3D display system and method employing stereo mapping coordinates

A three-dimensional (3D) display system comprising:

• a display panel having an array of subpixels configured to display an image according to stereo mapping coordinates associated with a viewer, the subpixels being located at subpixel locations in a grid having grid axes;
• a periodic optical element configured to direct light corresponding to the image from the display panel to the viewer, the periodic optical element being invariant along an optical axis having a slant angle relative to the grid axes;
• a viewer tracker configured to determine a location of the viewer;
• and
• a controller comprising a processor and memory storing instructions executable by the processor, the instructions being executable by the processor to perform data processing activities, the data processing activities comprising, for a selected subpixel of the array of subpixels:
• setting a quantity, q, to equal
• q
• =
• d
• /
• (
• n
• ⁢
• √
• (
• 〚
• zv
• 〛
• ^
• 22
• +
• (
• 21
• -
• 21
• /
• n
• ^
• 22
• )
• [
• 〚
• xv
• -
• xs
• )
• 〛
• ^
• 22
• +
• 〚
• (
• yv
• -
• ys
• )
• 〛
• ^
• 22
• ]
• )
• )
• ,
• wherein:
• quantity d is a separation between the periodic optical element and the display panel;
• quantity n is a refractive index of a material disposed between the periodic optical element and the display panel;
• quantity xv is an x-component of the location of the viewer;
• quantity yv is a y-component of the location of the viewer;
• quantity zv is a z-component of the location of the viewer;
• quantity xs is an x-component of the location of the selected subpixel;
• and
• quantity ys is a y-component of the location of the selected subpixel;
• setting an x-coordinate of an intermediate location, xi, to equal
• x
• ⁢
• i
• =
• xs
• +
• q
• ⁡
• (
• xv
• -
• xs
• )
• ;
• setting a y-coordinate of the intermediate location, yi, to equal
• y
• ⁢
• i
• =
• y
• ⁢
• s
• +
• q
• ⁡
• (
• yv
• -
• ys
• )
• ;
• setting a phase value, φ, to equal
• ϕ
• =
• ϕ
• ⁢
• c
• +
• (
• xi
• +
• yi
• ⁢
• tan
• α
• )
• /
• px
• ,
• wherein:
• quantity φc is a phase value at a specified location of the periodic optical element;
• quantity α is the slant angle;
• and
• quantity px is a period of the periodic optical element, taken along an x-direction;
• and
• setting the stereo mapping coordinate, S, to equal
• S
• =
• ϕ
• ⁢
• mod
• 21.

A three-dimensional (3D) display comprising:

• a display panel having an array of subpixels configured to display an image according to stereo mapping coordinates associated with a viewer;
• a periodic optical element configured to direct light from the display panel to the viewer, the periodic optical element being invariant along an optical axis having a slant angle relative to the display panel;
• a viewer tracker configured to determine a location of the viewer;
• and
• a controller comprising a processor and memory storing instructions executable by the processor, the instructions being executable by the processor to perform data processing activities, the data processing activities comprising, for a selected subpixel of the array of subpixels:
• determining an intermediate location as a function of the location of the viewer, a location of the selected subpixel, a separation between the periodic optical element and the display panel, and a refractive index of a material disposed between the periodic optical element and the display panel;
• applying a phase function of the periodic optical element to the intermediate location to generate a phase value;
• and
• using the phase value to form the stereo mapping coordinate of the selected subpixel of the array of subpixels.