Holographic displays and methods

Abstract

A holographic display is provided. The display includes (i) an illumination source configured to emit at least partially coherent light, and (ii) a liquid crystal layer including an array of elements arranged to be illuminated by the light. The layer is configured such that (a) when a first electric field is applied across the elements of the liquid crystal layer, the light from the elements has a first polarization state, (b) when a second electric field is applied across the elements, the light has a second polarization state, and (c) when a third electric field is applied across the elements, the light has a third polarization state. The display further includes (iii) a controller configured to control the electric fields applied across the elements, and (iv) an output polarizing element configured to (a) remove a portion of the light having the first polarization state and transmit a portion of the light having the first polarization state, (b) remove substantially all of the light having the second polarization state, and (c) remove a portion of the light having the third polarization state and transmit a portion of the light having the third polarization state. In this display, one of: (1) the second electric field is greater than the first electric field and the third electric field is greater than the second electric field; and (2) the second electric field is less than the first electric field and the third electric field is less than the second electric field.

Description

[Technical field]

[0001] The present invention relates to a holographic display and a method for operating a holographic display. [Background technology]

[0002] Computer Generated Holography (CGH) is known. A holographic light field is determined for a display using coherent or at least partially coherent light, defined in terms of the amplitude and phase of each element (such as a pixel) of the display. This combination results in a light field with depth information that is perceived by the viewer.

[0003] An ideal spatial light modulator (SLM) for a holographic display would be capable of full-complex modulation, where the amplitude and phase values ​​at each pixel of the hologram can be varied to closely resemble the determined amplitude and phase of the light field. In other words, an ideal SLM would be able to display all possible combinations of phase and amplitude.

[0004] In fact, SLMs used for CGH cannot achieve full complex modulation. Typically, SLMs have only very limited values ​​that they can display. For example, SLMs may only have the ability to modulate either amplitude or phase. Resolution may also be limited to roughly 8-bit resolution (giving 256 or fewer displayable values), or in the case of a binary display, only two values.

[0005] As a result, the pixels of the full complex holographic image are quantized to values ​​that can be reproduced by the SLM for display. For example, in the extreme case of a binary SLM (digital micromirror device, DMD, etc.), each pixel of the display can only be in one of two states. Therefore, every point on the full complex Argand diagram needs to be mapped to one of two states. This process of quantization reduces the visible image quality in the perceived image, such that contrast and / or noise are reduced.

[0006] Fourier plane filtering can be used to encode complex CGH data for display on an amplitude-only SLM. In this case, a complex conjugate is added to the full complex value to create a real value, and an additional constant term is added to create a positive real value. The conjugate and constant terms are then filtered in the Fourier plane by a spatial filter, so that the remaining components are only related to the original full complex value. However, because a constant term must be added in this method, it introduces a significant zero-order component, requires precise spatial filtering, and reduces brightness.

[0007] Methods have been proposed to encode a full complex hologram by interfering light from two elements, such as Double Phase Amplitude Coding (DPAC), but it is difficult to achieve near-zero amplitude and adequate interference between pixels.

[0008] It is therefore desirable to improve the image quality of holographic displays. Summary of the Invention

[0009] Spatial light modulators (SLMs) can modulate light in a variety of ways. One method is to use liquid crystals arranged in an array of elements / pixels, which change the polarization state of incident light as it passes through the element. The liquid crystal layer is birefringent, meaning that the index of refraction is a function of the polarization state of the incident light relative to the axes of the crystals. The orientation of the crystals in each element can be changed by controlling the voltage applied between the electrodes of the element, which in turn applies an electric field to the liquid crystals. This voltage-controlled change in the orientation of the crystals thus controls the polarization / rotation of the light by the element. Thus, applying a voltage / electric field to a particular element will rotate the incident light beam by an angle that is dependent on the applied voltage / electric field. It will be understood that control of the effective strength of the applied electric field can be achieved via analog control by voltage (i.e. high / low electric field), pulse width modulation (i.e. applied voltage with a high / low duty cycle), or any other means.

[0010] In addition to the liquid crystal layer, the SLM may include an output polarizing element (such as an output polarizer) disposed after the liquid crystal layer. In some examples, the output polarizing element is separate from the SLM. At a certain electric field / voltage, the polarization state of the light after passing through the liquid crystal layer is such that substantially all of the light is transmittable by the output polarizing element. At a different electric field / voltage, the polarization state of the light after passing through the liquid crystal layer is such that the light is blocked / removed by the output polarizing element. Thus, the amplitude of the light can be controlled by controlling the voltages applied to the elements of the SLM (and therefore the electric field applied between the elements). As is well known, the transformation of the light as it passes through the liquid crystal layer can be expressed in terms of the Jones matrix that characterizes the liquid crystal layer.

[0011] An SLM may be reflective or transmissive, and references to "SLM" herein are not limited to reflective or transmissive SLMs. A transmissive SLM may be configured such that light is primarily transmitted through the SLM from one side to the other. A reflective SLM may be configured such that light is primarily reflected by the SLM. A reflective SLM includes a mirror such that light passes through an element of the liquid crystal layer, is reflected, and then passes through that element a second time in the opposite direction. Exemplary reflective SLMs include liquid crystal on silicon (LCoS) displays. For reflective SLMs such as LCoS, where reflection causes light to pass through the layer twice, it will be appreciated that the Jones matrix associated with the liquid crystal layer represents the transformation after a double pass through the liquid crystal layer. Thus, the Jones matrix associated with the liquid crystal layer represents the transformation of light passing once in the case of a transmissive SLM and twice in the case of a reflective SLM.

[0012] Existing amplitude-modulating SLMs (i.e., an SLM that includes a liquid crystal layer and an output polarizing element) modulate the amplitude of light between an "off" and an "on" state. For example, when the light is completely blocked / filtered / deflected, the amplitude of the light is said to be "0" (i.e., the SLM in the area of ​​that element / pixel can be "off"). When substantially all of the light is transmitted, the amplitude of the light is said to be "1" (i.e., the SLM in the area of ​​that element / pixel can be "on"). Thus, conventional SLMs modulate the amplitude in the range of 0 to 1.

[0013] Briefly, holograms calculated with a CGH are generally complex-valued, and these complex values ​​are quantized to a number of discrete values ​​that are displayed by the SLM. An ideal SLM should be able to modulate the complex values, i.e. the modulation associated with each pixel / element of the SLM is Ae iθ where A is the amplitude and θ is the phase, and each element of the SLM is used to individually control A in the range 0 to 1 (i.e., [0,1]) and θ in the range 0 to 2π (i.e., [0,2π]).

[0014] However, unlike these ideal SLMs, commercially available SLMs typically modulate only the phase or only the amplitude. That is, phase-only SLMs modulate e for θ in the range [0,2π]. iθ The amplitude-only SLM applies a modulation defined by Ae for A in the range [0,1]. if(A) We apply a modulation defined by: where f(A) is a function of amplitude. f(A) is ideally constant, but in some cases, an amplitude-only SLM may partially modulate the phase over a small range as the amplitude varies. Because this phase depends on the amplitude, the relationship of f(A) means that the phase is not modulated independently of the amplitude.

[0015] Methods exist to encode full complex holograms using phase-only or amplitude-only SLMs. For example, dual-phase amplitude coding (DPAC) uses two elements of a phase-only SLM to coherently interfere together to encode e iθ1 +e iθ2 where θ1 is the phase introduced by the first element and θ2 is the phase introduced by the second element. DPAC can be effective, but is very sensitive to precise control of the phase value to achieve near-zero amplitude, and proper interference of two phase-only elements can be difficult to achieve.

[0016] The inventors have recognised that an SLM may be modified to modulate the amplitude of light over a range extending to either side of "0" (i.e., zero amplitude) rather than the range 0 to 1 (i.e., [0,1]) when represented in an Argand diagram. A "negative" amplitude has the same intensity as a corresponding "positive" amplitude, but can be thought of as having a phase shift relative to light having the same positive amplitude, such that negative and positive amplitude light appear in different quadrants on the Argand diagram. In other words, the SLM is configured such that a substantially zero output amplitude is obtained at intermediate modulation values, rather than at the ends of the modulation range as is conventionally the case.

[0017] As an example, the SLM may be modified to modulate an amplitude in the range [-√0.5, +√0.5] on the Argand diagram (which corresponds to an intensity modulation in the range [-0.5, +0.5]). In one particular example, light with a negative amplitude may have a phase shift of π radians relative to light with a positive amplitude.

[0018] The inventors have discovered that operating the SLM to modulate the amplitude through a "zero" has several advantages.

[0019] First, the modified SLM can achieve amplitudes closer to zero than existing methods (such as DPAC) can: for example, a single element can be operated more precisely to achieve an amplitude of zero without having to interfere with light from another element.

