Image projection

1. A method of determining a hologram for display on a display device arranged to propagate spatially-modulated light to a viewing system, the method comprising:

(i) determining the location of an entrance pupil of the viewing system arranged to receive spatially-modulated light from the display device, the display device being arranged to propagate the spatially-modulated light to the viewing system through a waveguide pupil expander that is arranged to receive the spatially-modulated light from the display device and provide a plurality of different light propagation paths for the spatially-modulated light from the display device to the viewing system;

(ii) identifying at least one contributory area of the display device and at least one non-contributory area of the display device, wherein

each contributory area of the display device is an area of the display device from which light propagating from the display device through the waveguide pupil expander pass through the entrance pupil of the viewing system at the determined location,

each non-contributory area of the display device is an area of the display device from which light propagating from the display device through the waveguide pupil expander do not pass through the entrance pupil of the viewing system at the determined location;

(iii-a) identifying at least one primary contributory area of the display device that provides spatially modulated light contributing to a primary image received through the entrance pupil;

(iii-b) identifying at least one secondary contributory area of the display device that provides spatially modulated light contributing to a secondary image received through the entrance pupil, the secondary image being a lower-intensity replica of the primary image; and

(iv) determining the hologram based on the at least one primary contributory area of the display device.

2. The method of determining a hologram as claimed in claim 1 wherein step (ii) is carried out by determining a contributory area for each virtual image point of a plurality of virtual image points of the primary image and for each virtual image point of a plurality of virtual image points of the secondary image, and wherein determining a location of each contributory area for each virtual image point of the primary image and each virtual image point of the secondary image comprises identifying a location at which a light ray, travelling from the respective virtual image point to the entrance pupil, intersects the display device.

3. A method of determining a hologram as claimed in claim 1 wherein the step (iii-a) comprises, for each virtual image point of a plurality of virtual image points of the primary image, determining a number of internal reflections, B, within the waveguide pupil expander corresponding to the primary image.

4. The method as claimed in claim 1 wherein each primary contributory area and each secondary contributory area has a size based on a diameter of the entrance pupil.

5. The method as claimed in claim 1 wherein steps (ii), (iii-a) and (iii-b) comprise for each virtual image point of a plurality of virtual image points of the primary image and for each virtual image point of a plurality of virtual image points of the secondary image:

ray tracing from the respective virtual image point having coordinates [x virtual , y virtual , z virtual ] on a virtual image plane to a viewing plane of the viewing system for B light reflections within the waveguide pupil expander to identify a position [x sensor , y sensor ] on a viewing plane of the viewing system;

determining coordinates, [x LCOS (B), y LCOS (B)], of a chief light ray at the display device for light propagation with B reflections from the image point [x virtual , y virtual , z virtual ] to the position [x sensor , y sensor ] on the viewing plane; and

identifying active pixels of the display device within an area defined by [x LCOS (B), y LCOS (B)].

6. The method of determining a hologram as claimed in claim 5 further comprising, for one or more of the virtual image points of the primary image, identifying an additional primary contributory area of the display device associated with B+ΔB light reflections within the waveguide pupil expander, in which B+ΔB is a number of reflections different from B.

7. The method of determining a hologram as claimed in claim 6 wherein identifying the additional primary contributory area comprises for each of one or more points [x sensor , y sensor ] on the viewing plane:

ray tracing back from [x sensor , y sensor ] to the virtual image plane for B+ΔB light reflections within the waveguide pupil expander;

determining virtual image plane point coordinates, [x virtual (B+ΔB), y virtual (B+ΔB), z virtual ], that will image to [x sensor , y sensor ] for B+ΔB reflections;

determining the coordinates, [x LCOS (B+ΔB), y LCOS (B+ΔB)], of a chief light ray at the display device for light propagation from [x virtual (B+ΔB), y virtual (B+ΔB), z virtual ] to the point x sensor , y sensor ] on the viewing plane with B+ΔB bounces; and

identifying additional active pixels of the display device within a second area defined by [x LCOS (B+ΔB), y LCOS (B+ΔB)].

8. The method of determining a hologram as claimed in claim 7 , wherein step (iv) comprises

determining, for each virtual image point of the plurality of virtual image points of the primary image, a first sub-hologram within the respective at least one primary contributory area determined with respect to B reflections in the waveguide pupil expander;

determining, for each virtual image point of the plurality of virtual image points of the primary image, a second sub-hologram within the respective at least one additional primary contributory area determined with respect to B+ΔB reflections in the waveguide pupil expander; and

combining the first sub-holograms with the second sub-holograms to provide the hologram.

9. The method as claimed in claim 1 wherein step (iv) comprises determining one or more values for the hologram only in the at least one primary contributory area of the display device.

10. The method as claimed in claim 9 wherein step (iv) comprises excluding the at least one secondary contributory area during determination of the hologram.

11. The method as claimed in claim 1 wherein step (iv) comprises excluding values for the hologram in an area of the display device that is not comprised within the primary contributory area.

12. The method of determining a hologram as claimed in claim 1 wherein step (iv) comprises determining a sub-hologram within the respective at least one primary contributory area for each image point and combining the sub-holograms in order to form the hologram.

13. The method of determining a hologram as claimed in claim 12 wherein each sub-hologram comprises an amplitude and/or phase hologram component determined by propagating a light wave from [x virtual , y virtual , z virtual ] to the corresponding primary contributory area.

14. The method of determining a hologram as claimed in claim 1 , wherein

a hologram engine receives contribution information including the identifications of the primary contributory, secondary contributory and non-contributory areas of the display device; determines the hologram based on the primary contributory area; and outputs the hologram to the display device for display.

15. A method of image formation, the method comprising

determining a hologram by the method as claimed in claim 1 ;

displaying the hologram on the display device;

spatially modulating light in accordance with the hologram;

propagating the spatially-modulated light from the display device, through the waveguide pupil expander and to the entrance pupil of the viewing system; and

forming the primary image corresponding to the hologram from the spatially-modulated light at a viewing plane of the viewing system.

16. The method as claimed in claim 1 wherein step (iv) comprises excluding the at least one secondary contributory area during determination of the hologram.

17. The method as claimed in claim 1 , wherein in step (iv) the hologram determination is limited solely to the at least one primary contributory area of the display device.