HOLOGRAPHIC DISPLAYS AND METHODS

Abstract

A holographic display is provided. The display comprises (i) an illumination source configured to emit at least partially coherent light, (ii) a liquid crystal layer comprising 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 an element of the liquid crystal layer, the light from the element has a first polarisation state, (b) when a second electric field is applied across the element, the light has a second polarisation state, and (c) when a third electric field is applied across the element, the light has a third polarisation state. The display further comprises (iii) a controller configured to control electric fields applied across the elements, and (iv) an output polarising element, configured to: (a) remove a portion of light having the first polarisation state and also transmit a portion of the light having the first polarisation state, (b) remove substantially all of the light having the second polarisation state, and (c) remove a portion of the light having the third polarisation state and also transmit a portion of the light having the third polarisation 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 lower than the first electric field, and the third electric field is lower than the second electric field.

Claims

1. A holographic display, comprising: an illumination source configured to emit at least partially coherent light; a liquid crystal layer comprising an array of elements arranged to be illuminated by the light and configured such that: when a first electric field is applied across an element of the liquid crystal layer, the light from the element has a first polarisation state; when a second electric field is applied across the element of the liquid crystal layer, the light from the element has a second polarisation state; and when a third electric field is applied across the element of the liquid crystal layer, the light from the element has a third polarisation state; a controller configured to control electric fields applied across the elements of the liquid crystal layer; and an output polarising element configured to: remove a portion of light having the first polarisation state and also transmit a portion of the light having the first polarisation state; remove substantially all of the light having the second polarisation state; and remove a portion of the light having the third polarisation state and also transmit a portion of the light having the third polarisation state; wherein one of: the second electric field is greater than the first electric field, and the third electric field is greater than the second electric field; and the second electric field is lower than the first electric field, and the third electric field is lower than the second electric field.

2. The holographic display according to claim 1, wherein: the controller is configured to control electric fields applied across the elements of the liquid crystal layer by controlling voltages applied to the elements of the liquid crystal layer; and the liquid crystal layer is configured such that: 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; and when the element is operated at a third voltage level, the third electric field is applied across the element.

3. The holographic display according to claim 2, wherein: 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 a zero voltage; the second voltage level is a non-zero voltage; and the third voltage level is a non-zero voltage; and when the second electric field is lower than the first electric field, and the third electric field is lower 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.

4. The holographic display according to claim 1, wherein light incident upon the element of the liquid crystal layer is linearly polarised and wherein the output polarising element comprises a linear output polariser.

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

6. The holographic display according to claim 4, wherein the light incident upon the liquid crystal layer has a polarisation state, and the output polarising element is orientated to transmit substantially all light having the particular polarisation state.

7. The holographic display according to claim 6, wherein the liquid crystal layer forms at least part of a reflective spatial light modulator, SLM, and the light is configured to pass through the output polarising element, both: before being incident upon the element of the liquid crystal layer; and after passing through the element of the liquid crystal layer.

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

9. The holographic display according to claim 1, wherein light incident upon the element of the liquid crystal layer is circularly polarised and wherein the output polarising element comprises a linear output polariser.

10. The holographic display according to claim 9, wherein the liquid crystal layer comprises liquid crystals that are configured to: align perpendicular to a plane of the liquid crystal layer when the electric field applied across the element is zero; and rotate towards the plane when the electric field applied across the element is non-zero.

11. The holographic display according to claim 9, wherein the liquid crystal layer comprises liquid crystals that are configured to align parallel to a plane of the liquid crystal layer when the electric field applied across the element is zero, and rotate away from the plane when a non-zero electric field is applied.

12. The holographic display according to claim 1, wherein: light incident upon the element of the liquid crystal layer has an initial polarisation associated with a first Jones vector; the output polarising element is associated with a second Jones vector; the element of the liquid crystal layer is associated with a Jones matrix, wherein the Jones matrix for 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.

13. The holographic display according to claim 1, wherein the display further comprises: a polarisation modifying element arranged between the output polarising element and the liquid crystal layer and configured to modify a polarisation state of light; and a polarising beam splitter comprising the output polarising element and configured to remove substantially all of the light having the second polarisation state, p; and wherein: the liquid crystal layer forms at least part of a reflective SLM; the element of the liquid crystal layer is associated with a Jones matrix, J(B), wherein the Jones matrix for the element is a function of the electric field, B, applied to the element; the polarisation modifying element is associated with a Jones matrix, R; and RJ(B)Rp=p, where J(B) is the Jones matrix associated with the element of the liquid crystal layer at the second electric field, B.