[0020] As a second advantage, unlike the encoding method of adding a constant value to map to a positive-only amplitude, the zeroth order diffracted light in the light field is much reduced (i.e., the energy of the zeroth order is much lower than when modulating in the range [0,1]). This results in a hologram of higher quality compared to conventional holographic displays, where the energy of the zeroth order light is high and must be removed with an additional step of spatial filtering. For example, as briefly mentioned, in many holographic displays, after the light is modulated by the SLM, a spatial filter can be used to remove unwanted components of the light by placing the spatial filter in the Fourier plane of the optical system. Thus, after passing through the SLM, the light enters a lens and is focused to the Fourier plane where the spatial filter is located. The spatial filter may physically block certain regions of the light field to remove unwanted components of the light, including the complex conjugate of the light field and the zeroth order of the light field. When the zeroth order contains a significant amount of power, filtering is often insufficient due to stray light and incomplete filtering. This reduces the image quality of the displayed hologram. By operating the SLM to modulate the amplitude on either side of the zero amplitude, the zero order does not necessarily have to be removed, resulting in holograms of higher quality compared to conventional holographic displays. Nevertheless, if the zero order is removed, in some cases filtering becomes much less of a problem due to the lower energy of the zero order, again resulting in lower overall noise.

[0021] Thus, in a first aspect of the invention, there is provided a holographic display comprising: (i) an illumination source configured to emit at least partially coherent light; and (ii) a liquid crystal layer including an array of elements arranged to be illuminated by the light. The liquid crystal layer is configured such that (a) when a first electric field is applied across the elements of the liquid crystal layer, light from the elements has a first polarization state, (b) when a second electric field is applied across the elements of the liquid crystal layer, light from the elements has a second polarization state, and (c) when a third electric field is applied across the elements of the liquid crystal layer, light from the elements has a third polarization state. The display further comprises (iii) a controller configured to control the electric fields applied across the elements of the liquid crystal layer, and (iv) an output polarizing element. The output polarizing element is configured to (a) remove a portion of the light having the first polarization state and transmit a portion of the light having the first polarization state, (b) remove substantially all of the light having the second polarization state, and (c) remove a portion of the light having the third polarization state and transmit a portion of the light having the third polarization state, and one of: (1) the second electric field is greater than the first electric field and the third electric field is greater than the second electric field, or (2) the second electric field is less than the first electric field and the third electric field is less than the second electric field.

[0022] In certain instances, the output polarizing element is (or includes) a transmissive polarizer and is therefore configured to remove light of a particular polarization state by blocking the light (i.e., the light is removed because it does not pass through the polarizer). Similarly, the output polarizing element is configured to transmit light of a particular polarization state by allowing the light to pass through the polarizer.

[0023] In other examples, the output polarizing element is (or includes) a reflective polarizer and is therefore configured to remove light of a particular polarization state by redirecting / reflecting the light in a particular direction so that it is not present in the displayed hologram. For example, light may be directed towards an absorptive element of the output polarizing element that absorbs the light. Because this removed light is absorbed, it is not "transmitted" by or from the output polarizing element. Similarly, the output polarizing element is configured to transmit light of a particular polarization state by redirecting / reflecting the light in a different direction (different from the direction of the light being removed) so that it is present in the displayed hologram. Thus, in certain examples, the output polarizing element includes a polarizer and an absorptive element. Together, they remove or transmit light incident on the output polarizing element. In some examples, the absorptive element is an inner wall or cavity of the holographic display housing.

[0024] In a further example, the output polarizing element is (or includes) a prism, such as a Wollaston prism. Light passes through the prism and is directed in a particular direction depending on the polarization state of the light. Such a prism is therefore configured to remove light of a particular polarization state so that it is not present in the displayed hologram, by directing / reflecting the light in a particular direction as it passes through the prism. In such a case, the light may still pass through the prism, but is blocked by the absorbing element of the output polarizing element and is not transmitted by the output polarizing element. Similarly, the output polarizing element is configured to transmit light of a particular polarization state by directing / reflecting the light in a different direction (different from the direction of the light being removed) so that it is present in the displayed hologram.

[0025] In some specific examples, the electric field is controlled by controlling the current. In general, however, the electric field is controlled by controlling the voltage applied to the elements of the liquid crystal layer. Thus, in some examples, the controller is configured to control the electric field applied across the elements of the liquid crystal layer by controlling the voltage applied to the elements of the liquid crystal layer. Thus, the liquid crystal layer is configured such that (a) a first electric field is applied across the elements when the elements operate at a first voltage level, (b) a second electric field is applied across the elements when the elements operate at a second voltage level, and (c) a third electric field is applied across the elements when the elements operate at a third voltage level.

[0026] Throughout this document, control of the electric field may be described as being achieved by operating elements at particular voltage levels, but it will be understood that any reference to operating elements of a liquid crystal layer or applying voltage levels to elements of a liquid crystal layer may equally refer to applying a particular electric field across the elements.

[0027] As mentioned above, the electric field can be varied by analog control of the voltage to the element, or by digital control of the voltage and adjustment of the duty cycle. Thus, it will be understood that when an electric field is applied across the element, this may mean a pulse width modulated (PWM) field with a varying duty cycle, rather than a smoothly variable electric field. Similarly, if an electric field is larger / smaller than another electric field, this may mean a PWM controlled electric field with a higher / lower duty cycle. Thus, when the duty cycle is varied within a certain period of time, an average electric field for that period is applied, even if the instantaneous electric field is changing rapidly. Thus, the average electric field within a first period of time may therefore be larger or smaller than the average electric field within a second period of time. Most LCoS displays are digitally driven rather than analog driven, but this is not always the case. Accordingly, in some examples, the liquid crystal layer is configured such that (a) a first electric field is applied across the element when the element operates with a first duty cycle for a first period of time, (b) a second electric field is applied across the element when the element operates with a second duty cycle for a second period of time, and (c) a third electric field is applied across the element when the element operates with a third duty cycle for a third period of time.

[0028] In some examples, the liquid crystal layer and the output polarizing element form at least part of the SLM. This may be the case, for example, of a transmissive SLM. In other examples, the liquid crystal layer forms at least part of the SLM and the output polarizing element is separate from the SLM. This may be the case, for example, of a reflective SLM. However, in some examples, the output polarizing element may be part of a reflective SLM. An SLM that has both a liquid crystal layer and an output polarizing element means that the SLM itself can achieve amplitude modulation.

[0029] In the above embodiment, when the first and third electric fields are applied across the element (e.g., the element is operated at the first and third voltage levels), only a portion of the total light intensity incident on the element is transmitted by the output polarizing element. This portion may be less than 80%, or less than 70%, or less than 60% of the total light intensity incident on the element. In one example, the portion of light intensity remaining is about 50% of the total light intensity incident on the element, which may be the case when zero amplitude is obtained at the midpoint of the modulation amplitude range.

[0030] In one example, when the second electric field is greater than the first electric field and the third electric field is greater than the second electric field, the first voltage level is zero voltage, the second voltage level is a non-zero voltage, and the third voltage level is a non-zero voltage. Thus, the second voltage level is at a higher voltage than the first voltage level, and the third voltage level is at a higher voltage than the second voltage level. Thus, the voltage (and the electric field) may be said to be "increasing" when changing from the first voltage level through the second voltage level to the third voltage level. The first voltage level may be a minimum voltage, and the third voltage level may be a maximum voltage. When the element is operating at zero voltage, the element may be said to be in a quiescent state.

[0031] Alternatively, in another example, when the second electric field is less than the first electric field and the third electric field is less than the second electric field, the first voltage level is a non-zero voltage, the second voltage level is a non-zero voltage, and the third voltage level is a zero voltage. Thus, the second voltage level is at a lower voltage than the first voltage level, and the third voltage level is at a lower voltage than the second voltage level. Thus, the voltage (and the electric field) may be said to be "decreasing" when changing from the first voltage level through the second voltage level to the third voltage level. The third voltage level may be a minimum voltage, and the first voltage level may be a maximum voltage.

[0032] In some examples, the first voltage may be known as an initial voltage, the third voltage may be known as a final voltage, and the second voltage may be known as an intermediate voltage.

[0033] In some examples, when a first electric field is applied across the element, the light has a first phase, and when a third electric field is applied across the element, the light has a second phase, and the first and second phases are located in different quadrants on the Argand diagram. Thus, light transmitted by / through the output polarizing element at a first voltage level has a phase in the first quadrant of the Argand diagram, and light transmitted by the output polarizing element at a third voltage level has a phase in the second quadrant of the Argand diagram, and the first and second quadrants are different.

[0034] Thus, the liquid crystal layer and output polarizing element are configured such that the amplitude of the light changes from the first quadrant of the Argand diagram (e.g., "positive" or "negative" amplitude), through zero amplitude, to the second quadrant of the Argand diagram (e.g., "negative" or "positive" amplitude) as the voltage changes (increases or decreases) from a first level through a second (intermediate) level to a third level. The viewer sees the light change from on to off and back on as the voltage applied to the element changes. This differs from a conventional amplitude-modulated SLM, which operates such that the amplitude of the light changes in the range [0,1] as the voltage increases (or decreases) from the first level through the second level to a third level. A viewer of a conventional SLM sees the light change from off to on with various levels of brightness as the voltage applied to the element changes.

