Tensor displays
In exemplary implementations of this invention, an automultiscopic display device includes (1) one or more spatially addressable, light attenuating layers, and (2) a controller which is configured to perform calculations to control the device. In these calculations, tensors provide sparse, memory-efficient representations of a light field. The calculations include using weighted nonnegative tensor factorization (NTF) to solve an optimization problem. The NTF calculations can be sufficiently efficient to achieve interactive refresh rates. Either a directional backlight or a uniform backlight may be used. For example, the device may have (1) a high resolution LCD in front, and (2) a low resolution directional backlight. Or, for example, the device may have a uniform backlight and three or more LCD panels. In these examples, all of the LCDs and the directional backlight (if applicable) may be time-multiplexed.
1. A method comprising, in combination:
(a) using a backlight to provide light to a display device, which display device includes one or more spatially addressable, light attenuating layers;
(b) using the layers to display a temporal sequence of frames; and
(c) using one or more processors
(i) to perform an optimization calculation to compute, for each respective frame in the sequence and each respective layer in the one or more layers, attenuation of the light at respective pixels of the respective layer; and
(ii) to output control signals to control the attenuation;
wherein
(I) the optimization calculation includes at least one mathematical operation on an N th -order, rank-M tensor, where M is equal to the number of frames in the sequence, and N is equal to the number of the layers, if the backlight is uniform, and N is equal to the number of the layers plus one, if the backlight is directional,
(II) the optimization calculation includes applying a weighted nonnegative tensor factorization, and
(III) either (A) the backlight is uniform and the number of the layers is at least three or (B) the backlight is directional and the number of the layers is at least one.
2. The method of claim 1 , wherein the backlight is directional.
3. The method of claim 1 , wherein the backlight is directional and the number of the layers is at least two.
4. The method of claim 1 , wherein the backlight is uniform and the number of the layers is at least three.
5. The method of claim 1 , wherein the tensor is sparse.
6. The method of claim 1 , wherein the display device is configured to produce an automultiscopic display.
7. The method of claim 6 , wherein:
(a) the automultiscopic display has one or more fields of view;
(b) the display device has a front display surface;
(c) each respective field of view, out of the one or more fields of view, is centered about a viewing axis; and
(d) the method further comprises (i) dynamically varying the viewing axis of each field of view, respectively, including to orientations that are not normal to the front display surface, and (ii) tracking gaze or head position of a human user of the display device.
8. Apparatus comprising, in combination:
(a) a display device, which display device includes one or more spatially addressable, light attenuating layers, which layers are configured to display a temporal sequence of frames;
(b) a backlight, the backlight being configured to provide light to the display device; and
(c) one or more processors, the one or more processors being configured
(i) to perform an optimization calculation to compute, for each respective frame in the sequence and each respective layer in the one or more layers, attenuation of the light at respective pixels of the respective layer; and
(ii) to output control signals to control the attenuation;
wherein
(I) the backlight is directional and the number of the layers is at least one,
(II) the optimization calculation includes at least one mathematical operation on an rank-M tensor, M being equal to the number of frames in the sequence, and
(III) the optimization calculation includes applying a weighted nonnegative tensor factorization.
9. The apparatus of claim 8 , wherein the tensor has an order equal to N+1, where N is the number of the layers.
10. The apparatus of claim 9 , wherein the number of the layers is equal to at least two.
11. The apparatus of claim 8 , wherein:
(a) the backlight comprises a lens and a spatially addressable light modulating layer;
(b) the lens has a focal length, and
(c) the light modulating layer is positioned at a distance from the lens, which distance is equal to the focal length.
12. The apparatus of claim 8 , wherein the display device is configured to produce an automultiscopic display.
13. The apparatus of claim 8 , wherein the tensor is sparse.
14. The apparatus of claim 8 , wherein the optimization calculation optimizes based at least in part on perception error metrics.
15. The apparatus of claim 8 , wherein the optimization calculation calculates a set of per pixel attenuations, which set minimizes error between a light field transmitted from the display device and a light field that would be created by a target 3D scene.
16. The apparatus of claim 8 , wherein at least one of the layers comprises both (i) optical elements configured to transmit light and (ii) optical elements configured to emit light.
17. Apparatus comprising, in combination:
(a) a display device, which display device includes one or more spatially addressable, light attenuating layers, the layers being configured to display a temporal sequence of frames;
(b) a backlight, the backlight being configured to provide light to the display device; and
(c) one or more processors, the one or more processors being configured
(i) to perform an optimization calculation to compute, for each respective frame in the sequence and each respective layer in the one or more layers, attenuation of light at respective pixels of the respective layer; and
(ii) to output control signals to control the attenuation;
wherein
(I) the backlight is uniform,
(II) the optimization calculation includes at least one mathematical operation on an N th -order, rank-M tensor, M being equal to the number of frames in the sequence and N being equal to the number of the layers,
(III) the optimization calculation includes applying a weighted nonnegative tensor factorization, and
(IV) the number of the layers is at least three.
18. The apparatus of claim 17 , wherein:
(a) the display device is configured to produce an automultiscopic display, which display concurrently has one or more fields of view;
(b) the display device has a front display surface;
(c) each respective field of view, out of the one or more fields of view, is centered about a viewing axis; and
(d) the display device is configured to dynamically vary the viewing axis of each field of view, respectively, including to orientations that are not normal to the front display surface.
19. The apparatus of claim 18 , wherein the apparatus is configured to track gaze or head position of a human user of the display device.
20. The apparatus of claim 17 , wherein the tensor is sparse.