HOLOGRAPHIC DISPLAYS AND METHODS

Abstract

An example holographic display may comprise an angularly dispersive micromirror array and an optical assembly configured to emit, towards the micromirror array, a first ray of light having a first wavelength and a second ray of light having a second wavelength, the second wavelength being different to the first wavelength. The first ray of light is incident upon the micromirror array at a first angle of incidence and the second ray of light is incident upon the micromirror array at a second angle of incidence, the second angle of incidence being different to the first angle of incidence by a predetermined amount to at least partially compensate for the dispersive effects of the micromirror array along an optical axis of the holographic display.

Claims

1. A holographic display for displaying a computer-generated hologram, the display comprising: an angularly dispersive micromirror array; and an optical assembly configured to emit, towards the micromirror array, a first ray of light having a first wavelength and a second ray of light having a second wavelength, the second wavelength being different to the first wavelength; wherein the first ray of light is incident upon the micromirror array at a first angle of incidence and the second ray of light is incident upon the micromirror array at a second angle of incidence, the second angle of incidence being different to the first angle of incidence by a predetermined amount to at least partially compensate for the dispersive effects of the micromirror array along an optical axis of the holographic display.

2. A holographic display according to claim 1, wherein the optical assembly comprises: an illumination assembly configured to emit the first ray of light having the first wavelength and the second ray of light having the second wavelength; and an angularly dispersive optical element arranged between the illumination assembly and the micromirror array, such that the first and second rays of light travel from the illumination assembly to the micromirror array via the angularly dispersive optical element; wherein the angularly dispersive optical element has a substantially equal and opposite angularly dispersive effect to that of the micromirror array, such that the first and second rays of light are transmitted from the optical element in different directions and are separated by an angle equal to the predetermined amount.

3. A holographic display according to claim 2, wherein the optical element is a diffraction grating.

4. A holographic display according to claim 3, wherein the diffraction grating has: a pitch substantially corresponding to a pixel pitch of the micromirror array; and a blaze angle substantially corresponding to a mirror tilt angle of the micromirror array.

5. A holographic display according to claim 2, wherein the optical element is a second micromirror array.

6. A holographic display according to claim 5, wherein the micromirror array and the second micromirror array have substantially the same pixel pitch and mirror tilt angle.

7. A holographic display according to claim 2, wherein: maximum intensities of the first ray of light and the second ray of light, reflected from the micromirror array, occur substantially at a particular diffraction order, n.sub.micromirror, of each ray; maximum intensities of the first ray of light and the second ray of light, reflected from the optical element, occur substantially at a particular diffraction order, n.sub.OE, of each ray; the micromirror array has a pixel pitch, p.sub.micromirror and the optical element has a pitch, p.sub.OE; and n.sub.micromirror/p.sub.micromirror=n.sub.OE/p.sub.OE, such that the angularly dispersive optical element has a substantially equal and opposite angularly dispersive effect to that of the micromirror array.

8. A holographic display according to claim 7, wherein n.sub.micromirror=n.sub.OE for each ray of light, and p.sub.micromirror=p.sub.OE.

9. A holographic display according to claim 2, wherein the illumination assembly comprises an illumination source configured to emit a plurality of rays of light having a range of wavelengths, the plurality of rays of light including the first ray of light having the first wavelength and the second ray of light having the second wavelength.

10. A holographic display according to claim 9, wherein the illumination source comprises a light emitting diode, LED.

11. A holographic display according to claim 9, wherein the illumination source is a first illumination source, and the illumination assembly further comprises: a second illumination source configured to emit a second plurality of rays of light having a second range of wavelengths, the second plurality of rays of light including a third ray of light having a third wavelength and a fourth ray of light having a fourth wavelength, wherein: the third and fourth rays of light travel from the illumination assembly to the micromirror array via the angularly dispersive optical element; such that the third and fourth rays of light are transmitted from the optical element in different directions and are separated by a second angle equal to a second predetermined amount to at least partially compensate for the dispersive effects of the micromirror array on the second plurality of rays along the optical axis of the holographic display; and the first illumination source is arranged such that the first and second rays of light are incident upon the optical element at a third angle, and the second illumination source is arranged such that the third and fourth rays of light are incident upon the optical element at a fourth angle, wherein the third and fourth angles are different.

12. A holographic display according to claim 11, wherein the first ray and the second ray are spatially separated from the third ray and the fourth ray at their incidence on the angularly dispersive optical element.

13. A holographic display, according to claim 1, wherein the optical assembly comprises: a first illumination source, configured to emit the first ray of light having the first wavelength; and a second illumination source, configured to emit the second ray of light having the second wavelength; wherein one of: the first illumination source is orientated with respect to the second illumination source such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence; and one or more optical elements are arranged between the optical assembly and the micromirror array such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence.

14. A holographic display, according to claim 13, wherein the first and second illumination sources are lasers.

15. A holographic display, according to claim 1, wherein the optical assembly comprises: a first illumination source, configured to emit the first ray of light having the first wavelength; and a second illumination source, configured to emit the second ray of light having the second wavelength; a first angularly dispersive optical element arranged in an optical path between the first illumination source and the micromirror array; a second angularly dispersive optical element arranged in an optical path between the second illumination source and the micromirror array; wherein the first and second optical elements have a substantially equal and opposite angularly dispersive effect to that of the micromirror array, and are arranged such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence.