[0035] In one example, the output polarizing element is positioned such that when the applied voltage is equal to a first voltage level, the light has a maximum amplitude and decreases in amplitude as the voltage is increased or decreased toward a second voltage level, at which the light amplitude is zero (i.e., substantially no light is transmitted from the output polarizing element), and as the voltage is continued to be increased or decreased toward a third voltage level, the light amplitude increases again to its maximum.

[0036] In some instances, the amplitude of the transmitted light may be "mirrored" to either side of zero. Thus, if a beam of light with a particular amplitude is desired, for example to produce a holographic image, one of two voltages may be applied to the element, with the actual voltage selected of these two voltages depending on the phase modulation required.

[0037] In some examples, the holographic display is configured such that light from a first element does not interfere with light from a second element. Thus, a desired amplitude and / or phase of light from an element is achieved without the need to interfere light from two or more elements of the liquid crystal layer. Thus, light from an element is transmitted to an observer / viewer without interference with light from another element (such as light from an adjacent or nearby element).

[0038] In some examples, the controller is further configured to control the illumination source. In one example, the controller may control the brightness / intensity of the illumination source such that the amplitude depends on the operation of both the illumination source and the liquid crystal layer.

[0039] In some configurations, when a second electric field is applied across the liquid crystal element, the polarization state of the light is adjusted relative to the first polarization state. Similarly, when a third electric field is applied across the element, the polarization state of the light is adjusted relative to the second polarization state. Thus, in some examples, the first, second, and third polarization states are different.

[0040] In one example, the polarization state of the light is adjusted by the element relative to an initial polarization state of the light incident on the element when the first electric field is applied, while in another example, the polarization state does not change relative to an initial polarization state of the light incident on the element when the first electric field is applied.

[0041] As mentioned above, the liquid crystal layer may include a number of elements / pixels, such as an array of elements. An element may correspond to a pixel or a sub-pixel (such as a sub-pixel of an RGB pixel).

[0042] The illumination source may include a single light emitter or multiple light emitters and has an illumination area sufficient to illuminate the liquid crystal layer.

[0043] In certain examples, there is a single output polarizing element that receives light from an entire area of ​​the liquid crystal layer. In other examples, there are multiple output polarizing elements that receive light from one or more elements of the liquid crystal layer. In certain examples, there is a separate output polarizing element for each element of the liquid crystal layer.

[0044] In one embodiment, the illumination source, the liquid crystal layer, and the output polarizing element are positioned along an optical axis / path. Positioning along the optical axis ensures that the light of the display can be transmitted through each component of the display. The output polarizing element is therefore positioned such that the light passes through the liquid crystal layer and enters the output polarizing element. Thus, the output polarizing element may be said to be positioned "after" the liquid crystal layer with respect to the optical path starting from the illumination source. The liquid crystal layer may be physically positioned between the illumination source and the output polarizing element.

[0045] In some examples, there may further be an input polarizing element (also known as an input polarizer) placed "before" the liquid crystal layer with respect to the optical path starting from the illumination source to polarize the light incident on the liquid crystal layer. Thus, the input polarizing element may be placed between the illumination source and the liquid crystal layer. The input polarizing element may also be placed on the optical axis of the holographic display. In other examples, the illumination source itself is configured to output polarized light, such that the input polarizing element may be omitted. The input polarizing element may still be used with a polarized illumination source, for example, to change the polarization to one that best suits the properties of the liquid crystal layer.

[0046] In some examples, the output polarizing element is positioned at a specific angle relative to the initial polarization of the light incident on the liquid crystal layer. In some examples, the angle may be predetermined. The angle of the output polarizing element relative to the polarization state of the light may allow the SLM to achieve a "through zero" modulation.

[0047] More generally, the relationship between the output polarizing element, the initial polarization state of the light incident on the liquid crystal layer, and the liquid crystal layer itself can be defined in terms of Jones matrices and vectors. Thus, specific matrices / vectors can be constructed to achieve modulation through zero.

[0048] As briefly mentioned above, the "behavior" (i.e., transformation) of light as it passes through a liquid crystal layer can be described by a Jones matrix and a Jones vector. The liquid crystal layer (and thus each element of the liquid crystal layer) is associated with a Jones matrix, which can be determined. The Jones matrix of each element is a function of the electric field applied to the element. Similarly, the polarization state of light is represented by a Jones vector, and the output polarizing element can also be described by a Jones vector. Thus, the change in rotation / polarization through an element of the liquid crystal layer can be mathematically quantified, and the transmission through the output polarizing element can be predicted. It can be useful to determine the Jones matrix of the liquid crystal layer so that a particular voltage and / or output polarizing element can be determined, so that the SLM can be appropriately configured to modulate the light through zero.

[0049] Thus, light incident on an element of the liquid crystal layer has an initial polarization associated with a first Jones vector, the output polarizing element is associated with a second Jones vector, the element of the liquid crystal layer is associated with a Jones matrix, the Jones matrix of the element is a function of the electric field applied to the element, and the second Jones vector is based on the Jones matrix and the first Jones vector. In a particular example, the second Jones vector can be adjusted by adjusting the angle of the output polarizing element relative to the initial polarization state of the light incident on the liquid crystal layer.

[0050] In an example, the light incident on the liquid crystal layer element is linearly polarized and the output polarizing element comprises a linear output polarizer. The incident light may be polarized using a linear input polarizing element.

[0051] In one particular example where the light is linearly polarized, the liquid crystal layer is an in-plane switching (IPS) based liquid crystal layer. In such an IPS liquid crystal layer, the liquid crystal stays in a plane defined by the liquid crystal layer and rotates within that plane when different electric fields / voltages are applied. Thus, the liquid crystal layer may include liquid crystals configured to align parallel to the plane of the liquid crystal layer when a first electric field, a second electric field, and a third electric field are applied across the element (i.e., when the element is operating at a first voltage level, a second voltage level, and a third voltage level). Such a liquid crystal layer may be associated with a Jones matrix that is approximately proportional to the real column.

[0052] It will be understood, of course, that the terms "parallel" and "vertical" with respect to alignment of liquid crystals are understood to mean "nearly parallel" and "nearly perpendicular." Those skilled in the art will appreciate that a typical liquid crystal layer will have liquid crystals that are not perfectly parallel or perpendicular to the plane defined by the liquid crystal layer. Furthermore, liquid crystals aligned parallel to a plane means that the axis defined by each liquid crystal lies in the plane, rather than perpendicular to the plane.

[0053] In a particular arrangement, the output polarizing element is oriented in the same sense as the input polarization direction. Thus, light entering the liquid crystal layer has a polarization state, and the output polarizing element is oriented to transmit substantially all light having the particular polarization state. In a particular example, this allows the use of a reflective SLM, so that light passes through the polarizing element in both the input and output paths. The output polarizing element can therefore also function as the input polarizing element. The liquid crystal layer can thus form at least part of a reflective spatial light modulator, SLM, where light is configured to pass through the output polarizing element both (i) before entering the element of the liquid crystal layer, and (ii) after passing through the element of the liquid crystal layer. Thus, light passes through the output polarizing element in a first direction before entering the element, and in a second direction after passing through the element, the first and second directions being opposite to each other. Since the input and output polarizations have the same orientation, the output polarizing element can be part of a reflective SLM (i.e., since the incident light can pass through the output polarizing element unaltered).

[0054] In another example where the light is linearly polarized, the liquid crystal layer is a twisted nematic (TN) based liquid crystal layer. In a TN liquid crystal layer, when zero voltage is applied, the liquid crystal is parallel to a plane defined by the liquid crystal layer and rotates away from that plane when a different electric field / voltage is applied. Thus, the liquid crystal layer may include liquid crystals that are configured to (i) align parallel to the plane of the liquid crystal layer when the electric field applied across the element is zero (i.e., operating at a zero voltage level) and (ii) rotate away from the plane (towards being perpendicular to the plane) when the electric field applied across the element is non-zero (i.e., operating at a non-zero voltage level).

[0055] In the alternative, the light incident on the liquid crystal layer element is circularly polarized and the output polarizing element comprises a linear output polarizer. The incident light may be polarized using a circular input polarizing element (more commonly called a polarization modifying element) such as a waveplate.

[0056] In a particular example where the light is circularly polarized, the liquid crystal layer is a vertically aligned (VA) based liquid crystal layer. In such a VA liquid crystal layer, when zero voltage is applied, the liquid crystal is perpendicular to the plane defined by the liquid crystal layer, and when a different electric field / voltage is applied, it rotates towards that plane. Thus, the liquid crystal layer may include liquid crystals that are configured to (i) align perpendicular to the plane of the liquid crystal layer when the electric field applied across the element is zero (i.e., operating at a zero voltage level), and (ii) rotate towards the plane when the electric field applied across the element is non-zero (i.e., operating at a non-zero voltage level).

