordance with another aspect, there is provided a filter delimiting an aperture that corresponds to a Fourier Transform, F(H), of a target light field, H, in a Fourier plane, wherein the Fourier Transform F(H) does not overlap with (i) its complex conjugate, F(H*), (ii) a Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH*), (iii) a Fourier transform of a square of the target light field, F(H2), and (iv) a Fourier transform of a square of the complex conjugate of the light field F(H*2) in the Fourier plane. Positioning such a filter in a holographic display may allow the display to benefit from the image quality improvements discussed herein, when combined with controlling the display to display a corresponding target light field H. The filter and the aperture may have any of the features discussed above for the filter and the aperture.
In use, the filter may be positioned at different positions in the optical path, such as occupying a “pupil-plane” or an “image-plane”. A pupil-plane is a plane corresponding to an image of the modulator as will be reproduced on a viewer's pupil, and may allow more freedom in the design of the aperture. Pupil-planes, and pupil-like planes, have the property that gaps may be present in the aperture without significantly altering the viewed image. When the filter is not positioned in a pupil-plane or a pupil-like-plane, then it is said to be in an image-plane. When the filter is positioned in an image plane, gaps in the aperture may be visible to a viewer, so that it is preferred to avoid such gaps in the aperture. Examples will be described later with reference to
According to a further aspect, there is provided a method comprising: determining a target light field, H, for quantisation, the target light field having a Fourier transform, F(H), that it does not overlap (i) a Fourier transform of its complex conjugate, F(H*), (ii) a Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH*), (iii) a Fourier transform of a square of the target light field, F(H2), and (iv) a Fourier transform of a square of the complex conjugate of the light field F(H*2); and displaying a quantised version of the target light field through a filter delimiting an aperture corresponding to an extent of F(H) in a Fourier plane such that components corresponding to F(H*), F(HH*), F(H2), and F(H*2) resulting from quantisation are substantially blocked by the filter.
A Fourier transform of the target light field, F(H), therefore is limited in extent and occupies only part of the Fourier plane. While this may result in a dimmer image and/or reduced viewing area, the constraints mean that components introduced by quantisation are filtered and do not reach a viewer's eye, improving image quality.
F(H) may additionally not overlap a Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH*). In further examples F(H) additionally does not overlap at least one of (i) Fourier transform of the square of the target light field, F(H2) and (ii) the Fourier transform of the square of the complex conjugate of the light field F(H*2).
Although the shape or extent of F(H) in the Fourier plane can be anything that meets the constraints, in some examples, an extent of F(H) in the Fourier plane has at least one straight perimeter. The extent of F(H) in the Fourier plane may have a quadrilateral perimeter. The extent of F(H) in the Fourier plane may comprise at least two discontinuous regions.
A target light field having F(H) in the correct region of the Fourier plane can be determined in any suitable manner. For example, it can be determined by applying a mask to an initial light field in the Fourier Plane. In this way the extent of the target light field is limited in the Fourier plane. The initial light field can be a full-complex representation of a target light filter occupying the full addressable extent of the Fourier plane. The mask may be applied in the Fourier Domain by setting values under the mask to zero or a predetermined value.
Display of the quantised image can happen in any suitable way, for example by illuminating a spatial light modulator with coherent or semi-coherent light and controlling the SLM to adopt the inverse Fourier transform of the masked light field.
An advantage of the method of the invention is that it reduces computation requirements, through the positioning of the filter and the limits of F(H), the processing can be thought of as allowing noise to be put into ‘don't care’ areas blind. In other words the aperture design ensures that the noise will be reduced without needing to evaluate the exact noise field. This is unlike Iterative Fourier Transform Algorithms (IFTAs) such as Gerchberg Saxton (GS). In GS and other IFTAs the replay field of the image must be reconstructed computationally and iteratively improved, requiring significant processing resources. Some examples may use IFTA in combination with the aperture. This may allow an improved image quality with reduced processing because fewer iterations are required due the action of the filter to reduce noise.
As such any suitable quantisation method and resolution, quantised in phase and/or amplitude, can be used. For example, the quantisation may be the nearest value that can be reproduced by the display, the nearest value that can be produced by the display without increasing an amplitude, the nearest value that can be produced by the display without increasing a phase, and so on. Some examples may apply a real offset, such as to the masked light field, before quantising. The real value offset may be based on an average amplitude of the values prior to quantisation, such as a root mean square (rms) amplitude. Another example may quantise |H+c|∧2. In such examples the preferred quantisation may not be the quantisation scheme that minimises the total quantisation power at the SLM. If we denote the quantised version of H as HQ, then the quantisation error can be written as an additional noise field, EQ=HQ−H. Ordinarily the total noise power in F(H) would be minimised by minimising EQ, which may be achieved by quantising each pixel to the nearest available value. However, certain quantisation schemes may be used which increase the combined noise power in F(H*), F(H2), F(H*2) and F(HH*), but reduce the noise power in F(H). Such quantisation schemes may increase the noise power E Q compared to nearest-neighbour quantisation, whilst still reducing the noise power in F(H) that is transmitted through the aperture.