16. A method, comprising: emitting a first ray of light having a first wavelength and a second ray of light having a second wavelength, the second wavelength being different to the first wavelength; controlling an angle of incidence of the first ray of light upon a micromirror array, such that the first ray of light is incident upon the micromirror array at a first angle of incidence; and controlling an angle of incidence of the second ray of light upon the micromirror array, such that the second ray of light is incident upon the micromirror array at a second angle of incidence; wherein the second angle of incidence is different to the first angle of incidence by a predetermined amount to at least partially compensate for the dispersive effects of the micromirror array.

17. A method according to claim 16, wherein controlling an angle of incidence of the first ray of light upon a micromirror array and controlling an angle of incidence of the second ray of light upon the micromirror array, comprises emitting the first and second rays of light towards an angularly dispersive optical element to introduce a first wavelength-dependent dispersive effect; and wherein the micromirror array introduces a second wavelength-dependent dispersive effect substantially equal and opposite in direction to the first wavelength-dependent dispersive effect.

18. A method according to claim 16, wherein emitting the first ray of light having the first wavelength and the second ray of light having the second wavelength, comprises: emitting the first ray of light from a first illumination source; and emitting the second ray of light from a second illumination source.

19. A method according to claim 17, wherein emitting the first ray of light having the first wavelength and the second ray of light having the second wavelength, comprises: emitting the first and second rays of light from the same illumination source.

20. A method according to claim 19, comprising: emitting the first and second rays of light from a first illumination source; emitting, from a second illumination source, a third ray of light having a third wavelength and a fourth ray of light having a fourth wavelength, towards the angularly dispersive optical element to introduce a first wavelength-dependent dispersive effect on the third and fourth rays of light, wherein the micromirror array introduces a second wavelength-dependent dispersive effect on the third and fourth rays of light that is substantially equal and opposite in direction to the first wavelength-dependent dispersive effect; controlling an angle of incidence of the first and second rays of light emitted by the first illumination source upon the optical element, such that the first and second rays of light are incident upon the micromirror array at a third angle of incidence; and controlling an angle of incidence of the third and fourth rays of light emitted by the second illumination source upon the optical element, such that the third and fourth rays of light are incident upon the micromirror array at a fourth angle of incidence, wherein the third and fourth angles of incidence are different.

21. A method according to claim 20, wherein the first ray and the second ray are spatially separated from the third ray and the fourth ray at their incidence on the angularly dispersive optical element.

22. A method according to claim 16, wherein: emitting the first ray of light having the first wavelength and the second ray of light having the second wavelength, comprises: emitting the first ray of light from a first illumination source; and emitting the second ray of light from a second illumination source; and controlling an angle of incidence of the first ray of light upon a micromirror array and controlling an angle of incidence of the second ray of light upon the micromirror array, comprises one of: orientating the first illumination source and second illumination source with respect to each other such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence; and controlling the light path of at least one of the first ray of light and the second ray of light such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence.

23. A method according to claim 16, wherein: emitting the first ray of light having the first wavelength and the second ray of light having the second wavelength, comprises: emitting the first ray of light from a first illumination source; and emitting the second ray of light from a second illumination source; and wherein controlling an angle of incidence of the first ray of light upon a micromirror array and controlling an angle of incidence of the second ray of light upon the micromirror array, comprises: emitting the first ray of light towards a first angularly dispersive optical element to reflect the first ray of light towards the micromirror array such that it is incident upon the micromirror array at the first angle of incidence; and emitting the second ray of light towards a second angularly dispersive optical element to reflect the second ray of light towards the micromirror array such that it is incident upon the micromirror array at the second angle of incidence.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] FIG. 1 is a diagrammatic representation of an example micromirror array in an on state;

[0057] FIG. 2 is a diagrammatic representation of an example micromirror array in an off state;

[0058] FIG. 3 is an example representation of the dispersive effects of an example micromirror array;

[0059] FIG. 4 depicts spectral curves for example red (R), green (G) and blue (B) LEDs;

[0060] FIG. 5 depicts an example arrangement to compensate for the inter-source dispersive effects of an example micromirror array when using narrowband illumination sources;

[0061] FIG. 6 illustrates how the arrangement of FIG. 5 only partially compensates for the dispersive effects of an example micromirror array when using broadband illumination sources;

[0062] FIG. 7 is a diagrammatic representation of an example optical element used to compensate for the intra-source dispersive effects of an example micromirror array;

[0063] FIG. 8A is a first diagrammatic representation of an example optical element used to compensate for both inter-source and intra-source dispersive effects of an example micromirror array when using broadband illumination sources;

[0064] FIG. 8B is a second diagrammatic representation of an example optical element used to compensate for both inter-source and intra-source dispersive effects of an example micromirror array when using broadband illumination sources;

[0065] FIG. 9 illustrates how the arrangements of FIGS. 8A and 8B compensate for both inter-source and intra-source dispersive effects of an example micromirror array when using broadband illumination sources; and

[0066] FIG. 10 is an example flow diagram illustrating an example method of compensating for the dispersive effects of a micromirror array.

DETAILED DESCRIPTION

[0067] FIG. 1 depicts a diagrammatic representation of a cross section of an example micromirror array 100 (which in this example takes the form of a digital micromirror device, DMD) comprising an array of adjustable micromirrors 102, each representing a pixel (or part of a pixel) in the holographic image to be displayed. Such a DMD 100 may be found within a holographic display used to display a computer-generated hologram.