[0057] In another example where the light is circularly polarized, the liquid crystal layer is a twisted nematic (TN) based liquid crystal layer. As described above, in a TN liquid crystal layer, when zero voltage is applied, the liquid crystal is parallel to a plane defined by the liquid crystal layer, and when a different electric field / voltage is applied, the liquid crystal rotates away from the plane. Thus, the liquid crystal layer may include liquid crystals configured to (i) align parallel to the plane of the liquid crystal layer when the electric field applied across the element is zero (i.e., operating at a zero voltage level), and (ii) rotate away from the plane (towards being perpendicular to the plane) when the electric field applied across the element is non-zero (i.e., operating at a non-zero voltage level). Both VA and TN liquid crystal layers may be associated with Jones matrices having complex terms.

[0058] In some examples, the display further includes a beam splitter. In certain examples, the display includes a polarizing beam splitter. As such, the polarizing beam splitter may include an output polarizing element. Thus, the polarizing beam splitter may function as an input polarizing element and an output polarizing element. As briefly mentioned, the SLM may be reflective, and the beam splitter may be useful in displays in which the liquid crystal layer forms at least a portion of the reflective SLM. In some cases, the display further includes a polarization modifying element, such as a waveguide. Light from the polarizing beam splitter passes through the polarization modifying element and enters the liquid crystal layer. After reflecting through the liquid crystal layer, the light may pass through the polarization modifying element a second time, in the opposite direction. Similarly, the light may again enter the polarizing beam splitter. Thus, the polarization modifying element may change the polarization state of the light both before the light enters the element and after the light has passed through the element. Thus, the polarization modifying element is disposed between the output polarizing element and the liquid crystal layer along the optical axis / path. The polarization-modifying element may be selected such that when a second electric field is applied across the elements of the liquid crystal layer, the polarization state of the light after passing through the polarization-modifying element is such that substantially all of the light is removed / blocked by the polarizing beam splitter.

[0059] Thus, in one example, the display further comprises a polarization modifying element disposed between the output polarizing element and the liquid crystal layer, the polarization modifying element being configured to modify the polarization state of the light, and a polarizing beam splitter comprising the output polarizing element, the polarizing beam splitter being configured to reject substantially all of the light having a second polarization state p. The liquid crystal layer forms at least a part of a reflective SLM, the elements of the liquid crystal layer being associated with a Jones matrix J(B), the Jones matrix for the elements being a function of the electric field, B, applied to the elements. The polarization modifying element is associated with a Jones matrix, R, such that RJ(B')Rp=p, where J(B') is the Jones matrix associated with the elements of the liquid crystal layer at the second electric field, B'. Thus, the polarization modifying element is selected such that RJ(B')Rp=p.

[0060] Thus, when the light has the second polarization state p (the same as the incident polarization state), the light travels back along the incident path - the remaining light transmitted to the viewer is the component of the reflected light that is orthogonal to p (which is nothing when the light has the second polarization state). By configuring the display in this way, so that the outgoing polarization is orthogonal to the incident polarization, much higher light efficiency can be achieved by using a polarizing beamsplitter to separate the incoming and outgoing paths.

[0061] In a particular case, the polarization-modifying element is a waveplate with half the retardance of J(B') and its slow axis aligned with the fast axis of J(B'). J(B) can be described by a pure retardance.

[0062] As mentioned, after the light is modulated using the liquid crystal layer and the output polarizing element, the light may be filtered to improve image quality. Thus, in some examples, the holographic display further includes (i) a lens arranged to receive the light from the output polarizing element and configured to generate a Fourier transform of the target light field, F(H), at a focal plane of the lens, and (ii) a spatial filter arranged at the focal plane and configured to remove a Fourier transform of a complex conjugate of the target light field, F(H*). In some examples, the spatial filter is further configured to remove the zeroth order of the target light field. As mentioned above, because of the "through zero" amplitude modulation scheme, the energy of the zeroth order is much lower than in conventional systems. This means that the effects of imperfect filtering of any of this zeroth order are much less severe than in SLMs that modulate in the range [0,1].

[0063] In some examples, the spatial filter is configured to remove the Fourier transform of the complex conjugate of the target light field, F(H*), without filtering the zeroth order of the target light field. Thus, as described above, because the SLM is configured to modulate the amplitude over a range that spans zero, the amount of power contained in the zeroth order is small, and thus no filtering is required, resulting in improved image quality. The filter may be configured to allow the zeroth order of the target light field to pass through.

[0064] In some examples, the lens has a focal length, and the SLM and lens are spaced apart a distance equal to the focal length of the lens. In some examples, the lens and SLM are spaced apart a distance greater or less than the focal length. In such cases, the converging / diverging light may be collimated using additional optics further along the optical path. It may be desirable to space the lens and SLM apart by the focal length to provide a more compact display (since additional optics can be omitted).

[0065] In one example, the focal plane of the lens and the lens are spaced apart by a distance equal to the focal length of the lens, and therefore the lens and the filter are spaced apart by a distance equal to the focal length of the lens.

[0066] The filter can physically block a portion of the light received from the lens, such as the portion that contains the Fourier transform, F(H*), of the complex conjugate of the target light field.

[0067] According to a second aspect of the invention, there is provided a method of modulating the amplitude of light in a holographic display, comprising: (i) operating an illumination source to emit at least partially coherent light towards an element of a liquid crystal layer; (ii) applying a first electric field across the element such that the light from the element has a first polarization state; (iii) applying a second electric field across the element such that the light from the element has a second polarization state; (iv) applying a third electric field across the element such that the light from the element has a third polarization state; and (v) polarizing the first polarization state using an output polarizing element. (vi) using an output polarizing element to remove substantially all of the light having a second polarization state and transmit a portion of the light having the third polarization state; and (vii) using an output polarizing element to remove a portion of the light having a third polarization state and transmit a portion of the light having the third polarization state, wherein one of: (1) the second electric field is greater than the first electric field and the third electric field is greater than the second electric field; and (2) the second electric field is less than the first electric field and the third electric field is less than the second electric field.

[0068] In some examples, applying a first electric field across the element includes operating the element at a first voltage level, applying a second electric field across the element includes operating the element at a second voltage level, and applying a third electric field across the element includes operating the element at a third voltage level.

[0069] In some examples, the method further includes (i) determining a Jones matrix for the liquid crystal layer, and (ii) determining an angle based on the Jones matrix and the initial polarization of the light.

[0070] In some examples, the method further includes (i) passing the light representing the holographic target light field, H, through a lens to generate a Fourier transform of the target light field, F(H), at a focal plane of the lens, and (ii) passing the light through a spatial filter disposed at the focal plane to remove a Fourier transform of a complex conjugate of the target light field, F(H*). In some examples, passing the light through the spatial filter includes filtering a zero order of the target light field. In other examples, passing the light through the spatial filter includes passing the light through the spatial filter without filtering a zero order of the target light field.

[0071] Further features and advantages of the present invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, made with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0072] [Figure 1] 1 is a diagrammatic representation of an exemplary holographic display according to one embodiment. [Diagram 2] FIG. 2 is a schematic diagram of the holographic display of FIG. 1. [Diagram 3] FIG. 2 is an Argand diagram showing the range of phase and amplitude modulation using the holographic display of the first embodiment. [Figure 4] 2 is a schematic diagram of another holographic display, according to an example. [Diagram 5] FIG. 11 is an Argand diagram showing the range of phase and amplitude modulation using the holographic display of the second embodiment. [Figure 6] FIG. 1 is a schematic diagram of a holographic display including lenses and filters. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0073] 1 and 2 show a system 100 forming at least a portion of a holographic display according to an example. The system 100 includes an illumination source 102 configured to emit at least partially coherent light. In this example, the illumination source 102 is a single light emitter that emits a beam of light toward the liquid crystal layer 104 of the SLM 106. In another example, the illumination source 102 includes multiple light emitters that together illuminate the liquid crystal layer 104. Examples using multiple light emitters may also have the ability to control the emitters individually or by region, allowing for reduced power consumption and / or improved contrast. In this example, the illumination source 102 is controlled to emit red, green, or blue light using time division multiplexing. Other examples may use an illumination source 102 that emits light having a single wavelength, or light having wavelengths within a single wavelength range.

[0074] A light beam emitted by the illumination source 102 travels from at least the illumination source 102 to the liquid crystal layer 104. The light beam follows a path along an optical axis 116 from the illumination source 102 towards the eye of an observer viewing the holographic display.

[0075] The liquid crystal layer 104 includes an array of pixels / elements 104a. A voltage / bias can be applied to each element 104a individually to control the electric field applied across the elements 104a. The presence of an electric field can cause the liquid crystals to rotate, thus changing the polarization state of light as it passes through the elements 104a.

[0076] The SLM 106 in this example further includes an output polarizing element 110 positioned along the optical path after the liquid crystal layer 104 .

[0077] In this example, the SLM 106 includes both the liquid crystal layer 104 and the output polarizing element 110, but in other examples, the SLM 106 may not include the output polarizing element 110. The output polarizing element 110 may even be separate from the SLM 106.