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

15. The holographic display according to claim 1, further comprising: a lens arranged to receive light transmitted by the output polarising element and configured to generate a Fourier transform, F(H), of a target light field at a focal plane of the lens; and a spatial filter positioned at the focal plane and configured to remove a Fourier transform of complex conjugate of target light field, F(H*).

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

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

18. The holographic display according to claim 1, wherein: 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; wherein the first phase and the second phase are located in different quadrants on an Argand diagram.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0073] FIG. 1 is a diagrammatic representation of an example holographic display according to an embodiment;

[0074] FIG. 2 is a schematic diagram of the holographic display of FIG. 1;

[0075] FIG. 3 is an Argand diagram showing the range of phase and amplitude modulation using a holographic display of a first embodiment;

[0076] FIG. 4 is a schematic diagram of another holographic display, according to an example;

[0077] FIG. 5 is an Argand diagram showing the range of phase and amplitude modulation using a holographic display of a second embodiment; and

[0078] FIG. 6 is a schematic diagram of a holographic display including a lens and filter.

DETAILED DESCRIPTION

[0079] FIGS. 1 and 2 depict a system 100 forming at least part 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 light rays towards a liquid crystal layer 104 of an SLM 106. In other examples, the illumination source 102 comprises a plurality of light emitters which together illuminate the liquid crystal layer 104. Examples using a plurality of light emitters may also have the ability to control light emitters individually or by region, enabling reduced power consumption and/or increased 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 range of a single wavelength.

[0080] Light rays, emitted by the illumination source 102, travel at least from the illumination source 102 to the liquid crystal layer 104. The light rays follow an optical path along an optical axis 116, from the illumination source 102 towards the eyes of an observer that is viewing the holographic display.

[0081] The liquid crystal layer 104 comprises 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 the electric field causes a rotation of the liquid crystals and therefore may alter the polarisation state of light as it passes through the element 104a.

[0082] The SLM 106 of this example further comprises an output polarising element 110 positioned after the liquid crystal layer 104 along the optical path.

[0083] Although in this example the SLM 106 comprises both the liquid crystal layer 104 and the output polarising element 110, in other examples, the SLM 106 may not comprise the output polarising element 110. The output polarising element 110 may then be separate to the SLM 106.

[0084] Light rays, emitted by the illumination source 102, therefore travel through the liquid crystal layer 104 and are incident upon the output polarising element 110 along the optical path. Depending upon the polarisation of the light as it reaches the output polarising element 110 (which can be influenced by the voltage applied to the particular element 104a), the light may be blocked, or may partially pass through the output polarising element 110.

[0085] In FIGS. 1 and 2, the output polarising element 110 is shown as being a transmissive polariser, in which the polariser itself can absorb at least a portion of the light incident upon it (and/or allow at least a portion of the light to pass through). It will be appreciated that the same concepts are applicable to other types of polarisers also. In some examples, the output polarising element 110 comprises a polarising element and an absorbing element, where the absorbing element absorbs light reflected from and/or transmitted through the polarising element. For example, the polarising element may be a reflective polariser that separates light into two separate beams and directs unwanted light towards an absorbing element. Regardless of the type, the output polarising element 110 is configured to either: (i) remove a portion of light having a particular polarisation state (such as a first or third polarisation state) and also transmit a portion of the light having the particular polarisation state, or (ii) remove substantially all of the light having a different polarisation state (such as a second polarisation state). In this example, the output polarising element 110 is a linear polariser. The output polarising element 110, is positioned after the liquid crystal layer 104 along the optical path taken by the light.

[0086] Similarly, in FIGS. 1 and 2, the SLM 106 is shown as being transmissive such that the light enters one side of the layer (such as the front side) and passes out of a different side of the layer (such as a rear side). Again, it will be appreciated that the same concepts are applicable to other types of SLM too. For example, the SLM may be a reflective liquid crystal layer, such that the light enters and passes out of the same side it entered (such as the front side). As noted earlier, in cases where the SLM is reflective, the output polarising element 110 may generally not be considered as part of the SLM. An example reflective SLM is discussed later and is illustrated in FIG. 4.

[0087] The output polarising element 110, together with the liquid crystal layer 104, therefore modulate the amplitude of light rays from the liquid crystal layer 104. For example, if a light ray that is linearly polarised along a vertical axis 112 is traveling in a direction along the optical axis 116 (and therefore has a particular Jones vector), and is incident upon a vertically orientated output polarising element (again, having a particular Jones vector), the light ray transmitted by the output polarising element 110 may have substantially 100% of its initial intensity (i.e., the amplitude of the transmitted light ray is unchanged and/or is at maximum). Such a vertically orientated output polarising element may be said to be aligned with the linearly polarised light ray and is therefore arranged an angle of 0 radians relative to the linearly polarised light ray incident upon the output polarising element. Conversely, if a light ray is linearly polarised along the horizontal axis 114 and is incident upon a vertically orientated output polarising element, the light ray may have substantially 0% of its initial intensity after interacting with the output polarising element (i.e., the amplitude of the transmitted light ray is at a minimum, or zero). Such a vertically orientated output polarising element may be said to be crossed with the horizontally polarised light ray and is therefore arranged an angle of /2 radians relative to the linearly polarised light ray incident upon the output polarising element. When substantially all of the light incident upon the output polarising element is blocked/removed by the output polarising element, the output polarising element may be said to remove substantially all of the light having a particular polarisation state.