[0068] Each micromirror 102 may be rotated via an electrostatic force between the micromirror 102 and electrodes (not shown) positioned below each micromirror 102. Typically, the micromirrors 102 can be rotated between around 100 to 20, and may be in an on or off state. In the on state, light from an illumination source is reflected in a desired direction (such as normal to the plane of the DMD 100, as shown in FIG. 1) where it may pass through one or more further optical components (such as lenses) of the holographic display to display a pixel (or part of a pixel) for viewing by a user. In the off state, the micromirrors 102 are rotated into a different orientation, and light is directed elsewhere (usually onto an absorption element, such as a ray dump), so that no light is seen by the user for that pixel. In the on state, the micromirrors 102 may be arranged in the position shown in FIG. 1, and in the off state, the micromirrors 102 may be arranged in the position shown in FIG. 2. As shown in FIG. 2, the angle at which the micromirrors 102 are arranged is different to that in FIG. 1.

[0069] FIGS. 1 and 2 both show a ray of light 104 incident upon the DMD 100 before being reflected. In FIG. 1, the reflected ray of light 106 is reflected in the desired direction (i.e., in a direction parallel to the normal of the DMD 100), and in FIG. 2, the reflected ray of light 106 is reflected in towards an absorption element. Although FIGS. 1 and 2 show all of the micromirrors 102 arranged in the same position (i.e., all on or all off), it will be appreciated that the micromirrors 102 can be individually controlled, so that some may be arranged in the on position, and some may be arranged in the off position at any one time.

[0070] As mentioned, DMDs 100 behave in the same way as a diffraction grating, and so produce diffraction patterns with peaks and troughs as light rays reflected from the micromirrors 102 interfere with each other. FIGS. 1 and 2 therefore show a grating efficiency Sinc.sup.2 profile of the diffracted light. In this particular example, the grating efficiency peak contains the highest energy of the diffracted light because the wavelength is the blaze wavelength for this particular DMD 100.

[0071] FIG. 1 shows a single collimated ray of light 104 incident upon the DMD 100 at a particular angle of incidence 108 (where the angle of incidence is measured from the normal (the y-axis as depicted) of a plane defined by the DMD 100 (the x-axis as depicted). The angle of reflection, .sub.out, of the reflected ray of light 106 having the highest energy (i.e., where the peak of the Sinc.sup.2 profile occurs) is similarly measured from the normal. In the example of FIG. 1, .sub.out=0 (i.e., it lies along the normal) for the particular reflected ray 106.

[0072] It can be shown mathematically that an angle of reflection of 0 for the peak of the Sinc.sup.2 profile can be achieved by setting the angle of incidence, .sub.1, equal to twice the mirror tilt angle, .sub.mirror, 110 in the on state. Accordingly, in FIG. 1, .sub.1=2.sub.mirror. It is therefore apparent that changing the angle of incidence or the mirror tilt angle adjusts the position of the Sinc.sup.2 profile. For example, in FIG. 2, the angle of incidence is the same as in FIG. 1, but the mirrors are angled differently, meaning the reflected light 106 no longer lies along the normal.

[0073] Furthermore, as is well known, the angle of reflection, .sub.out, of any output ray can be calculated using the equation: sin(.sub.out)=sin(.sub.i)n/p, where n is an integer (the diffraction order), is the wavelength of the light ray, and p is the pixel pitch 112 of the DMD 100. In this way, the position of the peaks in the diffraction pattern can be determined.

[0074] Each ray leaving the optical element will therefore have an output angle (.sub.out) which depends on its wavelength () and its incidence angle on the optical element (.sub.i). The difference between output angles of two rays can be calculated using:

[00001]$=\arcsin \left(\sin \left({}_{i2}\right)-\left(n/p\right)*{}_2\right)-\mathrm{arc}\sin \left(\sin \left({}_{i1}\right)-\left(n/p\right)*{}_1\right)$

[0075] This angular separation (which may be a predetermined amount) depends on the wavelength and incidence angles of the rays. This predetermined amount may be different for each pair of rays.

[0076] As mentioned, for spectrally broadband sources (e.g., LEDs), the diffractive properties of the DMD 100 reduce the quality of the output reconstructed image because a diffraction pattern is produced for each wavelength and the angular positions of the peaks for each light ray are different for each wavelength. In other words, the corresponding non-zero diffraction orders for each wavelength do not occur at the same angular position. More particularly, the particular diffraction order where the maximum intensities occur for each wavelength do not occur at the same angular position.

[0077] FIG. 3 shows an example in which incident light 204 comprises light rays having two different wavelengths, each being incident upon the DMD 100 at the same angle of incidence, while also satisfying .sub.i=2.sub.mirror, so that the grating efficiency peak of both Sinc.sup.2 envelopes are at 0 from the normal in this on state. In this example, the incident light 204 from one or more illumination sources (not shown) comprises a first ray of light having a first wavelength and a second ray of light having a second wavelength, where the second wavelength is different to the first wavelength. In other examples, there may be three or more rays having three or more different wavelengths. In a particular example, both the first and second rays may be emitted from a single broadband source, such as an LED.