[0078] Thus, light rays emitted by illumination source 102 travel through liquid crystal layer 104 and along an optical path incident on output polarizing element 110. Depending on the polarization of the light when it reaches output polarizing element 110 (which can be affected by the voltage applied to a particular element 104a), the light may be blocked or may partially pass through output polarizing element 110.

[0079] In Figures 1 and 2, the output polarizing element 110 is shown as being a transmitting polarizer, which itself can absorb at least a portion of the light incident thereon (and / or allow at least a portion of the light to pass through). It will be understood that the same concept is applicable to other types of polarizers. In some examples, the output polarizing element 110 includes a polarizing element and an absorbing element, where the absorbing element absorbs the light reflected from the polarizing element and / or transmitted through the polarizing element. For example, the polarizing element may be a reflective polarizer that splits the light into two separate beams and directs the "unwanted" light towards the absorbing element. Regardless of the type, the output polarizing element 110 is configured to either (i) reject a portion of the light having a particular polarization state (e.g., a first or third polarization state) and also transmit a portion of the light having a particular polarization state, or (ii) reject substantially all of the light having a different polarization state (e.g., a second polarization state). In this example, the output polarizing element 110 is a linear polarizer. An output polarizing element 110 is positioned after the liquid crystal layer 104 along the optical path followed by the light.

[0080] Similarly, in Figures 1 and 2, the SLM 106 is shown as being transmissive, such that light enters one side of the layer (e.g., the front side) and exits a different side of the layer (e.g., the back side). Again, it will be understood that the same concepts are applicable to other types of SLMs. For example, the SLM may be a reflective liquid crystal layer, such that light enters and exits from the same side (e.g., the front side) that it entered. As mentioned above, if the SLM is reflective, the output polarizing element 110 may not generally be considered part of the SLM. An exemplary reflective SLM is described below and shown in Figure 4.

[0081] Thus, the output polarizer 110, together with the liquid crystal layer 104, modulates the amplitude of the light beam from the liquid crystal layer 104. For example, if a light beam linearly polarized along the vertical axis 112 travels in a direction along the optical axis 116 (and thus has a particular Jones vector) and is incident on a vertically oriented output polarizer (again, with a particular Jones vector), the light beam transmitted by the output polarizer 110 may have substantially 100% of its initial intensity (i.e., the amplitude of the transmitted light beam is unchanged and / or is maximum). Such a vertically oriented output polarizer is said to be aligned with the linearly polarized light beam, and is therefore positioned at an angle of 0 radians with respect to the linearly polarized light beam incident on the output polarizer. Conversely, if a light beam is linearly polarized along the horizontal axis 114 and is incident on a vertically oriented output polarizer, the light beam may have substantially 0% of its initial intensity after interacting with the output polarizer (i.e., the amplitude of the transmitted light beam is minimal or zero). Such a vertically oriented output polarizer is said to be "crossed" with horizontally polarized light rays and is therefore positioned at an angle of π / 2 radians with respect to the linearly polarized light rays incident on the output polarizer. When substantially all of the light incident on the output polarizer is blocked / rejected by the output polarizer, the output polarizer may be said to reject substantially all of the light having a particular polarization state.

[0082] In another example, if a ray of light linearly polarized along the longitudinal axis 112 travels in a direction along the optical axis 116 and enters an output polarizing element positioned at an angle of π / 4 radians with respect to the longitudinal axis 112, the ray may have approximately 50% (i.e., 0.5) of its initial intensity after interacting with the output polarizing element (i.e., the amplitude of the transmitted ray is √0.5). Thus, an output polarizing element with such an orientation is positioned at an angle of π / 4 radians with respect to the linearly polarized ray incident on the output polarizing element. When a portion (such as 50% of the light intensity) is transmitted by the output polarizer, the output polarizing element may be said to reject a portion of the light having a particular polarization state and also to transmit a portion of the light having a particular polarization state. The rejected portion may be absorbed, for example, by the polarizing element, or by an absorbing element.

[0083] In some examples, the system 100 includes an input polarizing element 108 disposed between the illumination source 102 and the liquid crystal layer 104. The input polarizing element 108 can polarize light such that polarized light is incident on the liquid crystal layer 104. In some examples, the input polarizing element 108 is omitted if the light emitted by the illumination source 102 is already polarized in a desired manner. In some examples, the input polarizing element 108 is a linear polarizer (as shown in FIG. 1), while in other examples, the input polarizing element 108 is a different type of polarizer, such as a circular polarizer.

[0084] 2 shows a controller 120 that can control the electric field / voltage applied to each element of the liquid crystal layer 104 to provide complete control over the modulation of the amplitude (and possibly phase) of the light output by the system 100. The controller 120 can also control the operation of the illumination source 102.

[0085] 1 and 2 also show a linear arrangement of holographic displays, other arrangements may include image folding components, for example a folded optical path may be provided.

[0086] As discussed, the inventors have recognized that an optical system can be configured such that when element 104a is controlled at a particular voltage level, it is possible to modulate the amplitude of the light "through zero" as the voltage increases or decreases.

[0087] To explain this more clearly, several embodiments will be described in sequence.

[0088] In-Plane Switching (IPS) based liquid crystal layer In a first embodiment, the liquid crystal layer 104 is an in-plane switching (IPS) based liquid crystal layer 104. FIG. 3 shows an exemplary Argand / Phasor diagram of an exemplary system including an IPS based liquid crystal layer 104. The phasor diagram represents the amplitude and phase of the light after interaction with the output polarizing element 110. The amplitude of the light ray after interaction with the output polarizing element 110 is given by the magnitude of the value on the real axis (Re). The sign of the amplitude corresponds to the sign of the real part of the complex number projected onto the real axis. The phase of the light ray is given by the azimuth angle between the positive real axis and the position of the point on the diagram. The position of the point on the phasor diagram can be adjusted by controlling the voltage(s) applied to the element 104a of the liquid crystal layer 104.

[0089] 3 represents an exemplary system including an IPS-based liquid crystal layer 104, a particular polarization of light incident on layer 104, and a particular orientation of output polarizing element 110. In this case, the light incident on liquid crystal layer 104 is linearly polarized, and output polarizing element 110 includes a linear polarizer.

[0090] The IPS-based liquid crystal layer 104 may be characterized as having a Jones matrix that contains only real terms, or that is approximately proportional to the real matrix. More generally, the IPS liquid crystal layer 104 includes liquid crystal molecules that (i) align parallel to the layer / display (in-plane) and (ii) are reoriented (as a result of an applied voltage) while remaining essentially parallel to the layer. For example, in the absence of an applied voltage, the liquid crystals may align parallel to the plane of the layer 104, and in the presence of an applied voltage, the liquid crystals remain parallel to the plane of the layer 104, but assume different respective orientations about an axis in the plane of the layer. With reference to FIG. 1, the longitudinal axis of the liquid crystals may align to the plane defined by axes 112 and 114, and thus rotate around the optical axis 116. Thus, the optical axis 116 is perpendicular to the plane defined by the liquid crystal layer 104.

[0091] In one particular example, the liquid crystal layer 104 has a Jones matrix given by a rotation matrix approximately proportional to:

number

[0092] It will be appreciated that the above Jones matrix representation (and any other example representations discussed herein) is not an accurate description of an actual liquid crystal layer, but rather an approximate model used to communicate candidate polarizer configurations. The examples have been found to be sufficiently accurate models for the purposes, but are idealized representations.

[0093] In a similar manner, the polarization state of light can be represented by a Jones vector, and the particular orientation / configuration of the output polarizer can be represented by a Jones vector. Thus, light entering the liquid crystal layer 104 can have a first Jones vector, and the output polarizer 110 can have a second Jones vector.

[0094] Thus, for linearly polarized light (light incident on the IPS liquid crystal layer 104), application of a voltage to a particular element 104a of the liquid crystal layer 104 can be shown to cause a net rotation of the polarization state of the light by an angle of 2φ. The incident light may be linearly polarized, for example, by a linear input polarizing element 108.

[0095] In this exemplary system, the output polarizing element 110 is positioned at a particular angle 118 relative to the initial polarization of the light, so that as the voltage applied to the element 104a is increased, the amplitude of the light passes through zero. For any particular type of liquid crystal layer 104, this can be achieved by selecting the appropriate angle 118 and initial polarization. The orientation angle 118 of the output polarizing element 110 may be defined as an angle extending around the optical axis 116 (with respect to a reference point such as the longitudinal axis 112). The unique properties of the output polarizing element 110 and the angle 118 are represented by the Jones vector of the output polarizing element 110.