[0088] In another example, if a light ray that is linearly polarised along a vertical axis 112 is traveling in a direction along the optical axis 116, and is incident upon an output polarising element that is arranged at an angle of /4 radians relative to the vertical axis 112, the light ray may have approximately 50% (i.e., 0.5) of its initial intensity after interacting with the output polarising element (i.e., the amplitude of the transmitted light ray is {square root over (0.5)}). Such an orientated output polarising element is therefore arranged an angle of /4 radians relative to the linearly polarised light ray incident upon the output polarising element. When a portion (such as 50% of the light intensity) is transmitted by the output polariser, the output polarising element may be said to remove a portion of light having a particular polarisation state and also transmit a portion of the light having the particular polarisation state. The removed portion may be absorbed by the polarising element, or an absorbing element, for example.

[0089] In some examples, the system 100 comprises an input polarising element 108 arranged between the illumination source 102 and the liquid crystal layer 104. An input polarising element 108 can polarise light such that the polarised light is incident upon the liquid crystal layer 104. In some examples the input polarising element 108 is omitted if the light emitted by the illumination source 102 is already polarised in the desired way. In some examples, the input polarising element 108 is a linear polariser (as depicted in FIG. 1), but in other examples, the input polarising element 108 is a different type of polariser, such as a circular polariser.

[0090] FIG. 2 depicts a controller 120 that can control the electric fields/voltages applied to each element of the liquid crystal layer 104 to provide full control over the amplitude (and possibly phase) modulation of light output by the system 100. The controller 120 may also control operation of the illumination source 102.

[0091] FIGS. 1 and 2 also depict a linear arrangement of the holographic display but other arrangements may include image folding components. For example, a folded optical path may be provided.

[0092] As discussed, the inventors have realised that an optical system can be configured such that when an element 104a is controlled at particular voltage levels, it is possible to modulate the amplitude of light through zero as the voltage is increased or decreased.

[0093] To illustrate this more clearly, several embodiments will be discussed in turn.

In-Plane Switching (IPS) Based Liquid Crystal Layer

[0094] In a first embodiment, the liquid crystal layer 104 is an In-Plane Switching (IPS) based liquid crystal layer 104. FIG. 3 depicts an example Argand/phasor diagram for an example system comprising the IPS based liquid crystal layer 104. The phasor diagram represents the amplitude and phase of light after interaction with the output polarising element 110. The amplitude of a light ray after interaction with the output polarising 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 on the real axis. The phase of the light ray is given by the azimuthal angle between the positive real axis and the position of a point on the diagram. The location of a point on the phasor diagram can be adjusted by controlling the voltage(s) applied to an element 104a of the liquid crystal layer 104.

[0095] As mentioned, the phasor diagram of FIG. 3 is representative of an example system comprising the IPS based liquid crystal layer 104, a particular polarisation of light incident upon the layer 104, and a particular orientation of the output polarising element 110. In this case, the light incident upon the liquid crystal layer 104 is linearly polarised, and the output polarising element 110 comprises a linear polariser.

[0096] An IPS based liquid crystal layer 104 may be characterised as having a Jones matrix comprising only real terms, or having a Jones matrix that is approximately proportional to a real matrix. In more general terms, IPS liquid crystal layers 104 comprise liquid crystal molecules that are: (i) aligned parallel to the layer/display (in-plane), and (ii) reoriented (as a result of the applied voltage) while remaining essentially parallel to the layer. For example, in absence of an applied voltage, the liquid crystals may be aligned 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 at different respective orientations about an axis that is perpendicular to the plane of the layer. With regard to FIG. 1, a longitudinal axis of a liquid crystal may be aligned in plane defined by axes 112 and 114, and thus rotate about the optical axis 116. The optical axis 116 is therefore perpendicular to a plane defined by the liquid crystal layer 104.

