Hologram calculation
Systems and methods of determining a hologram of an image for a system comprising a display device and viewing system are disclosed. Some embodiments implement a multi-stage procedure comprising (i) determining a first complex light field at an entrance pupil of the viewing system, (ii) determining a second complex light field at a sensor plane of a sensor of the viewing system, (iii) determining a third complex light field at the entrance pupil, and (iv) determining a fourth complex light field at the display plane. Some embodiments include extracting a hologram from a data set corresponding to the fourth complex light field.
1 . A method of determining a hologram of a target image for a system comprising a display device arranged to display the hologram at a hologram plane and a viewing system that comprises an entrance pupil, a lens, and a sensor, wherein the viewing system is arranged to view the hologram through a pupil expander that provides a plurality of light propagation paths from the display device to viewing system, the method comprising:
a first stage, for a first light propagation path, comprising determining a first complex light field at the entrance pupil of the viewing system, wherein the first complex light field results from propagation of light from the hologram plane of the display device, along the first light propagation path, to the entrance pupil, and cropping the light field of the first light propagation path in accordance with at least one of a size, a shape, or a position of the entrance pupil to form the first complex light field;
a second stage comprising determining a second complex light field at a sensor plane of the sensor of the viewing system, wherein the second complex light field results from propagation of light of the first complex light field from the entrance pupil to the sensor, via the lens of the viewing system, and replacing an amplitude component of the complex light field that arrives at the sensor plane with an amplitude component that is based on the amplitude component of the target image;
a third stage comprising determining a third complex light field at the entrance pupil, wherein the third complex light field results from reverse propagation of light of the second complex light field from the sensor plane back through the lens and cropping in accordance with the entrance pupil;
a fourth stage comprising determining a fourth complex light field at the display plane, wherein the fourth complex light field results from reverse propagation of light of the third complex light field back along the first light propagation path and cropping the propagated light, at the hologram plane, in accordance with at least one of the size or position of a pixel area of the display device; and
a fifth stage comprising extracting a hologram from a data set corresponding to the fourth complex light field.
2 . The method of claim 1 , comprising repeating the first to fourth stages for one or more additional light propagation paths of the plurality of light propagation paths provided by the pupil expander.
3 . The method of claim 2 , wherein the first to fourth stages are carried out for each light propagation path of the plurality of light propagation paths in order to extract a hologram for each light propagation path, wherein a plurality of holograms corresponding to the plurality of respective light propagation paths are combined in order to form the hologram for display on the display device.
4 . The method of claim 1 , wherein the light propagated from the hologram plane in the first stage comprises a zeroth complex light field comprising a random phase distribution.
5 . The method of claim 1 , wherein the first to fourth stages are iteratively repeated before the fifth stage of extracting the hologram from a final iteration, and wherein the light propagated from the hologram plane of the display device for a second and subsequent iterations comprises a phase distribution of the fourth complex light field of an immediately preceding iteration.
6 . The method of claim 1 , wherein the hologram is extracted from a phase component of a fourth data set corresponding to the fourth complex light field.
7 . The method of claim 1 , wherein the hologram is a hologram of a plurality of images, wherein each image has a different respective image distance, and the second stage of the method is independently carried out for each image.
8 . The method of claim 1 , wherein each complex light field is determined by wave propagation optics comprising Fresnel propagation.
9 . The method of claim 1 , wherein replacing the amplitude component of the complex light field that arrives at the sensor plane with an amplitude component that is based on the amplitude component of the target image comprises replacing the amplitude component of the second complex light field with that of the target image or weighting the amplitude component of the second complex light field based on the amplitude component of the target image.
10 . The method of claim 1 , wherein each step of cropping comprises cropping in accordance with at least one of size and position.
11 . The method of claim 1 , wherein an individual image comprises a virtual image.
12 . The method of claim 1 , wherein the viewing system comprises an eye of a viewer and wherein the method further comprises eye or head tracking the viewer in order to determine at least one of a size and position of the entrance pupil of the viewing system.
13 . The method of claim 1 , wherein propagation along the first light propagation path of the pupil expander comprises propagation along multiple light propagation paths of the plurality of light propagation paths of the pupil expander and combining respective individual complex light fields resulting from those multiple different light propagation paths of the pupil expander, or wherein the individual complex light fields are combined by addition.