[0078] FIG. 3 depicts the dispersive nature of the DMD 100, and two separate diffraction patterns are produced (one diffraction pattern for each ray) due to their different wavelengths. For example, the reflected light of the first ray (shown with solid lines) produces a first diffraction pattern, and the reflected light of the second ray (shown with dashed lines) produces a second diffraction pattern, and the non-zero diffraction orders (1, 2, 3, etc.) of both diffraction patterns do not coincide/overlap. For simplicity, only two diffraction patterns are shown (corresponding to the two incident rays of light having different wavelengths), however, it will be appreciated that there may be a plurality of diffraction patterns produced for the plurality of wavelength emitted by an illumination source. For example, an LED may emit a plurality of light rays, each ray having a different wavelength.

[0079] The vertical lines shown within the Sinc.sup.2 envelopes 216, 218 occur at whole integer diffraction orders and their lengths illustrate the relative intensity of the diffraction pattern at that diffraction order. In this example, the diffraction order having the highest/maximum intensity for both wavelengths occurs at the third diffraction order (n=3). Lower intensity reflections occur at different diffraction orders, as indicated by the vertical extent of the lines drawn at other diffraction orders.

[0080] In this example, the peak of the first Sinc.sup.2 envelope 216 for the first ray of light occurs at the third diffraction order (n=3), which corresponds to the maximum intensity for the first light ray, because the first wavelength corresponds to the blaze wavelength. In contrast, the peak of the second Sinc.sup.2 envelope 218 for the second ray of light does not occur at the same location as the maximum intensity for the second light ray. Instead, the peak of the second Sinc.sup.2 envelope 218 occurs between the second and third diffraction orders. The angle 214, between the whole integer diffraction orders (in this case n=3) nearest the maximum intensity for both reflected rays is shown in FIG. 3. This means that the rays are effectively being reflected in different directions, which can reduce the quality of the displayed reconstructed image.

[0081] In this example, the diffraction orders for where the maximum intensities occur is the same (n=3), which may be the case when the difference between the first and second wavelengths is relatively small, such as when both rays are emitted from a single illumination source (such as a single LED). However, in examples where the difference between the first and second wavelengths is relatively large (which may be the case when the rays are emitted from different illumination sources, such as different LEDs), the difference between the diffraction orders for where the maximum intensities occur could be equal to or greater than 1. As an example, green light reflecting from a DMD 100 may have a maximum intensity at the sixth (n=6) diffraction order, blue light may have a maximum intensity at the seventh (n=7) diffraction order, and red light may have a maximum intensity at the fifth (n=5) diffraction order. In one example, if the first and second rays are both from the same LED, both rays will have a maximum intensity at the same diffraction order. In another example, if one ray is from the blue LED, and the other ray is from the red LED, the difference between the diffraction orders where the maximum intensity occurs will be equal to 2.

[0082] As discussed, it may be desirable to use LEDs as illumination sources within a holographic display. Typically, LEDs do not emit a single wavelength ray of light, but may instead emit a plurality of rays having similar but different wavelengths around a dominant wavelength. Although the difference in wavelength between any two emitted rays may be relatively small, it may be great enough to affect the quality of the displayed reconstructed image, for the reasons illustrated in FIG. 3.

[0083] FIG. 4 shows spectral curves for example red (R), green (G) and blue (B) LEDs. FIG. 4 therefore shows the broad spectrum of the LED illumination sources that may be used in an example holographic display.

[0084] One method to compensate for the dispersive effects of the DMD is to use illumination sources that have a negligible spectral bandwidth, such as lasers, and arrange the illumination sources with respect to each other so that the rays (assumed to have a single, well defined wavelength), are incident upon the DMD 100 at the different angles of incidence, where the difference is sufficient to compensate for the inter-source dispersive effects of the DMD 100 along a particular direction (in this case a normal to the DMD 100). The use of illumination sources that have a negligible spectral bandwidth removes the need to further compensate for intra-source dispersion. To illustrate this, FIG. 5 shows an arrangement in which there are two separate illumination sources 516, 518 and these are arranged/orientated with respect to each other. In this example, the first illumination source 516 emits a first ray of light having a first wavelength and a second illumination source 518 emits a second ray of light having a second wavelength, and the first illumination source 516 is orientated with respect to the second illumination source 518 such that the first ray of light is incident upon the micromirror array at a first angle of incidence and the second ray of light is incident upon the micromirror array at a second angle of incidence, and the second angle of incidence is different to the first angle of incidence by an amount to compensate for the inter-source dispersive effects of the DMD along the particular direction (such as the normal). For example, the difference between the angles of incidence may be equal to the angular separation between the maximum intensities of the diffraction patterns for the case when the angles of incidence are equal (i.e., the angle 214, shown in FIG. 3).

[0085] FIG. 5 therefore shows that by adjusting the angle of incidence of the second ray of light by a certain amount, the diffraction orders for the highest intensity reflected rays now coincide. Accordingly, the angular separation of the input rays causes the maximum intensity orders (n=3 for both rays) to overlap at the output of the DMD. Accordingly, in contrast to the example shown in FIG. 3, the n=3 diffraction orders now coincide along the optical axis (in this case the normal). Because the angle of incidence of the second light ray has changed (compared to that shown in FIG. 3), the Sinc.sup.2 profile has moved.

[0086] It will be appreciated that this solution would not fully compensate for all of the dispersive effects introduced by the DMD 100 if the illumination sources 516, 518 were broadband emitters (such as LEDs), because within each beam of light emitted by the LEDs, there are a plurality of rays of light having different wavelengths. As such, the arrangement of FIG. 5, only holds true for the case of monochromatic illumination sources (where the linewidths, 0). When each illumination source instead has a spectral bandwidth >0 (such as an LED) then arranging the illumination sources in this way would not angularly separate rays (having different wavelengths) emitted within an illumination source. At best, arranging two LEDs in this way would compensate for the dominant wavelength of each source, but not the other wavelengths. As such, there would still be some intra-source dispersion present because the intensity of each wavelength from an LED is dispersed over a range of output angles.