[0097] In one particular example, the liquid crystal layer 104 has a Jones matrix given by a rotation matrix approximately proportional to:

[00001]$\left(\begin{array}{cc}{\cos \left(\right)}^2-{\sin \left(\right)}^2& 2\sin \left(\right)\cos \left(\right)\\ 2\sin \left(\right)\cos \left(\right)& {\sin \left(\right)}^2-{\cos \left(\right)}^2\end{array}\right)$

[0098] Where angle, is the fast axis orientation angle measured with respect to the orientation in the quiescent state, and is a function of the applied voltage to the particular element of the liquid crystal layer 104. In this particular example, is in the range [0, /4]. This particular Jones matrix is a model describing a half wave plate rotated at an angle from its orientation in the quiescent state. For example, linear light polarised light at an angle (measured from the orientation of the fast axis of the liquid crystal in the quiescent state) will be transformed to linearly polarised light at an angle 2, so if is set to be 0 then the liquid crystal layer 104 can therefore rotate the polarisation of light in the range [0, /2], where the rotation angle of the polarised light is twice the fast axis orientation angle.

[0099] It will be appreciated that the Jones matrix representation above (and any other example representations discussed herein) are approximate models, which are used to inform the candidate polariser configurations, rather than exact descriptions of a real liquid crystal layer. The examples have been found to be a sufficiently accurate models for that purpose, but are idealised representations.

[0100] In a similar way, a polarisation state of light can be represented by a Jones vector and the particular orientation/configuration of the output polarising element can be represented by a Jones vector. Light incident upon the liquid crystal layer 104 may therefore have a first Jones vector, and the output polarising element 110 may have a second Jones vector.

[0101] It can therefore be shown that for linearly polarised light (that is incident upon the IPS liquid crystal layer 104), applying a voltage to a particular element 104a of the liquid crystal layer 104 causes a pure rotation of the polarisation state of the light by an angle of 2. The incident light may be linearly polarised by a linear input polarising element 108, for example.

[0102] In this example system, the output polarising element 110 is arranged at a specific angle 118 relative to the initial polarisation of the light, such that as the voltage applied to an 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 an appropriate angle 118 and an initial polarisation. The orientation angle 118 of the output polarising element 110 may be defined as an angle extending around the optical axis 116 (relative to a reference point, such as the vertical axis 112). The inherent properties of the output polarising element 110 and the angle 118 are represented by the Jones vector of the output polarising element 110.

[0103] At a first point in time, a first voltage level is applied to an element 104a. In this example, the first voltage level is zero (or 0V). The element 104a is accordingly in a quiescent state because there is no electric field applied to the liquid crystals in the element 104a. In this case, when the element is in its quiescent state, =0. Light passing through the element has a first polarisation state (which may be unchanged from its initial polarisation state). As mentioned above, the linearly polarised light, the voltage level and the angle 118 relative to the initial polarisation, are such that the intensity of light is attenuated by around 50% by the output polarising element 110 (thus, a portion of light is removed and a portion of light is transmitted). This can be achieved by orientating the polariser 110 at an angle of /4 radians relative to the polarisation state of the linearly polarised light ray that has passed through the element 104a. More generally, the output polariser 110 may be arranged at an angle between /8 radians and 3/8 radians (although this would affect the intensity of light that is attenuated).

[0104] Due to the initial polarisation (characterised by the first Jones vector), and the type of liquid crystal layer 104 (characterised by the Jones matrix), it can be shown that at such a voltage level, the light does not undergo a phase modulation. The light is therefore represented on the phasor diagram by point 202, where the light has 50% of its initial, incident intensity (an amplitude of +{square root over (0.5)}, as shown in FIG. 3) and no phase modulation.

[0105] Later, if the voltage is increased from the first voltage level (in this case 0V), to a second (higher, non-zero) voltage level, the linearly polarised light is rotated within the element 104a. The light passing through the element 104a therefore has a second polarisation state, different to when the element 104a was operated at the first voltage level. In this case, =/8 radians. This rotation increases the angle between the output polarising element 110 and the light. At this second voltage level the angle between the output polarising element 110 and the light ray may be approximately /2 radians such that the light ray having the second polarisation state is blocked/absorbed by the output polarising 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 rotated by /4 radians relative to the light ray in the quiescent state and therefore be perpendicular to the polariser 110 such that an angle of /2 radians is subtended between the light ray and the polariser 110. The light is therefore represented on the phasor diagram by point 204, where the light has approximately 0% of its incident intensity and amplitude (shown by its location at the origin of the Argand diagram in FIG. 3).

