Ordered geometries for optomized holographic projection

1. An energy waveguide system for defining a plurality of energy propagation paths comprising:

an array of energy waveguides, the array comprising a first side and a second side, and being configured to direct energy therethrough along a plurality of energy propagation paths extending through a plurality of energy locations on the first side;

wherein a first subset of the plurality of energy propagation paths extend through a first energy location and a first energy waveguide of the array of energy waveguides, wherein the first subset of the plurality of energy propagation paths fill at least a portion of an aperture of the first energy waveguide and extend towards the second side of the array in a first direction which is determined at least by the first energy location, the first subset of the plurality of energy propagation paths comprising a chief ray path and additional paths that are substantially parallel to the chief ray path on the second side of the array; and

wherein each waveguide of the array of waveguides comprises a shape of a set of one or more shapes configured to tessellate across a transverse plane of the energy waveguide system, the array of energy waveguides being arranged in a tiling of the one or more shapes across the transverse plane of the energy waveguide system, wherein the tiling of the energy waveguides results in the energy waveguides across the tiling operable to propagation energy differently depending on the configuration of each energy waveguide.

2. The energy waveguide system of claim 1 , wherein there are substantially no empty spaces between the energy waveguides of the array of energy waveguides.

3. The energy waveguide system of claim 1 , wherein energy directed along the first energy propagation path through the first energy waveguide substantially fills a first aperture of the first energy waveguide; and

the energy waveguide system further comprising an energy inhibiting element positioned to limit propagation of energy along a portion of the first subset of the plurality of energy propagation paths that do not extend through the first aperture;

wherein a first portion of the plurality of energy propagation paths extend through a first region, and a second portion of the plurality of energy propagation paths extend through a second region, the first and second regions separated by the energy inhibiting element, and wherein the first and second portions of energy propagation paths intersect at the second side of the array.

4. The energy waveguide system of claim 3 , wherein the energy inhibiting element is located on the first side between the array of energy waveguides and the plurality of energy locations.

5. The energy waveguide system of claim 3 , wherein the first energy waveguide comprises a two-dimensional spatial coordinate, and wherein the unique direction determined at least by the first energy location comprises a two-dimensional angular coordinate, whereby the 2D spatial coordinate and the 2D angular coordinate form a four-dimensional (4D) coordinate set.

6. The energy waveguide system of claim 5 , wherein energy directed along the first energy propagation path comprises one or more energy rays directed through the first energy waveguide in a direction that is substantially parallel to the first chief ray.

7. The energy waveguide system of claim 3 , wherein energy directed along the first energy propagation path converges with energy directed along a second energy propagation path through a second energy waveguide.

8. The energy waveguide system of claim 7 , wherein the first and second energy propagation paths converge at a location on the first side of the array, on the second side of the array, or between the first and second sides of the array.

9. The energy waveguide system of claim 3 , wherein each energy waveguide comprises a structure for directing energy, the structure selected from a group consisting of:

a structure configured to alter an angular direction of energy passing therethrough;

a structure comprising at least one numerical aperture;

a structure configured to redirect energy off at least one internal surface; and

an energy relay.

10. The energy waveguide system of claim 3 , wherein the energy inhibiting element comprises a structure for attenuating or modifying energy propagation paths, the structure selected from a group consisting of:

an energy blocking structure;

an element configured to alter a first energy propagation path to alter a fill factor of the first aperture; and

a structure configured to limit an angular extent of energy proximate the first energy location.

11. The energy waveguide system of claim 10 , wherein, when the energy inhibiting element is configured to limit an angular extent of energy proximate the first energy location.

12. The energy waveguide system of claim 10 , wherein the energy inhibiting structure comprises at least one numerical aperture or a baffle structure.

13. The energy waveguide system of claim 10 , wherein the energy inhibiting structure is positioned adjacent to the first energy waveguide and generally extends towards the first energy location or adjacent to the first energy location and generally extends towards the first energy waveguide.

14. The energy waveguide system of claim 1 , wherein each waveguide of the array of waveguides comprises a cross-sectional shape of a set of one or more shapes along the transverse plane of the energy waveguide system, the one or more shapes configured to form the tiling across the transverse plane of the energy waveguide system.

15. The energy waveguide system of claim 1 , wherein the array of energy waveguides are arranged to form a planar surface or a curved surface.

16. The energy waveguide system of claim 1 , wherein energy directed along the first energy propagation path is electromagnetic energy defined by a wavelength, the wavelength belonging to a regime selected from a group consisting of:

visible light;

ultraviolet;

infrared; and

x-ray.

17. The energy waveguide system of claim 1 , wherein energy directed along the first energy propagation path is mechanical energy defined by pressure waves, the pressure waves comprising:

tactile pressure waves; or

acoustic sound vibrations.

18. The energy waveguide system of claim 1 , wherein the array of waveguides comprises an array of lenslets disposed side-by-side in an arrangement selected from a group consisting of:

a hexagonal packing arrangement;

a square packing arrangement; and

a non-regular packing arrangement.

19. The energy waveguide system of claim 1 , wherein the array of waveguides comprises an array of lenslets, the array of lenslets comprising Fresnel lenses.

20. The energy waveguide system of claim 1 , wherein the array of waveguides comprises an array of lenslets, and wherein a shape of a first lenslet of the array of lenslets is configured to additionally alter the unique direction which is determined at least by the first energy location.

21. The energy waveguide system of claim 1 , wherein the energy waveguide system further comprises interstitial regions between tiles of the tiling of the array of waveguides.

22. The energy waveguide system of claim 21 , wherein the interstitial regions are configured to inhibit energy propagation in at least the transverse plane of the energy waveguide system.

23. The energy waveguide system of claim 21 , wherein the array of waveguides are configured to direct energy of a first energy domain, and the interstitial regions are configured to direct energy of a second energy domain, different than the first energy domain.

24. The energy waveguide system of claim 21 , wherein the interstitial regions comprise an absence of material.

25. The energy waveguide system of claim 1 , wherein the array of waveguides comprises two or more sets of waveguides, a first set of the two or more sets of waveguides configured to direct energy of a first energy domain, and a second set of the two or more sets of waveguides configured to direct energy of a second energy domain.

26. The energy waveguide system of claim 25 , wherein the first and second energy domains comprise one or more of the following properties: first and second energy types, first and second energy wavelength ranges, first and second numerical apertures, and first and second angular distributions of energy, respectively.

27. An energy waveguide system for defining a plurality of energy propagation paths comprising:

an array of energy waveguides, the array comprising a first side and a second side, and being configured to direct energy therethrough along a plurality of energy propagation paths extending through a plurality of energy locations on the first side;

wherein a first subset of the plurality of energy propagation paths extend through a first energy location and a first energy waveguide of the array of energy waveguides, wherein the first subset of the plurality of energy propagation paths fill at least a portion of an aperture of the first energy waveguide and extend towards the second side of the array in a first direction which is determined at least by the first energy location, the first subset of the plurality of energy propagation paths comprising a chief ray path and additional paths that are substantially parallel to the chief ray path on the second side of the array; and

wherein each waveguide of the array of waveguides comprises a shape of a set of one or more shapes configured to tessellate across a transverse plane of the energy waveguide system, the array of energy waveguides being arranged in a tiling of the one or more shapes across the transverse plane of the energy waveguide system.