14 . The method of claim 13 , wherein the pupil expander is a waveguide pupil expander and each light propagation path corresponds to a different number of internal reflections within the waveguide.
15 . The method of claim 14 , wherein combining the respective individual complex light fields comprises determining a lateral position of each respective individual complex light field on a plane of the entrance pupil.
16 . The method of claim 14 , wherein combining the respective individual complex light fields further comprises determining a total phase shift associated with the internal reflections of each light propagation path.
17 . A hologram engine arranged to determine a hologram of a target image for viewing using a head-up display, wherein the head-up display comprises:
a display device arranged to display the hologram at a hologram plane; and
a pupil expander arranged to receive light spatially modulated in accordance with the hologram, wherein the hologram engine is arranged to:
determine a first complex light field at an entrance pupil of a viewing system, wherein a plurality of light propagation paths of the pupil expander are defined between the hologram plane of the display device and the entrance pupil, wherein the first complex light field results from propagation of light along a first light propagation path, and cropping the light field of the first light propagation path in accordance with at least one of a size, a shape, or a position of the entrance pupil, to form the first complex light field;
determine a second complex light field at a sensor plane of a sensor of the viewing system, wherein the second complex light field results from the propagation of light of the first complex light field from an entrance aperture through a lens of the viewing system and replacing an amplitude component of the complex light field that arrives at the sensor plane with an amplitude component that is based on the amplitude component of the target image;
determine a third complex light field at the entrance pupil, wherein the third complex light field results from reverse propagation of light of the second complex light field from the sensor plane back through the lens and cropping in accordance with the entrance pupil;
determine a fourth complex light field at the hologram plane, wherein the fourth complex light field results from reverse propagation of light of the third complex light field back along the first light propagation path and cropping the propagated light, in accordance with at least one of the size or the position of a pixel area of the display device; and
extract the hologram from a data set corresponding to the fourth complex light field.
18 . A system comprising:
a display device configured to display a hologram at a hologram plane;
a viewing system that comprises an entrance pupil, a lens, and a sensor, wherein the viewing system is configured to view the hologram through a pupil expander configured to provide a plurality of light propagation paths from the display device to viewing system;
one or more processors; and
tangible, non-transitory computer-readable media comprising program instructions executable by the one or more processors such that the system is configured to determine the hologram of a target image according to a method comprising:
determining, for a first light propagation path, a first complex light field at the entrance pupil of the viewing system, wherein the first complex light field results from propagation of light from the hologram plane of the display device along the first light propagation path to the entrance pupil, and cropping the light field of the first light propagation path in accordance with at least one of a size, a shape, or a position of the entrance pupil of the viewing system, to form the first complex light field;
determining a second complex light field at a sensor plane of the sensor of the viewing system, wherein the second complex light field results from propagation of light of the first complex light field from the entrance pupil to the sensor, via the lens of the viewing system, and replacing an amplitude component of the complex light field that arrives at the sensor plane with an amplitude component that is based on the amplitude component of the target image;
determining a third complex light field at the entrance pupil, wherein the third complex light field results from reverse propagation of light of the second complex light field from the sensor plane back through the lens and cropping in accordance with the entrance pupil;
determining a fourth complex light field at the display plane, wherein the fourth complex light field results from reverse propagation of light of the third complex light field back along the first light propagation path and cropping the propagated light in accordance with at least one of the size or position of a pixel area of the display device; and
extracting a hologram from a data set corresponding to the fourth complex light field.
19 . The system of claim 18 , wherein the plurality of light propagation paths provided by the pupil expander comprise the first light propagation path.
20 . The system of claim 18 , wherein the first light propagation path is one of the plurality of light propagation paths provided by the pupil expander, and wherein each of determining the first complex light field, determining the second complex light field, determining the third complex light field, and determining the fourth complex light field is carried out for each light propagation path of the plurality of light propagation paths to extract a hologram for each light propagation path, wherein a plurality of holograms corresponding to the plurality of light propagation paths are combined in order to form the hologram for display on the display device.