[0106] Later still, if the applied voltage continues to be increased from the second voltage level to a third (higher, non-zero) voltage level (which may be a maximum voltage), the light is rotated further and has a third polarisation state, different to the second polarisation state. In this case, =/4 radians. This rotation further increases the angle between the output polarising element 110 and the light. At this third voltage the angle between the output polarising element 110 and the light ray may be approximately 3/4 radians such that the output light again has an intensity of approximately 50% of its maximum intensity (thus, a portion of light is removed and a portion of light is transmitted). For example, at the third voltage level, the light passing through the element 104a may have rotated by /4 radians relative to the light ray at the second voltage level and therefore /2 radians relative to the light ray in the quiescent state. Due to the extent of the rotation beyond /2 radians, the light is represented in a different quadrant on the phasor diagram. This is effectively represented as light having a negative amplitude. Accordingly, the light is represented on the phasor diagram by point 206, where the light has approximately 50% of its maximum intensity (an amplitude of {square root over (0.5)}, as shown in FIG. 3) and an effective phase modulation of radians.

[0107] FIG. 3 therefore illustrates how the amplitude of light can be modulated through zero by arranging an output polarising element 110 at a specific angle 118 such that as the voltage applied to an element is increased from a first voltage level to a third voltage level via a second voltage level, the intensity decreases from a particular level to zero and then increases again. The zero amplitude is achieved at this second, intermediate voltage level. As discussed, this is achieved by having a linear input polarisation state aligned to the quiescent orientation of the liquid crystals (i.e., the first Jones vector may be (1, 0)), and a linear output polarising element at /4 radians to the input polarisation (i.e., the second Jones vector may be (1, 1; 1, 1)).

[0108] In summary, in this embodiment, the light incident upon the liquid crystal layer has a linear polarisation (in any orientation), and the linear output polariser is orthogonal to the light from the liquid crystal layer at an intermediate value of (e.g. at =/8). This modulates the output amplitude according to sin(2(/8)), achieving pure amplitude modulation in the range [{square root over (0.5)}, +{square root over (0.5)}]. A particular example has an output polariser which matches the input polarisation state, meaning that the polariser can be part of a reflective SLM, and light is passed through both on input and output paths. For example, an input orientation of (cos(/8), sin(/8)) will be transformed to (cos(3/8), sin(3/8)) when =/8, which is orthogonal to an output polariser passing (cos(/8), sin(/8)).

[0109] It will be appreciated that the same effect can be achieved when the voltage is decreased from a first voltage level to a third voltage level. For example, the first voltage level may be a maximum voltage level, and it is decreased to a third, zero voltage level, via a second intermediate voltage level.

[0110] In a variation of the above embodiment, is in the range [0, /2] for a custom IPS based liquid crystal layer. This may be achieved by driving an IPS based liquid crystal layer with greater electric field to achieve more rotation. In this variation, the light incident upon the liquid crystal layer has a linear polarisation (in any orientation), and the linear output polariser is orthogonal to the light from the liquid crystal layer at an intermediate value of (e.g. at (=/4). This modulates the output amplitude according to sin(2(/4)), achieving pure amplitude modulation in the range [1, +1]. As such, by reference 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 polariser which matches the input polarisation state, meaning that the polariser can be part of a reflective SLM, and light is passed through both on input and output paths. For example, an input orientation of (1, 0) will be transformed to (0, 1) when =/4, which is orthogonal to an output polariser passing (1, 0).

Twisted Nematic (TN) Based Liquid Crystal Layer

[0111] FIG. 3 is also representative of an example system 100, where the liquid crystal layer 104 is a TN based liquid crystal layer 104. As with the first embodiment discussing IPS based liquid crystal layers, in this second embodiment, the light incident upon the liquid crystal layer 104 is linearly polarised (for example, has a Jones vector of (1, 0)) and the output polarising element 110 is arranged at an angle of /4 radians relative to the reference axis 112.

[0112] A TN based liquid crystal layer 104 may be characterised as having liquid crystal molecules that are: (i) aligned parallel to a plane defined by the liquid crystal layer 104 in absence of an applied electric field/voltage (when the electric field/voltage is zero), and (ii) reoriented (as a result of a non-zero electric field/voltage being applied) away from the plane. Reorientating away from the plane may be referred to as rotating towards being perpendicular to the plane.

[0113] In one particular example, the liquid crystal layer 104 has a Jones matrix given by a rotation matrix approximately proportional to:

[00002]$\left(\begin{array}{cc}\cos \left(\right)& \sin \left(\right)\\ -\sin \left(\right)& \cos \left(\right)\end{array}\right)$

[0114] As for the IPS based liquid crystal layer variation discussed above, is in the range [0, /2], and =0 when an element of liquid crystal layer is in a quiescent state, and =/2 when the electric field applied to the element is at a maximum. In this embodiment, the light incident upon the liquid crystal layer has a linear polarisation (in any orientation), and the linear output polariser is arranged at /4 degrees relative to the input polarisation. This modulates the output amplitude according to (cos -sin )/{square root over (2)}, achieving pure amplitude modulation in the range [{square root over (0.5)}, +{square root over (0.5)}]. As such, by reference to the Argand diagram of FIG. 3, the amplitude at point 202 is +{square root over (0.5)}, the amplitude at point 204 is 0, and the amplitude at point 206 is {square root over (0.5)}.