[0096] At a first time, a first voltage level is applied to the element 104a. In this example, the first voltage level is zero (or 0V). Thus, the element 104a is in a quiescent state since there is no electric field applied to the liquid crystals in the element 104a. In this case, φ=0 when the element is in its quiescent state. The light passing through the element has a first polarization state (which may be unchanged from the initial polarization state). As described above, the linearly polarized light, voltage levels, and angle 118 relative to the initial polarization are such that the intensity of the light is attenuated by about 50% by the output polarizing element 110 (thus a portion of the light is rejected and a portion of the light is transmitted). This can be achieved by orienting the polarizer 110 at an angle of π / 4 radians relative to the polarization state of the linearly polarized light beam that passed through the element 104a. More generally, the output polarizer 110 can be positioned at an angle between π / 8 radians and 3π / 8 radians (although this will affect the intensity of the light that is attenuated).

[0097] It can be shown that at such voltage levels, the light does not experience phase modulation due to the initial polarization (characterized by the first Jones vector) and the type of liquid crystal layer 104 (characterized by the Jones matrix). Thus, the light is represented by point 202 on the phasor diagram, where the light has 50% of its initial incident intensity (an amplitude of +√0.5 as shown in FIG. 3) and no phase modulation.

[0098] Then, when the voltage is increased from a first voltage level (in this case 0V) to a second (higher, non-zero) voltage level, the linearly polarized light rotates within the element 104a. Thus, the light passing through the element 104a has a second polarization state that is different from when the element 104a was operated at the first voltage level. In this case, φ=π / 8 radians. This rotation increases the angle between the output polarizing element 110 and the light. At this second voltage level, the angle between the output polarizing element 110 and the light ray may be approximately π / 2 radians, and as a result, the light ray with the second polarization state is blocked / absorbed by the output polarizing element 110 and therefore has an amplitude of approximately zero. For example, at the second voltage, the light ray passing through the element 104a may have been rotated by π / 4 radians relative to the resting light ray and therefore may be perpendicular to the polarizer 110, so that an angle of π / 2 radians is between the light ray and the polarizer 110. Thus, the light is represented by point 204 on the phasor diagram, and the light has approximately 0% of its incident intensity and amplitude (as indicated by its position at the origin of the Argand diagram of FIG. 3).

[0099] Then, if the applied voltage still continues to increase from the second voltage level to a third (higher, non-zero) voltage level (which may be the maximum voltage), the light will rotate further and have a third polarization state different from the second polarization state. In this case, φ=π / 4 radians. This rotation further increases the angle between the output polarizing element 110 and the light. At this third voltage, the angle between the output polarizing element 110 and the light beam may be approximately 3π / 4 radians, so the output light will again have an intensity of approximately 50% of its maximum intensity (so a portion of the light is rejected and a portion of the light is transmitted). For example, at the third voltage level, the light passing through element 104a will have rotated by π / 4 radians relative to the light beam at the second voltage level, and therefore may be π / 2 radians relative to the light beam at rest. Because the degree of rotation exceeds π / 2 radians, the light will be represented in a different quadrant on the phasor diagram. This is effectively represented as light having a "negative" amplitude. The light is therefore represented by point 206 on the phasor diagram, and the light has approximately 50% of its maximum intensity (an amplitude of −√0.5 as shown in FIG. 3) and an effective phase modulation of π radians.

[0100] Thus, FIG. 3 shows how the amplitude of the light can be modulated through zero, with the intensity decreasing from a particular level to zero and then increasing again, by positioning the output polarizing element 110 at a particular angle 118 such that the voltage applied to the element increases from a first voltage level through a second voltage level to a third voltage level. The zero amplitude is achieved at this second intermediate voltage level. As discussed, this is achieved by having a linear input polarization state aligned with the rest orientation of the liquid crystal (i.e., the first Jones vector can be (1,0)), and a linear output polarizing element at π / 4 radians relative to the input polarization (i.e., the second Jones vector can be (1,-1;-1,1)).

[0101] In summary, in this embodiment, the light incident on the liquid crystal layer has a linear polarization (at any orientation), and the linear output polarizer is orthogonal to the light leaving the liquid crystal layer at intermediate values ​​of φ (e.g., φ=-π / 8). This modulates the output amplitude according to sin(2(φ-π / 8)), achieving a pure amplitude modulation in the range [-√0.5,+√0.5]. A particular example has an output polarizer that matches the input polarization state, meaning that the polarizer can be part of a reflective SLM and the light passes through both the input and output paths. For example, an input orientation of (cos(-π / 8), sin(-π / 8)) is transformed to (cos(3π / 8), sin(3π / 8)) when φ=π / 8, which is orthogonal to the output polarizer passing through (cos(-π / 8), sin(-π / 8)).

[0102] It will be appreciated that the same effect can be achieved when the voltage is reduced from a first voltage level to a third voltage level, for example, the first voltage level can be a maximum voltage level, and the first voltage level is reduced through a second intermediate voltage level to a third zero voltage level.

[0103] In a variation of the above embodiment, for a custom IPS-based liquid crystal layer, φ is in the range [0,π / 2]. This can be achieved by driving the IPS-based liquid crystal layer with a larger electric field to achieve more rotation. In this variation, the light incident on the liquid crystal layer has a linear polarization (at any orientation) and the linear output polarizer is orthogonal to the light leaving the liquid crystal layer at an intermediate value of φ (e.g., φ=π / 4). This modulates the output amplitude according to sin(2(φ-π / 4)), achieving a pure amplitude modulation in the range [-1,+1]. Thus, referring to the Argand diagram of FIG. 3, the amplitude at point 202 is +1, the amplitude at point 204 is 0, and the amplitude at point 206 is -1. Another example has an output polarizer that matches the input polarization state, meaning that the polarizer can be part of a reflective SLM and the light passes through both the input and output paths. For example, an input orientation of (1,0) is transformed to (0,1) when φ=π / 4, which is orthogonal to the output polarizer passing through (1,0).

[0104] Twisted nematic (TN) based liquid crystal layer 3 also depicts an exemplary system 100 in which the liquid crystal layer 104 is a TN-based liquid crystal layer 104. Similar to the first embodiment described for an IPS-based liquid crystal layer, in this second embodiment, the light incident on the liquid crystal layer 104 is linearly polarized (e.g., having a Jones vector of (1,0)), and the output polarizing element 110 is oriented at an angle of π / 4 radians with respect to the reference axis 112.

[0105] A TN-based liquid crystal layer 104 may be characterized as having liquid crystal molecules that (i) are aligned parallel to the plane defined by the liquid crystal layer 104 when no electric field / voltage is applied (when the electric field / voltage is zero), and (ii) are reoriented away from the plane (as a result of an applied non-zero electric field / voltage). Reorienting away from the plane is sometimes referred to as rotating towards being perpendicular to the plane.

[0106] In one particular example, the liquid crystal layer 104 has a Jones matrix given by a rotation matrix approximately proportional to:

number

[0107] For the IPS-based liquid crystal layer variants described above, φ is in the range [0, π / 2], with φ=0 when the elements of the liquid crystal layer are in a quiescent state, and φ=π / 2 when the electric field applied to the elements is at a maximum. In this embodiment, the light incident on the liquid crystal layer has a linear polarization (of any orientation) and the linear output polarizer is placed at π / 4 degrees with respect to the input polarization. This modulates the output amplitude according to (cosφ-sinφ) / √2, achieving a pure amplitude modulation in the range [-√0.5, +√0.5]. Thus, referring to the Argand diagram of FIG. 3, the amplitude at point 202 is +√0.5, the amplitude at point 204 is 0, and the amplitude at point 206 is -√0.5.

[0108] Reflective SLM 4 is a schematic diagram illustrating another system 150 forming at least a portion of a holographic display according to an example. The system 150 includes an illumination source 152 configured to emit at least partially coherent light. The illumination source 152 may correspond to the illumination source 102 described above. A light beam emitted by the illumination source 152 travels from the illumination source 152 to at least a liquid crystal layer 154. The light beam follows a nonlinear optical path from the illumination source 152 to the eye of an observer viewing the holographic display.

[0109] The liquid crystal layer 154 includes an array of pixels / elements. In contrast to the examples of Figures 1 and 2, the liquid crystal layer 154 is reflective, such that light passes through the liquid crystal layer 154 a first time, reflects, and then passes through the liquid crystal layer 154 a second time. As discussed, a voltage / bias can be applied to each element individually to control the electric field applied across the element. The presence of an electric field can cause the liquid crystals to rotate, thus changing the polarization state of the light as it passes through the element.

[0110] The system in this example further includes a polarizing beam splitter 160 that splits the beam of light from the illumination source 152 into a transmitted beam and a reflected beam, where the reflected beam is reflected towards and subsequently incident on the liquid crystal layer 154. The transmitted beam may be absorbed anywhere within the system 150. After passing through the liquid crystal layer 154, the light enters the polarizing beam splitter 160 and is again split into a transmitted beam and a reflected beam, where the reflected beam is reflected back towards the illumination source 152, and finally the transmitted beam is seen by an observer of the holographic display. In addition to splitting the beam, the polarizing beam splitter 160 can also polarize the light incident on it. In this example, the polarizing beam splitter 160 is a linear polarizer.