[0087] FIG. 6 shows the result of arranging three LEDs at different angles to each other (in the same way as depicted in FIG. 5). While the spectral peaks all coincide around the normal (.sub.out=0) (so inter-source dispersion has been compensated for), there is still intra-source dispersion present, as shown by the widths of the three curves. FIG. 6 therefore shows a large spread in .sub.out, and it is desirable to reduce the spread/widths of each curve, to produce a higher quality reconstructed image. This therefore shows that the arrangement in FIG. 5 is less useful when using broadband illumination sources, such as LEDs.

[0088] The graph depicted in FIG. 6 was produced using an example DMD from Texas Instruments, in this case the DLP670S model DMD and 3 example LEDs from Thorlabs (in this case, models: M625F2, M530F2 and M470F3). This particular DMD has a mirror tilt angle .sub.mirror=17.5, and a pixel pitch, p=5.4 m.

[0089] When using one or more LEDs, the inventors have realised that the intra-source dispersive effects of the DMD 100 can be compensated for along a particular direction (such as the direction normal to the DMD) by using an angularly dispersive optical element, such as a second DMD or a diffraction grating, where the optical element has a substantially equal and opposite angularly dispersive effect to that of the DMD. The use of such an optical element therefore pre-disperses the rays in an equal-but-opposite way before they are incident upon the DMD. In contrast to the arrangement of FIG. 5 (when used with LEDs), the optical element provides a wavelength-dependent output angle for each and every wavelength, which becomes a wavelength dependent incidence angle at the DMD.

[0090] FIG. 7 shows an example arrangement that can be used to compensate for the intra-source dispersive effects of the DMD 100 when using LEDs, and thereby improve the quality of a displayed reconstructed image, by altering/controlling the angle of incidence of light having different wavelengths.

[0091] As mentioned, to achieve this, the holographic display additionally comprises an angularly dispersive optical element 300, such as a second DMD or a diffraction grating, where the optical element 300 has a substantially equal and opposite angularly dispersive effect to that of the DMD 100.

[0092] In addition to the optical element 300, FIG. 7 shows an illumination assembly 316 configured to emit a first ray of light 318 having the first wavelength and a second ray of light 320 having the second wavelength, towards the optical element 300. In this example, the illumination assembly 316 comprises a single illumination source, such as an LED. In other examples, the illumination assembly 316 may comprise two or more illumination sources, such as first and second illumination sources.

[0093] The optical element 300 is arranged to introduce an equal but opposite dispersive effect to that of the DMD 100, thereby to cancel out the dispersive effects introduced by the DMD 100. Accordingly, the optical element 300 may behave in substantially the same way as the DMD 100, such that two diffraction patterns are produced when the light diffracts from the optical element 300 in the same way as illustrated and described in relation to FIG. 3. This diffracted/reflected light then travels towards the DMD 100, and each ray is incident upon the DMD 100 at a different angle of incidence. The rays 318, 320 shown between the optical element 300 and the DMD 100 are where the maximum intensities of each wavelength occurs. It will be appreciated that there will also be zero-order and higher-order diffraction paths, but these are omitted for simplicity. When each of these highest intensity rays undergo further dispersion due to the DMD 100, the dispersion is equal and opposite in direction to the dispersion introduced by the optical element 300. Thus, FIG. 7 shows the intra-source dispersive effects of the DMD 100 being compensated for along a desired direction (in this case, along a direction parallel to the normal of the DMD 100).

[0094] Accordingly, in this example, the third diffraction orders of both rays overlap along the desired direction. Counteracting the DMD's diffractive effects by pre-dispersing the rays with an optical element 300 greatly reduces the intra-source dispersion of the reflected rays from the DMD 100, meaning that the resulting reconstructed image quality is improved.

[0095] FIG. 7 therefore depicts the first ray of light 318 (having first being reflected from the optical element 300) incident upon the DMD 100 at a first angle of incidence 322 and the second ray of light (having first being reflected from the optical element 300) incident upon the DMD 100 at a second angle of incidence 324. The second angle of incidence 324 is different to the first angle of incidence 322 by a predetermined amount to compensate for the intra-source dispersive effects of the DMD 100 along the optical axis of the holographic display. As such, the difference 326 is equal to .sub.out (angle 214, shown in FIG. 3). Thus, when the DMD introduces angular dispersion of .sub.out, the two are cancelled out, meaning that a particular diffraction order of both rays overlap along the desired direction (the particular diffraction order being the order having the highest intensity for the wavelength of that ray).

[0096] FIG. 7 shows the first and second rays 318, 320 incident upon the optical element 300 being parallel and with spatial separation. This ensures the resultant rays from the DMD 100 are colinear (so are not spatially separated).

[0097] It will be appreciated that for one, and in some cases both rays of light, the peak of the Sinc.sup.2 profile may be offset from the optical axis because the angle of incidence upon the DMD 100 does not satisfy .sub.i=2.sub.mirror.