Reflective SLM

[0115] FIG. 4 depicts a schematic diagram of another system 150 forming at least part 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 discussed earlier. Light rays, emitted by the illumination source 152, travel at least from the illumination source 152 to a liquid crystal layer 154. The light rays follow a non-linear optical path, from the illumination source 152 towards the eyes of an observer that is viewing the holographic display.

[0116] The liquid crystal layer 154 comprises an array of pixels/elements. In contrast to the example of FIGS. 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 elements. The presence of the electric field causes a rotation of the liquid crystals and therefore may alter the polarisation state of light as it passes through the element.

[0117] The system of this example further comprises a polarising beam splitter 160 that splits the beam of light from the illumination source 152 into a transmitted and reflected beam, the reflected beam being reflected towards and subsequently incident upon the liquid crystal layer 154. The transmitted beam may be absorbed elsewhere in the system 150. After passing through the liquid crystal layer 154, the light is incident upon the polarising beam splitter 160, and is again split into a transmitted and reflected beam, the reflected beam being reflected back towards the illumination source 152 and the transmitted beam being ultimately viewable by an observer of the holographic display. In addition to splitting the beam, the polarising beam splitter 160 can also polarise the light incident upon it. In this example, the polarising beam splitter 160 is a linear polariser.

[0118] The system of this example further comprises a waveplate 156. In this example, the waveplate 156 is a circular/elliptical polariser, such that circularly or elliptically polarised light is incident upon the liquid crystal layer 154, and subsequently, circularly or elliptically polarised light is incident upon the polarising beam splitter 160 after passing through the liquid crystal layer 154, and the waveplate 156 a second time.

[0119] FIG. 4 further depicts a controller 158 that can control the electric fields/voltages applied to each element of the liquid crystal layer 154 to provide full control over the amplitude (and possibly phase) modulation of light output by the system 150. The controller 158 may also control operation of the illumination source 152.

[0120] In another example, rather than having a polarising beam splitter, the system comprises a non-polarising beam splitter, an input polariser and an output polariser, where both polarisers are circular/elliptical polarisers. The light would travel from the illumination source, through the input polariser, through the beam splitter, through the liquid crystal layer, through the beam splitter, and then through the output polariser.

[0121] Use of a polarising beam splitter can be beneficial over a non-polarising beam splitter by reducing efficiency losses. In both examples, the SLM comprises the liquid crystal layer and the polariser(s) are separate to the SLM.

[0122] Mathematically, the SLM (that is, the reflective liquid crystal layer 154) can be described with a Jones matrix J(B), where B is the applied electric field 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 polarising beam splitter 160 can be described as removing polarisation p from the output.

[0123] R can be chosen such that RJ(B)Rp=p for some intermediate value of B, denoted B (by operating an element of the liquid crystal layer 154 at the second/intermediate electric field). This may be achieved by setting RJ(B)R=I, where I is the identity matrix. This means that the polarisation of the waveplate cancels out the polarisation effects of the SLM at B. As a result, when the element is operated at B, the light incident on the polarising beam splitter 160 (after passing through the element) has the same polarisations state as it was when it was originally incident on the polarising beam splitter 160 (i.e., before being incident upon the element). This means that if the light was reflected by the polarising beam splitter 160 towards the element on the first pass, then it is reflected again on the second pass (i.e., it is reflected back to where it came from originally (i.e., back towards the illumination source). That means no light is seen by the viewer, since the light is removed by the polarising beam splitter 160. Conversely, to be seen by a viewer, the light needs to pass through the beam splitter in a direction it did not originally come from (i.e., be transmitted by the polarising beam splitter 160). This is achieved by operating the liquid crystal layer at other values of B, which changes the polarisation state of the light, which therefore allows at least some light get routed to the output (and be seen by the viewer).

[0124] As discussed earlier, for reflective liquid crystal layers 154, the Jones matrix of the liquid crystal layer 154, J, describes a double-pass through the SLM. In this example, the light undergoes pure retardance through the SLM (it can be shown that a double pass in opposite directions causes the rotations introduced by the liquid crystal layer to cancel out, leaving only a retardance).

[0125] In one example, R is a waveplate with half the retardance of J(B), and its slow axis aligned to the fast axis of J(B).