[0111] The system in this example further includes a wave plate 156. In this example, the wave plate 156 is a circular / elliptical polarizer such that circularly or elliptically polarized light is incident on the liquid crystal layer 154, and then the circularly or elliptically polarized light is incident on the polarizing beam splitter 160 after passing through the liquid crystal layer 154, and passes through the wave plate 156 a second time.

[0112] 4 further shows a controller 158 that can control the electric field / voltage applied to each element of the liquid crystal layer 154 so as to provide complete control over the amplitude (and possibly phase) modulation of the light output by the system 150. The controller 158 can also control the operation of the illumination source 152.

[0113] In another example, rather than having a polarizing beam splitter, the system includes a non-polarizing beam splitter, an input polarizer, and an output polarizer, where both polarizers are circular / elliptical polarizers. Light travels from the illumination source through the input polarizer, through the beam splitter, through the liquid crystal layer, through the beam splitter, and then through the output polarizer.

[0114] The use of a polarizing beam splitter can be beneficial over a non-polarizing beam splitter by reducing efficiency losses. In both examples, the SLM includes a liquid crystal layer and the polarizer(s) are separate from the SLM.

[0115] Mathematically, the SLM (i.e., the reflective liquid crystal layer 154) can be described by a Jones matrix J(B), where B is the electric field applied to a particular element of the liquid crystal layer 154 and J is a function of B. The waveplate 156 can have a Jones matrix R, and the polarizing beam splitter 160 can be described as removing polarization p from the output.

[0116] R can be chosen such that RJ(B')Rp=p for some intermediate value of B, denoted by B' (by operating the elements of the liquid crystal layer 154 at a second / intermediate electric field). This can be achieved by setting RJ(B')R=I, where I is the identity matrix. This means that the polarization of the waveplate cancels the polarization effect of the SLM at B'. As a result, when the element is operated at B', the light incident on the polarizing beam splitter 160 (after passing through the element) has the same polarization state as when it first entered the polarizing beam splitter 160 (i.e. before entering the element). This means that if the light is reflected by the polarizing beam splitter 160 towards the element on the first pass, it is then reflected again on the second pass (i.e., reflected back to where it originally emitted (i.e., back towards the illumination source). This means that the viewer does not see the light because it is "filtered" by the polarizing beam splitter 160. Conversely, to be seen by the viewer, light needs to pass through the beam splitter in a direction other than the direction it was originally emitted (i.e., be transmitted by the polarizing beam splitter 160). This is achieved by operating the liquid crystal layer with other values ​​of B, which changes the polarization state of the light, thereby allowing at least some of the light to be routed to the output (see by the viewer).

[0117] As mentioned above, for a reflective liquid crystal layer 154, the Jones matrix, J, of the liquid crystal layer 154 describes a double pass through the SLM. In this example, the light experiences pure retardance through the SLM (it can be shown that a double pass in the opposite direction cancels the rotation caused by the liquid crystal layer, leaving only the retardance).

[0118] In one example, R is a waveplate with half the retardance of J(B') and its slow axis is aligned with the fast axis of J(B').

[0119] In this manner, the light beam emitted by illumination source 152 thus travels through liquid crystal layer 154 and along an optical path incident on polarizing beam splitter 160. Depending on the polarization of the light as it reaches polarizing beam splitter 160 (which can be affected by the voltages applied to certain elements), the light may be blocked (when B=B′) or may partially pass through polarizing beam splitter 160.

[0120] Vertically Aligned (VA) Based Liquid Crystal Layer 5 shows an exemplary Argand / Phasar diagram of exemplary system 150, where liquid crystal layer 154 is a VA-based liquid crystal layer 154. In this second embodiment, the light incident on liquid crystal layer 154 is circularly polarized (by waveplate 156) and polarizing beam splitter 160 includes a linear polarizer.

[0121] VA-based liquid crystal layer 154 is typically found in liquid crystal on silicon (LCoS) SLMs. VA-based liquid crystal layer 154 may be characterized as having liquid crystal molecules that (i) align perpendicular (i.e., vertically) to a plane defined by liquid crystal layer 154, and (ii) are reoriented (as a result of an applied voltage) toward the plane. For example, in the absence of an applied voltage, the liquid crystal may align in a vertical configuration perpendicular to the plane of layer 154, and in the presence of an applied voltage, the liquid crystal may rotate toward the plane. This causes the Jones matrix of VA liquid crystal layer 154 to have complex terms.

[0122] In one particular example, the liquid crystal layer 154 has a Jones matrix given by a rotation matrix proportional to:

number

[0123] Thus, for circularly polarized input light, such as right-hand circularly polarized light (i.e., proportional to (1;-i)), and a linear output polarizer 160 positioned with the fast axis of the liquid crystal layer at π / 4 degrees, it can be shown that applying a voltage to a particular element of the liquid crystal layer 154 results in both amplitude and phase modulation, as shown in Figure 5. The phase modulation is amplitude dependent, giving the relationship shown in Figure 5.

[0124] As described for the first embodiment, the output polarizing element 160 is arranged in a particular configuration (and thus has a particular Jones vector) such that as the voltage applied to the element increases (or decreases), the amplitude of the light passes through zero.

[0125] At a first time, a first voltage level is applied to the element. In this example, the first voltage level is zero (or 0V). The element is therefore in a quiescent state as there is no electric field applied to the liquid crystals in the element. When the element is in its quiescent state, φ=0. At this voltage level, the light interacts with the output polarizing element of the polarizing beam splitter 160 and can be shown to have a particular non-zero amplitude (i.e., a percentage of the maximum amplitude in the absence of the output polarizing element) and a particular phase modulation. Thus, the light is represented by point 302 on the phasor diagram, and the light has a particular percentage of its maximum intensity and phase modulation.

[0126] If the voltage is then increased from the first voltage level (in this case 0V) to a second (higher, non-zero) voltage level, the linear polarization rotates within the element. This rotation adjusts the polarization state, and when the light interacts with the output polarization element of the polarizing beam splitter 160, the light beam has approximately zero amplitude and is therefore blocked by the output polarization element. For example, at this second voltage level, φ=π / 2 radians, and the right-hand circularly polarized light (represented as (1;-i)) is converted to linearly polarized light (represented by (1;1), i.e., +π / 4 radians), and the angle of the output polarization element can be set to -π / 4 radians. Thus, at this second voltage level, there is an angle of π / 2 radians between the polarization state of the light and the output polarization element, and therefore the light is blocked by the output polarization element (i.e., the amplitude is 0). Thus, the light is represented by point 304 on the phasor diagram, and the light has approximately 0% of its maximum intensity.

[0127] Then, if the applied voltage still continues to increase from the second voltage level to a third (higher, non-zero) voltage level (which may be the maximum voltage), the light rotates further. For example, at this third voltage level, φ=π radians. This rotation adjusts the polarization state, and when the light interacts with the output polarizing element of the polarizing beam splitter 160, the transmitted light beam has a non-zero amplitude (i.e., a percentage of the maximum amplitude in the absence of the output polarizing element) and a particular phase modulation. Depending on the degree of rotation, the light is represented in different quadrants on the phasor diagram. This is effectively represented as light having a "negative" amplitude. Thus, the light is represented by point 306 on the phasor diagram, where the light has a percentage of its maximum intensity and a particular phase modulation.

[0128] Thus, FIG. 5 shows how the amplitude of light can be modulated through zero by arranging an output polarizing element with a particular Jones vector such that the voltage applied to the element increases from a first voltage level through a second voltage level to a third voltage level, the amplitude decreases from the particular level to zero, then increases again, etc. The zero amplitude is achieved at this second intermediate voltage level. It will be appreciated that the same effect can be achieved when the voltage decreases from the first voltage level to a third voltage level. For example, the first voltage level can be a maximum voltage level, and the first voltage level decreases through a second intermediate voltage level to a third zero voltage level. The overall modulation scheme applied by the exemplary system is (1+ie iφ ) / 2.

[0129] A commercially available LCoS SLM is the Sony™ SXRD241A, which has a VA modality. A simplified model of the VA liquid crystal layer suggests a circular input polarization and a linear output polarization. Given this information, to achieve through-zero operation, the SLM is illuminated with circularly polarized light (e.g., achieved via waveplate 156), and the orientation of the linear output polarizer (such as polarizing beam splitter 160) is then set such that the modulation amplitude at zero voltage is approximately equal to the modulation amplitude at maximum voltage, and passes through zero at an intermediate voltage. In this particular Sony™ LCoS SLM, the orientation of the output polarizer is approximately 25 degrees from the y-axis (i.e., axis 112) of the SLM.

[0130] "Low twist" twisted nematic (TN) based liquid crystal layer FIG. 5 also illustrates an exemplary system 150 in which the liquid crystal layer 154 is a “low twist” TN-based liquid crystal layer 154. Some exemplary TN-based liquid crystal layers (e.g., double pass through a reflective TN layer) have little or no effect from the TN twist and can be described as pure retardance. Such TN-based liquid crystal layers can be referred to as “low twist” TN-based liquid crystal layers (as opposed to more typical TN liquid crystal layers as discussed above). As with the second embodiment describing a VA-based liquid crystal layer, in this third embodiment, the light incident on the liquid crystal layer 154 is circularly polarized (by the wave plate 156) and the polarizing beam splitter 160 includes a linear polarizer.