[0098] It can be determined, mathematically, that for each ray of light, the overall system of FIG. 7 (where the optical element 300 and DMD 100 are parallel) can be described by: sin(.sub.out)=sin(.sub.i)+n.sub.OE/p.sub.OE+n.sub.micromirror/p.sub.micromirror, where .sub.out is the angle of reflection for the ray reflected from the DMD 100 (in this case .sub.out=0, so sin(.sub.out)=0), .sub.i is the angle of incidence for the ray on the optical element 300 (in this case .sub.i=0, so sin(.sub.i)=0), n.sub.OE is the diffraction order of the maximum intensity of the diffraction pattern at the optical element 300, and n.sub.micromirror is the diffraction order of the maximum intensity of the diffraction pattern at the DMD 100. In this particular example where sin(.sub.out)=0 and sin(.sub.i)=0, this then gives the relationship: n.sub.OE/p.sub.OE=n.sub.micromirror/p.sub.micromirror.

[0099] For scenarios where the optical element 300 and the DMD 100 are not parallel (that is, the optical element 300 is rotated by an angle .sub.plane relative to the DMD 100), the system can be described by: sin(.sub.out)=cos(.sub.plane)[sin(.sub.i)+n.sub.OE/p.sub.OE]+sin(.sub.plane)[sqrt(1(sin(.sub.i)+n.sub.OE/p.sub.OE).sup.2]+n.sub.micromirror/p.sub.micromirror. When .sub.plane=0, and .sub.i=0 the equation reduces to the parallel plane case above.

[0100] In one example, the optical element 300 is a diffraction grating, such as a reflective diffraction grating. To effectively compensate for the dispersive effects of the DMD 100, the diffraction grating may be manufactured or selected that has a substantially equal angularly dispersive effect to that of the DMD 100. For example, the blaze angle 310 may be substantially the same as the mirror tilt angle 110 in the on state, and the pitch 312 may be substantially the same as the pixel pitch 112 of the DMD 100.

[0101] In another example, the optical element 300 is a second micromirror array, such as a DMD. To effectively compensate for the dispersive effects of the DMD 100, the second micromirror array may have a substantially equal dispersive effect to that of the DMD 100. For example, the mirror tilt angle 310 may be substantially the same as the mirror tilt angle 110 in the on state, and the pixel pitch 312 may be substantially the same as the pixel pitch 112 of the DMD 100.

[0102] Although it is preferable to select an optical element 300 that is optically identical to the DMD 100, sufficient correction of the intra-source dispersion can be achieved by selecting an optical element that satisfies: n.sub.OE/p.sub.OE=n.sub.micromirror/p.sub.micromirror. In the example discussed above using a green LED, then n.sub.micromirror6, p.sub.micromirror=5.4 m, and as such, could be compensated for by using an optical element 300 having n.sub.OE1 and p.sub.OE=0.9 m. For example, off-the-shelf diffraction gratings are typically blazed for n=1. However, a more preferable optical element 300 would have n.sub.OE=n.sub.micromirror and p.sub.OE=p.sub.micromirror.

[0103] As discussed above, for a typical DMD, the peak red, green and blue reflected rays represent different diffractive orders from the DMD. This complicates the process of compensating the dispersive effects (both inter-source and intra-source) of all 3 coloured LEDs. For the example DMD and LEDs discussed above (where the pixel pitch is 5.4 m and .sub.mirror=17.5), n.sub.R=5, n.sub.G=6 and n.sub.B=7. As mentioned above, the most effective solution for compensating for all wavelengths is to use an optical element 300 that has: n.sub.OE=n.sub.micromirror and p.sub.OE=p.sub.micromirror and illuminating the optical element 300 at normal incidence for all LEDs. However, in cases where no such diffraction grating is readily available, and other options, such as using a second DMD, may be too expensive, then an optical element is selected that satisfies: n.sub.OE/p.sub.OE=n.sub.micromirror/p.sub.micromirror. Further compensation may be needed, because n.sub.micromirror differs for each colour LED.

[0104] This additional compensation can be made by adjusting the angle of incidence upon the optical element 300, so that light rays from different LEDs are no longer incident on the optical element 300 at the same angle. This is not depicted in FIG. 7, which instead shows both the first and second rays of light 318, 320 incident upon the optical element 300 at the same angle of incidence. (FIGS. 8A and 8B, discussed below, do depict this adjustment in angle of incidence.) This additional adjustment compensates for the fact that an optical element may have been selected that is more suitable to correct the dispersive effects for one of the wavelengths, and less suitable for the other(s). This effectively combines the arrangements of FIG. 5 (by adjusting the angle of the illumination sources relative to each other, which compensates for the inter-source dispersive effects introduced by the DMD), with the optical element 300 of FIG. 7, which compensates for the intra-source dispersive effects introduced by the DMD. The light rays from different LEDs are also spatially separated from each other when incident on the optical element. This results in the first and second rays of a first illumination source being substantially colinear with a third and fourth ray (having third and fourth wavelengths) of a second illumination source at the output of the DMD, where all four rays are also colinear with an optical axis of the holographic display.

[0105] As such, the optical element 300 compensates for the difference between the first and second wavelengths of the first and second light rays emitted by the first illumination source, as well as compensating for the difference between the third and fourth wavelengths of the third and fourth light rays emitted by the second illumination source. Further, to compensate for the inter-source dispersion, the first illumination source is arranged such that the first and second rays of light are incident upon the optical element at a third angle, and the second illumination source is arranged such that the third and fourth rays of light are incident upon the optical element at a fourth angle.