[0126] As such, light rays, emitted by the illumination source 152, therefore travel through the liquid crystal layer 154 and are incident upon the polarising beam splitter 160 along the optical path. Depending upon the polarisation of the light as it reaches the polarising beam splitter 160 (which can be influenced by the voltage applied to the particular element), the light may be blocked (when B=B), or may partially pass through the polarising beam splitter 160.

Vertically Aligned (VA) Based Liquid Crystal Layer

[0127] FIG. 5 depicts an example Argand/phasor diagram for the example system 150, where the liquid crystal layer 154 is a VA based liquid crystal layer 154. In this second embodiment, the light incident upon the liquid crystal layer 154 is circularly polarised (as a result of the waveplate 156), and the polarising beam splitter 160 comprises a linear polariser.

[0128] VA based liquid crystal layers 154 are typically found in Liquid Crystal on Silicon (LCoS) SLMs. A VA based liquid crystal layer 154 may be characterised as having liquid crystal molecules that are: (i) aligned perpendicular to a plane defined by the liquid crystal layer 154 (i.e., vertically), and (ii) reoriented (as a result of the applied voltage) towards the plane. For example, in absence of an applied voltage, the liquid crystals may be aligned in a vertical arrangement, perpendicular to the plane of the layer 154, and in the presence of an applied voltage, the liquid crystals may be rotated towards the plane. This results in a Jones matrix of the VA liquid crystal layer 154 having complex terms.

[0129] In one particular example, the liquid crystal layer 154 has a Jones matrix given by a rotation matrix proportional to:

[00003]$\left(\begin{array}{cc}1& 0\\ 0& e^i\end{array}\right)$

[0130] Where is a function of the applied voltage to the particular element of the liquid crystal layer 154. Thus, light polarised along a given axis undergoes a phase retardation of radians when passing through the liquid crystal layer, and the magnitude of is controlled by the magnitude of the applied electric field. Here the polarisation orientation that does not receive a retardation upon an applied electric field is referred to as the fast axis, and the polarisation orientation that receives a retardation is referred to as the slow axis. In this example, the fast and slow axis are aligned with the axes 112 and 114, but in general the fast and slow axes do not need to be aligned with the x and y axes of the display. In this particular example, is in the range [0, ].

[0131] It can therefore be shown that for circularly polarised incident light, such as right hand circularly polarised light (i.e., that is proportional to (1;i)), and a linear output polarising element 160 arranged at /4 degrees to the fast axis of the liquid crystal layer, applying a voltage to a particular element of the liquid crystal layer 154 causes both amplitude and phase modulation as depicted in FIG. 5. The phase modulation is dependent on amplitude, giving the relationship shown in FIG. 5.

[0132] As mentioned for the first embodiment, the output polarising element 160 is arranged in a particular configuration (and thus has a particular Jones vector), such that as the voltage applied to an element is increased (or decreased), the amplitude of the light passes through zero.

[0133] At a first point in time, a first voltage level is applied to an element. In this example, the first voltage level is zero (or 0V). The element is accordingly in a quiescent state because there is no electric field applied to the liquid crystals in the element. When the element is in its quiescent state, =0. It can be shown that at this voltage level, the light interacts with the output polarising element of the polarising beam splitter 160 and has a particular non-zero amplitude (that is a percentage of a maximum amplitude in the absence of the output polarising element) and a particular phase modulation. The light is therefore represented on the phasor diagram by point 302, where the light has a particular percentage of its maximum intensity and a phase modulation.

[0134] Later, if the voltage is increased from the first voltage level (in this case 0V), to a second (higher, non-zero) voltage level, the polarised light undergoes a rotation within the element. This rotation adjusts the polarisation state and as the light interacts with the output polarising element of the polarising beam splitter 160, the light ray has an amplitude of approximately zero so is blocked by the output polarising element. For example, at this second voltage level, =/2 radians, the right hand circularly polarised light (represented as (1;i)) is converted into linearly polarised light (represented by (1;1), i.e., +/4 radians) and the angle of the output polarising element can be set to be /4 radians. Hence, at this second voltage level, there is angle of /2 radians between the polarisation state of the light and the output polarising element and so the light is blocked by the output polarising element (i.e., the amplitude is 0). The light is therefore represented on the phasor diagram by point 304, where the light has approximately 0% of its maximum intensity.

[0135] Later still, if the applied voltage continues to be increased from the second voltage level to a third (higher, non-zero) voltage level (which may be a maximum voltage), the light is rotated further. For example, at this third voltage level, = radians. This rotation adjusts the polarisation state and as the light interacts with the output polarising element of the polarising beam splitter 160, the transmitted light ray has a non-zero amplitude (that is a percentage of a maximum amplitude in the absence of the output polarising element) and a particular phase modulation. Due to the extent of the rotation, the light is represented in a different quadrant on the phasor diagram. This is effectively represented as light having a negative amplitude. Accordingly, the light is represented on the phasor diagram by point 306, where the light has a percentage of its maximum intensity and a particular phase modulation.