[0131] The low twist TN-based liquid crystal layer 154 may be characterized as having liquid crystal molecules that (i) align parallel to the plane defined by the liquid crystal layer 104 in the absence of an applied electric field / voltage (when the electric field / voltage is zero) and (ii) are reoriented / rotated away from the plane (as a result of the application of a non-zero electric field / voltage). Reorienting / rotating away from the plane may be referred to as rotating towards perpendicular to the plane. In one particular example, the liquid crystal layer 154 has a Jones matrix given by the same rotation matrix as the Jones matrix for the VA-based liquid crystal layer provided above. For a VA-based liquid crystal layer, φ is in the range [0,π], but in contrast to a VA-based liquid crystal layer, φ=π when the elements of the liquid crystal layer are in a quiescent state and φ=0 when the electric field applied to the elements is at a maximum. In this way, the TN-based liquid crystal layer 154 behaves similarly to a VA-based liquid crystal layer, and the overall modulation scheme applied by the exemplary system is (1+ie iφ ) / 2.

[0132] filtering FIG. 6 illustrates at least a portion of a holographic display 400 according to an example. The holographic display 400 includes the system 100 of FIGS. 1 and 2, or the system 150 of FIG. 4. In addition to the components of the systems 100, 150, the display 400 further includes a lens 402. The lens 402 has a focal length, f, and in this particular example is positioned one focal length from the SLM of the systems 100, 150. In other examples, the distance between the lens 402 and the SLM may be different. The display 400 further includes a filter 404, such as a spatial filter, that defines an aperture. The filter 404 is positioned on the opposite side of the lens 402 from the SLM and one focal length from the lens 402. As shown, the SLM, the lens 402, and the filter 404 are coaxial along the optical axis 116. Other configurations, such as a folded optical path, may be used, which may allow for a more compact display.

[0133] The SLM is configured to generate a light field that is a quantized representation of the target light field, H, as described above. The configuration of the holographic optical display 400 is such that a Fourier transform of the light field, F(H), is formed in a plane that coincides with the location of the filter 404. This plane is the Fourier plane of the SLM as imaged by the lens 402. The target light field is determined such that the Fourier transform of the target light field, F(H), does not overlap at least with the Fourier transform of the complex conjugate of the target light field, F(H*), in the Fourier plane of the SLM. Furthermore, the aperture of the filter 404 is positioned such that a portion of the target light field is blocked. For example, the filter is positioned to remove the Fourier transform of the complex conjugate of the target light field, F(H*). This may be effective in reducing the effects of quantization noise. As previously mentioned, due to the particular modulation schemes discussed in Figures 1-5, the filter does not necessarily have to filter the zeroth order of the target light field. However, as mentioned above, in some instances the zeroth order may still be filtered, but since the energy of the zeroth order is low, filtering is easier than in conventional systems, and therefore the zeroth order can still be filtered to remove any residual zeroth order.

[0134] The above embodiments are to be understood as illustrative examples of the present invention. Further embodiments of the present invention are envisioned. It is to be understood that any feature described in connection with 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 embodiment, or in any combination of any other embodiment. Moreover, equivalents and modifications not described above may be employed without departing from the scope of the present invention, which is defined in the appended claims.

Claims

1. 1. A holographic display comprising: an illumination source configured to emit at least partially coherent light; a liquid crystal layer including an array of elements arranged to be illuminated by said light, when a first electric field is applied across an element of the liquid crystal layer, the light from the element has a first polarization state; when a second electric field is applied across the element of the liquid crystal layer, the light from the element has a second polarization state; when a third electric field is applied across the element of the liquid crystal layer, the light from the element has a third polarization state. The liquid crystal layer, a controller configured to control an electric field applied across the elements of the liquid crystal layer; an output polarizing element, removing a portion of the light having the first polarization state and transmitting a portion of the light having the first polarization state; removing substantially all of the light having the second polarization state; removing a portion of the light having the third polarization state and transmitting a portion of the light having the third polarization state. and the output polarizing element configured as described above, the second electric field being greater than the first electric field and the third electric field being greater than the second electric field; and the second electric field being less than the first electric field and the third electric field being less than the second electric field. The holographic display.

2. the controller is configured to control a voltage applied to the elements of the liquid crystal layer, thereby controlling an electric field applied across the elements of the liquid crystal layer; The liquid crystal layer is when the element is operated at a first voltage level, the first electric field is applied across the element; when the element is operated at a second voltage level, the second electric field is applied across the element; when the element is operated at a third voltage level, the third electric field is applied across the element. The holographic display of claim 1 configured to:

3. when the second electric field is greater than the first electric field and the third electric field is greater than the second electric field, the first voltage level is zero voltage; the second voltage level is a non-zero voltage; the third voltage level is a non-zero voltage; when the second electric field is smaller than the first electric field and the third electric field is smaller than the second electric field, the first voltage level is a non-zero voltage; the second voltage level is a non-zero voltage; the third voltage level being zero voltage; The holographic display of claim 2.

4. light incident on said element of said liquid crystal layer is linearly polarized; 10. A holographic display as claimed in any preceding claim, wherein the output polarising element comprises a linear output polariser.

5. 5. The holographic display of claim 4, wherein the liquid crystal layer comprises liquid crystals configured to align parallel to a plane of the liquid crystal layer when the first electric field, the second electric field, and the third electric field are applied across the element.

6. 6. A holographic display as claimed in claim 4 or 5, wherein the light incident on the liquid crystal layer has a polarization state and the output polarizing element is oriented to transmit substantially all light having a particular polarization state.

7. The liquid crystal layer forms at least a part of a reflective spatial light modulator, SLM, and the light is before entering the element of the liquid crystal layer; and After passing through the element in the liquid crystal layer, and configured to pass the output polarizing element.

7. The holographic display of claim 6.

8. 5. The holographic display of claim 4, wherein the liquid crystal layer comprises liquid crystals configured to align parallel to a plane of the liquid crystal layer when the electric field applied across the element is zero and to rotate away from the plane when a non-zero electric field is applied.

9. light incident on said element of said liquid crystal layer is circularly polarized; The holographic display of any one of claims 1 to 3, wherein the output polarizing element comprises a linear output polarizer.

10. The liquid crystal layer includes a liquid crystal, and the liquid crystal comprises aligned perpendicular to the plane of the liquid crystal layer when the electric field applied across the element is zero; rotates towards the plane when the electric field applied across the element is non-zero; 10. The holographic display of claim 9 configured so as to

11. The liquid crystal layer includes a liquid crystal, and the liquid crystal comprises configured to align parallel to the plane of the liquid crystal layer when the electric field applied across the element is zero, and to rotate away from the plane when a non-zero electric field is applied.

10. The holographic display of claim 9.

12. light incident on the element of the liquid crystal layer has an initial polarization associated with a first Jones vector; the output polarizing element is associated with a second Jones vector; the elements of the liquid crystal layer are associated with Jones matrices, the Jones matrices of the elements being a function of the electric field applied to the elements; the second Jones vector is based on the Jones matrix and the first Jones vector; A holographic display according to any preceding claim.

13. The display comprises: a polarization modifying element disposed between the output polarizing element and the liquid crystal layer and configured to modify the polarization state of light; a polarizing beam splitter including the output polarizing element and configured to remove substantially all of the light having the second polarization state, p; the liquid crystal layer forms at least a portion of a reflective SLM; the elements of the liquid crystal layer are associated with a Jones matrix, J(B), the Jones matrix of the element being a function of the electric field, B, applied to the element; The polarization-modifying element is associated with a Jones matrix, R, RJ(B')Rp=p, where J(B') is the Jones matrix associated with the elements of the liquid crystal layer at the second electric field, B'; The holographic display according to any one of claims 1 to 11.

14. 14. The holographic display of claim 13, wherein the polarization-modifying element is a waveplate having half the retardance of J(B') and a slow axis aligned with the fast axis of J(B').

15. a lens positioned to receive light transmitted by the output polarizing element and configured to generate a Fourier transform of a target light field, F(H), at a focal plane of the lens; a spatial filter disposed at the focal plane and configured to remove a Fourier transform of a complex conjugate of a target light field, F(H*); 10. A holographic display according to any preceding claim, further comprising:

16. 16. The holographic display of claim 15, wherein the spatial filter is configured to reject a Fourier transform of a complex conjugate of the target light field, F(H*), and a zeroth order of the target light field.

17. 16. The holographic display of claim 15, wherein the spatial filter is configured to remove a Fourier transform of a complex conjugate of the target light field, F(H*), without filtering a zeroth order of the target light field.

18. when the first electric field is applied across the element, the light has a first phase; when the third electric field is applied across the element, the light has a second phase; The first phase and the second phase are arranged in different quadrants on an Argand diagram. A holographic display according to any preceding claim.

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