Degrees of freedom for diffraction elements in wave expander

A near-eye display device comprising:

• an imager to generate an image based on light from a light source;
• and
• a waveguide to expand a light wave representing the image into a plurality of expanded light waves exiting the waveguide in a common direction toward an optical receptor of a user of the near-eye display device, the waveguide including a plurality of periodic diffraction patterns, each of the periodic diffraction patterns being represented by a diffraction pattern vector, the periodic diffraction patterns being determined such that a weighted vector summation of the diffraction pattern vectors equals zero, wherein the weighted vector summation includes a plurality of addends, and wherein weights of the individual addends in the weighted vector summation are integer numbers;
• wherein the waveguide includes a plurality of diffractive optical elements (DOEs) in a common light path from an input of the waveguide to an output of the waveguide, each of the periodic diffraction patterns being on or within one of the DOEs;
• and
• wherein when the light wave propagates in a middle DOE in the middle of the common light path, the light wave is reflected an even number of times by a periodic diffraction pattern of the middle DOE and wherein a first DOE in the common light path includes two periodic diffraction patterns on each of two surfaces of the first DOE.

A method comprising:

• generating an image by an imager based on light from a light source;
• receiving a light wave representing the image incident upon a first diffractive optical element (DOE) of a waveguide in a first direction and redirecting the light wave to a second DOE of the waveguide by a first periodic diffraction pattern of the first DOE;
• expanding the light wave in a second direction by a second periodic diffraction pattern of the second DOE and redirecting the light wave to a third DOE of the waveguide;
• and
• further expanding the light wave in a third direction by a third periodic diffraction pattern of the third DOE and redirecting the light wave toward an optical receptor of a user in the first direction;
• wherein a weighted vector summation of diffraction pattern vectors of the first, second and third periodic diffraction patterns equals zero, wherein the weighted vector summation includes a plurality of addends, and wherein weights of the individual addends in the weighted vector summation are integer numbers;
• and
• wherein when the light wave propagates in the second DOE in the middle of the common light path, the light wave is reflected an even number of times by a periodic diffraction pattern of the second DOE and wherein the first DOE in the common light path includes two periodic diffraction patterns on each of two surfaces of the first DOE.