[0136] FIG. 5 therefore illustrates how the amplitude of light can be modulated through 0 by arranging an output polarising element having a particular Jones vector, such that as the voltage applied to an element is increased from a first voltage level to a third voltage level via a second voltage level, the amplitude decreases from a particular level to zero and then increases again. 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 is decreased from a first voltage level to a third voltage level. For example, the first voltage level may be a maximum voltage level, and it is decreased to a third, zero voltage level, via a second intermediate voltage level. The overall modulation scheme applied by the example system is given by (1+i e.sup.i)/2.

[0137] A commercially available LCoS SLM is the Sony SXRD241A, which has a VA modality. The simplified model for a VA liquid crystal layer suggests a circular input polarisation and a linear output polarisation. Informed by this, to achieve through-zero operation, the SLM is illuminated by circularly polarised light (achieved via the waveplate 156 for example), and the orientation of a linear output polariser (such as the polarising beam splitter 160) is then set such that the modulated amplitude at zero voltage is approximately equal to the modulated amplitude at maximum voltage, and passes through zero at an intermediate voltage. For this particular Sony LCoS SLM, the output polariser orientation is approximately 25 degrees from the y axis of the SLM (i.e., axis 112).

Low Twist Twisted Nematic (TN) Based Liquid Crystal Layer

[0138] FIG. 5 is also representative of an example system 150, where the liquid crystal layer 154 is a low twist TN based liquid crystal layer 154. Some example TN based liquid crystal layers (e.g., a double-pass through a reflective TN layer) can be described as a pure retardance, with little to no effect from the twist of the TN. Such TN based liquid crystal layers may be referred to as a low twist TN based liquid crystal layer (relative to a more typical TN liquid crystal layer, such as that described earlier). As with the second embodiment discussing VA based liquid crystal layers, in this third embodiment, the light incident upon the liquid crystal layer 154 is circularly polarised (as a result of the waveplate 156), and the polarising beam splitter 160 comprises a linear polariser.

[0139] A low twist TN based liquid crystal layer 154 may be characterised as having liquid crystal molecules that are: (i) aligned parallel to a plane defined by the liquid crystal layer 104 in absence of an applied electric field/voltage (when the electric field/voltage is zero), and (ii) reoriented/rotated (as a result of a non-zero electric field/voltage being applied) away from the plane. Reorientating/rotating away from the plane may be referred to as rotating towards being perpendicular to the plane. In one particular example, the liquid crystal layer 154 has a Jones matrix given by a rotation matrix that is the same as the Jones matrix for the VA based liquid crystal layer provided above. As for the VA based liquid crystal layer, is in the range [0, ], but in contrast to the VA based liquid crystal layer, = when an element of liquid crystal layer is in a quiescent state, and =0 when the electric field applied to the element is at a maximum. As such, the TN based liquid crystal layer 154 behaves similarly to the VA based liquid crystal layer, and the overall modulation scheme applied by the example system is given by (1+i e.sup.i)/2.

Filtering

[0140] FIG. 6 depicts at least part 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 system 100, 150, the display 400 further comprises 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 system 100, 150. In other examples, the distance between the lens 402 and the SLM may be different. The display 400 further comprises a filter 404, such as a spatial filter, delimiting an aperture. The filter 404 is positioned one focal length from the lens 402, on the opposite side of the lens 402 from the SLM. As shown, the SLM, lens 402 and filter 404 are coaxial along the optical axis 116. Other configurations may also be used, such as a folded light path that may allow a more compact display.

[0141] The SLM is configured to generate a light field which is a quantised representation of a target light field, H, as has been discussed above. The arrangement of the holographic optical display 400 is such that the Fourier transform of the light field, F(H), is formed at a plane coinciding with the position of the filter 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 the Fourier transform of the complex conjugate of the target light field, F(H*) in the Fourier plane of the SLM. Further, the aperture in the filter 404 is positioned such that portions of the target light field are blocked. For example, the filter is arranged to remove a Fourier transform of complex conjugate of target light field, F(H*). This can be effective to reduce the effect of quantisation noise. As mentioned, due to the specific modulation scheme discussed in FIGS. 1-5, the filter does not necessarily need to filter a zero order of the target light field. However, as mentioned, the zero-order may still be filtered, in some examples, but due to the lower energy in the zero-order, the filtering is easier than in conventional systems. The zero-order can therefore still be filtered to remove any residual zero-order.

[0142] The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.