The method may comprise generating a plurality of target light fields in different regions of the Fourier domain, each of the plurality of target light fields having the property that an extent of their Fourier transform does not overlap with an extent of the Fourier transform of their complex conjugate; and displaying a quantised version of each of the plurality of target light fields in rapid temporal succession through a respective filter delimiting an aperture corresponding to the extent of their Fourier transform in a Fourier plane. This can increase an area in which the hologram can be viewed.
According to another aspect, there is provided a computer-readable medium, such as a non-transitory computer readable medium, comprising instructions, that, when executed by a processor, cause a holographic display system discussed above to display a holographic image according to the method discussed above.
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 focusing 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.
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) of a display. 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 is a binary display, capable of generating images comprising pixels taking one of two possible amplitude or phase values. An example binary amplitude display 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, 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 components in the quantised hologram using a physical filter in the display apparatus. By approximating a quantised representation, HQ, of a target light field as a series expansion, a quantised field can be determined in which 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 despite 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.
H
Q
≅α+bH+cH*+dH
2
+eH*
2
+fHH*+ Eq. 1
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 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(HQ) can be expressed as equation 2 below:
F(HQ)=αF(1)+bF(H)+cF(H*)+dF(H2)+eF(H*2)+fF(HH*)+ Eq. 2
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, α, in Eq 1 is a delta function, multiplied by a, and centred at kx, =ky=0, as represented by the term αF (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
Once the position of F(H) in the Fourier plane is known, the position of the Fourier transform of H*, F(H*), can be determined from the position of F(H). Within the Fourier plane, this is a reflection in the line ky=−kx. The result is shown 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 filter delimiting an aperture corresponding to the region in the Fourier plane to which F(H) has been targeted. A 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 filter can therefore block 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 the considered noise components ensures that light corresponding to F(H) reaches the target plane while blocking 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
It follows that the maximum area that F(H) can occupy in the Fourier plane, while satisfying the condition of no overlap of noise components relating to F(H*), F(HH*), F(H*2) and F(H2), is ⅙th of the total area of the filter. Further, the shape of the aperture is constrained by the non-overlap condition described above.
The filters 200, 210, 220, 230, 240, 250 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 reflections 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 original 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
The aperture 242 has a base centred ¾ the way along the base of the filter 240 and having a length ⅙ the width of the filter 240. The aperture 242 further has a left edge centred ¾ the way up the left edge of the filter and having a length of ⅙ the width of the filter 240. The lower corner of the left edge of the aperture 242 is connected to the left corner of the base of the aperture 242 by a straight line, and the upper corner of the left edge is connected to the right edge of the base by a further straight line.
Portions of the filter 246, 248, shown as solid lines in the filter 240, indicate where the filter could alternatively delimit apertures to achieve the same effect by rotation and/or reflection of the apertures 242, 244.
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 other components 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. In further examples, 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 apertures 202, 212, 222, 232, 242, 252 shown in
The present disclosure is not however limited to the time-multiplexing technique discussed above being used in combination with the aperture conditions or/and quantisation schemes above. Other algorithmic methods, such as windowed IFTA, may use a delimiting aperture less than the area of a unit square in the Fourier plane (i.e. each sub-aperture spans less than one diffraction order) as a means for increasing image quality. That is, in some examples, windowed IFTA, such as windowed GS, can be utilised to constrain only a sub-region of the Fourier plane and to have a ‘don't care region’ or ‘noise region’ that is blocked by the filter, thereby improving image quality in the chosen sub-region, but at the cost of reducing either the field of view (when the filter is in the image plane) or the eyebox (when the filter is in the pupil plane). The full field of view or eyebox can be reproduced by time-multiplexing each sub-region and blocking the ‘don't care’ regions so that the viewer will perceive a single hologram, through persistence of vision. While this may increase requirements on processing resources, when computational power is available to apply such iterative methods, this may have advantages over other methods known in the art.
When spatial filtering is in an image plane, if the union of all the apertures of the spatial filter has any gaps, or an irregular outline etc, that is visible in the image, and this is constraining on the set of apertures that can be used, and on the specification of the actual physical switchable apertures. However, if the spatial filtering is in the pupil plane, then any gaps or irregular outlines are not apparent to the viewer (if there are gaps, non-uniformities or outlines then these are only visible as slight difference to the bokeh and point-spread-function, which viewers are unlikely to notice).
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 tiled within each unit cell of the filter so that multiple portions exist per unit cell, i.e. the portion of the filter with dimensions λf/p. The SLM may then be configured to generate the holographic light field, H, so that F(H) is targeted at one or more deactivated portions of the filter. Synchronising the deactivated 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. As discussed above with reference to
A central portion 317 of the filter 300 corresponding to the zero-order mode is always blocked to prevent light corresponding to F(HH*) and the zero order from passing through the filter 300. Further, with this particular arrangement of portions, an outer region 318 of the filter 300 is always blocked. The filter 300 provides a larger eyebox than is possible with the filters 200, 210, 220, 230, 240, 250 comprising static apertures 202, 212, 222, 232, 242, 252. The presence of the central portion 317, which is always blocked, makes this filter well-suited to use positioned in a pupil-plane: in that case the blocked central portion will not significantly affect the perceived image. The filter can also be used positioned in an image plane, but the blocked central portion may be more visible in that case.