[0106] To illustrate this, FIG. 8A depicts an example arrangement that combines the concepts discussed in FIGS. 5 and 7. This arrangement therefore compensates for both intra-source dispersive effects and inter-source dispersive effects when an optical element has been selected that is more suitable to correct the dispersive effects for one of the wavelengths, and less suitable for the other.

[0107] FIG. 8A therefore depicts the DMD 100, an optical element 300, and an illumination assembly comprising a first illumination source 402 and a second illumination source 404. The first illumination source 402 is configured to emit a first plurality of rays of light having a range of wavelengths including a first ray of light 402a having a first wavelength and a second ray of light 402b having a second wavelength. The first illumination source 402 in this example is an LED, such as a red LED. The second illumination source 404 is configured to emit a second plurality of rays of light having a range of wavelengths including a third ray of light 404a having a third wavelength and a fourth ray of light 404b having a fourth wavelength. The second illumination source 404 in this example is an LED, such as a blue LED. Further illumination sources may also be present, such as a green LED.

[0108] The first illumination source 402 is arranged such that the first and second rays of light 402a, 402b are incident upon the optical element 300 at a third angle 410 (in this case the angle of incidence upon the optical element 300 is 0, but other angles may be used) and the second illumination source 404 is arranged such that the third and fourth rays of light 404a, 404b are incident upon the optical element at a fourth angle 412, where the third and fourth angles are different. This offset in angle of incidence upon the optical element 300 therefore compensates for the inter-source dispersion i.e. the spectral peaks all coincide around the surface normal of the DMD (theta_out=0), as shown in FIG. 6. In examples where n.sub.OE=n.sub.micromirror and p.sub.OE=p.sub.micromirror, the third and fourth angles 410, 412 may be the same. For example, the first, second, third and fourth rays of light may all be incident normal to the optical element 300. In addition to this offset in angle of incidence upon the optical element 300, rays emitted by each illumination source may also be spatially separated. This ensures the resultant rays from the DMD 100 are colinear (so are not spatially separated at the output of the DMD).

[0109] As mentioned above, the optical element 300 has a substantially equal and opposite angularly dispersive effect to that of the micromirror array, such that: (a) the first and second rays of light 402a, 402b are transmitted from the optical element 300 in different directions and are separated by an angle 406 equal to a predetermined amount to at least partially compensate for the dispersive effects of the DMD 100 along the optical axis of the holographic display, and (b) the third and fourth rays of light 404a, 404b are transmitted from the optical element 300 in different directions and are separated by an angle 408 equal to a predetermined amount to at least partially compensate for the dispersive effects of the DMD 100 along the optical axis of the holographic display. This therefore compensates for the intra-source dispersion.

[0110] As shown in FIG. 8A, the first, second, third and fourth rays of light 402a, 402b, 404a, 404b travel from the illumination sources 402, 404 to the DMD 100 via the optical element 300. The rays 402a, 402b, 404a, 404b shown between the optical element 300 and the DMD 100 are where the maximum intensities of each wavelength occurs. It will be appreciated that there will also be zero-order and higher-order diffraction paths, but these are omitted for simplicity.

[0111] In the same way as discussed in FIG. 7, the first ray of light 402a is incident upon the DMD 100 at a first angle of incidence and the second ray of light 402b is incident upon the DMD 100 at a second angle of incidence, the second angle of incidence being different to the first angle of incidence by a predetermined amount to at least partially compensate for the dispersive effects of the DMD 100 along the optical axis of the holographic display. Similarly, the third ray of light 404a is incident upon the DMD 100 at another angle of incidence and the fourth ray of light 404b is incident upon the DMD 100 at further angle of incidence, the angles of incidence being different by a predetermined amount to at least partially compensate for the dispersive effects of the DMD 100 along the optical axis of the holographic display.

[0112] In this example where the first illumination source 402 is a red LED, red light reflecting from the DMD 100 (that is, both the first and second rays 402a, 402b) have a maximum intensity at the fifth (n=5) diffraction order. Similarly, in this example where the second illumination source 404 is a blue LED, blue light reflecting from the DMD 100 (that is, both the third and fourth rays 404a, 404 b) have a maximum intensity at the seventh (n=7) diffraction order. Accordingly, in this example, the fifth diffraction orders of the first and second rays 402a, 402b overlap with the seventh diffraction orders of the third and fourth rays 404a, 404b along the desired direction. In examples comprising a third illumination source, such as a green LED, two further rays from the third illumination source would have a maximum intensity at the sixth (n=6) diffraction order overlapping with the first, second, third and fourth rays. The third illumination source may also be arranged relative to the first and second illumination sources in the same way so as to compensate for the inter-source dispersive effects.

[0113] As an example, the inventors have found that when using the diffraction grating model GR50-1205 available from Thorlabs with red, green and blue LEDs (models: M625F2, M530F2 and M470F3 from Thorlabs), acceptable correction can be achieved by setting the angle of incidence upon the diffraction grating 300 for the red, green and blue beams of light as .sub.i(R)=10.0, .sub.i(G)=2.7, .sub.i(B)=2.6 respectively. In this example, for the diffraction grating model GR50-1205, n=1, the blaze angle=17.27 and p=0.83 m (or 1200 lines/mm)). These values can be calculated using the following equation: sin(.sub.i)=sin(.sub.out)n.sub.OE/p.sub.OE+n.sub.micromirror/p.sub.micromirror, where n.sub.OE=1 and .sub.out=0 for the dominant wavelengths of the LEDs, and n.sub.micromirror=5, 6 or 7.