The controllable portions of
Although the filter 300 of
In the previous discussion of
The SLM 404 is configured to generate a light field which is a quantised representation of a target light field, H, as has been discussed above. The arrangement of the holographic optical system 400 is such that the Fourier transform of the light field, F(H), is formed at a plane coinciding with the position of the filter 408. This plane is the Fourier plane of the SLM 404 as imaged by the lens 406. The target light field is determined such that the Fourier transform of the target light field, F(H), does not overlap at least the Fourier transform of the complex conjugate of the target light field, F(H*) and the second order components in the Fourier plane of the SLM 404. Further, the aperture in the filter 408 corresponds to F(H) in the Fourier plane, such that portions of the target light field outside of F(H) are blocked.
The light source 402 may, for example, comprise a laser module or an LED. The light source 402 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 404 may be configured to modulate at least one of the phase, amplitude, binary phase and binary amplitude of the light. The SLM 404 may be, for example, a DMD, an LCD, an amplitude LCoS or a phase LCoS.
The filter 408 corresponds to the area targeted by F(H) and may be any of the filters shown in
For clarity,
Having explained the theory and overall construction of a holographic display according to the present disclosure, its method of operation will now be explained.
Next, at 504, a quantised version of the target light field is displayed through a filter delimiting an aperture corresponding to the extent of F(H) in the Fourier plane, such that at least the Fourier transform of its complex conjugate, F(H*) and the second order components, are blocked by the filter.
The method 600 begins at block 602 by receiving a target light field. The target light field is a 2-dimensional array representing one image layer to be displayed by the holographic optical system. The target light field is converted into a complex target light field 602 by applying a respective random phase factor, ei9, to each pixel. This acts to rotate each pixel value in the complex plane, giving each pixel an imaginary component. The phase values have a statistically uniform distribution across the light field. Each random phase factor may comprise a matrix of random numbers to be applied to a target light field comprising a matrix of pixels.
At block 604, the complex target light field undergoes a Fourier transform (such as a Fast Fourier Transform, FFT) to simulate the light field at a viewer's pupil. The simulated pupil is then masked at block 606 to form an apertured pupil. Applying a mask could be setting the amplitude to zero, for all portions of the simulated light field outside the aperture. The apertured pupil is a subregion of less than all the field from block 604, wherein the shape of the subregion is dictated by the particular mask used. In practice, the particular mask used coincides with the aperture selected in the filter of the holographic optical system. For example, as shown in
So far, the image will be perceived as positioned at infinity, so at block 608 a defocus Zernike polynomial is applied to the output of block 606 resulting in a defocussed image at a target depth on a plane coinciding with the SLM. In general, the properties of the defocus Zernike polynomial are determined by the parameters of the holographic optical system. For example, the SLM has N×M pixels and a pixel pitch p. A lens with a focal length, f is positioned one focal length from the SLM, and the SLM is illuminated with light of a single wavelength, A. For a layer at depth d, and an SLM at optical infinity, the apertured pupil 606 is multiplied by a defocus Zernike: exp(2πi(2r2−1)/4dλ), where r is the radial distance (in metres) of each sample point from the centre of the apertured region. The spatial sampling of the pupil is fλ/pN in the x-direction and fλ/pM in the y-direction, from which the value of r for each point can be determined. The method is not limited to the use of Zernike polynomials, other methods may be used such as a parabolic phase function.
By applying the defocus Zernike polynomial after the masking at block 606, the processing required may be reduced because the extent of the field is smaller than if the polynomial was applied after block 604. However, block 608 may occur after block 604 and before block 606 in some examples.
The defocussed apertured pupil from block 608 undergoes an inverse Fourier transform at block 610, resulting in a light field at the depth of the SLM. It can be observed that although the aperture is restricted in the Fourier plane, the inverse Fourier transform means that the full extent of the SLM is still used to display the image. (In the same way that filtering a time-varying waveform in the Fourier domain still results in a time domain waveform of the same length in time, filtering the Fourier plane still results in the full extent of the SLM being used for display.)
The resulting light field from block 610 can then be quantised to form a quantised representation of the resulting light field. Any suitable quantisation scheme can be applied, as discussed above. The process 600 determines a holographic light field to be formed by an SLM, such as the SLM 404, such that the Fourier transform of the light field is formed in an area of the Fourier plane corresponding to a pre-defined aperture in a filter.
Looking at
As discussed so far,
In some examples the filter comprises a plurality of portions that can be selectively controlled to pass or block light, such as the filter 300 shown in
The apertures of
As shown in
As shown in
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 |
|---|---|---|---|
| 2110495.5 | Jul 2021 | GB | national |
This application is a continuation under 35 U.S.C. § 120 of International Application No. PCT/GB2022/051867, filed Jul. 19, 2022 which claims priority to United Kingdom Application No. GB 2110495.5, filed Jul. 21, 2021, 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/GB2022/051867 | Jul 2022 | US |
| Child | 18416480 | US |