[0114] As mentioned, as a modification of the arrangement of FIG. 8A, the illumination sources 402, 404 may instead be arranged parallel to each other, rather than being physically orientated with respect to each other. This means that the first and second rays of light 402a, 402b are parallel to the third and fourth rays of light 404a, 404b when emitted, such that there is no or only a minimal angular separation between the emitted rays of light from the respective illumination sources. In such cases, one or more further optical elements, such as a lens, may be used to adjust the optical path of one pair or both pairs of rays so that they are incident upon the optical element 300 at their desired/different angles of incidence 410, 412.

[0115] To illustrate, FIG. 8B depicts an arrangement in which there is a further optical element in the form of a lens 414 arranged between the first and second illumination sources 402, 404 and the optical element 300 such that the first and second rays of light 402a, 402b are incident upon the optical element 300 at the third angle 410 and the third and fourth rays of light 404a, 404b are incident upon the optical element 300 at the fourth angle 412. As shown, as the rays 402a, 402b, 404a, 404b travel from their respective illumination sources 402, 404, they are parallel to each other.

[0116] It will be appreciated that the principles discussed above can be applied to three illumination sources.

[0117] To illustrate the effect of the arrangements of FIGS. 8A and 8B, FIG. 9 shows the same three LEDs of FIGS. 4 and 6 illuminating diffraction grating model GR50-1205, which is only a near-match to the DMD 100. In FIG. 9, the input angles to the grating have been chosen in the same manner as discussed above to ensure that the beams are largely colinear at the DMD output. It can clearly be seen that the intra-source dispersion is greatly reduced by a factor of around ten times (compared to the case in FIG. 6, where there was no optical element 300).

[0118] This could be improved even further by using an optical element that exactly matches the DMD (i.e., n.sub.OE=n.sub.micromirror and p.sub.OE=p.sub.micromirror).

[0119] In contrast to the arrangement of FIG. 5, the compensation introduced by the use of an optical element 300 can be applied in all practical scenarios, and is therefore applicable to both monochromatic illumination sources (=0) and polychromatic illumination sources (>0).

[0120] As an alternative arrangement (not shown), each illumination source may be directed towards its own, separate, optical element that is more suitable for that wavelength. For example, a first illumination source (such as an LED) may emit a first ray of light having a first wavelength (as well as other rays having different wavelengths) and a second illumination source (such as an LED) may emit a second ray of light having a second wavelength (as well as other rays having different wavelengths). In that case, there may be a first angularly dispersive optical element to receive the first ray of light from the first illumination source and a second angularly dispersive optical element to receive the second ray of light from the second illumination source. Each optical element may satisfy n.sub.OE/p.sub.OE=n.sub.micromirror/p.sub.micromirror for the dominant wavelength emitted by the illumination source. Accordingly, the first and second optical elements have a substantially equal and opposite angularly dispersive effect to that of the DMD, and are arranged such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence.

[0121] In the same way, it will be appreciated that the illumination sources 516, 518 of FIG. 5 may not necessarily be physically orientated with respect to each other, yet the rays emitted by the illumination sources may still be incident upon the DMD 100 at their different angles of incidence. This could be achieved, for example, by using one or more further optical elements, such as mirrors or lenses to manipulate the light path from one or both of the illumination sources such that the rays emitted by the illumination sources may still be incident upon the DMD 100 at their different angles of incidence.

[0122] FIG. 10 depicts a flow diagram of a method 600 of at least partially compensating for the dispersive effects of a micromirror array, such as the DMD 100. In block 602, the method comprises emitting a first ray of light having a first wavelength and a second ray of light having a second wavelength, the second wavelength being different to the first wavelength. As mentioned, the first and second rays may be emitted by the same or different illumination sources. Block 604 comprises controlling an angle of incidence of the first ray of light upon a micromirror array, such that the first ray of light is incident upon the micromirror array at a first angle of incidence and block 606 comprises controlling an angle of incidence of the second ray of light upon the micromirror array, such that the second ray of light is incident upon the micromirror array at a second angle of incidence. The second angle of incidence is different to the first angle of incidence by a predetermined amount to at least partially compensate for the dispersive effects of the micromirror array.

[0123] In one example, such as that corresponding to the arrangement of FIG. 7, blocks 604 and 606 may comprise: emitting the first and second rays of light towards an angularly dispersive optical element to introduce a first wavelength-dependent dispersive effect, and the micromirror array introduces a second wavelength-dependent dispersive effect substantially equal and opposite in direction to the first wavelength-dependent dispersive effect.

[0124] In another example, such as that corresponding to the arrangement of FIG. 5, blocks 604 and 606 may comprise orientating a first illumination source and a second illumination source with respect to each other such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence. In another example, blocks 604 and 606 may comprise controlling the light path of at least one of the first ray of light and the second ray of light such that the first ray of light is incident upon the micromirror array at the first angle of incidence and the second ray of light is incident upon the micromirror array at the second angle of incidence.

[0125] It should be noted that the schematic depictions in FIGS. 5, 7, 8A and 8B are to aid understanding, and the skilled person will be aware that numerous variations can be used in conjunction with the methods described here. For example, other arrangements may include image folding or directing components so that the optical path has a different shape, such as a folded optical path.

[0126] 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.