3D display system and method employing stereo mapping coordinates

Abstract

In a three-dimensional (3D) display, a display panel having an array of sub-pixels may display an image according to stereoscopic mapping coordinates associated with a viewer. The periodic optical element may direct light from the display panel to a viewer. The periodic optical element may be unchanged along an optical axis having a tilt angle relative to the display panel. A viewer tracker may determine a position of a viewer. The stereomapped coordinates of selected sub-pixels in the array of sub-pixels may be a function of the viewer position, the position of the selected sub-pixels, a phase function of the periodic optical element, a pitch 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.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application Serial Nos. 63 / 478,162, 63 / 478,163, and 63 / 478,164, filed on January 1, 2023, each of which is incorporated herein by reference in its entirety.

[0003] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0004] none Background Art

[0005] Multi-view displays, such as 3D displays, can direct different views of an image to a viewer's eyes. Efforts are underway to reduce or eliminate artifacts associated with these views. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Various features of examples and embodiments according to the principles described herein may be more readily understood by reference to the following detailed description taken in conjunction with the accompanying drawings, wherein like reference numerals denote like structural elements, and wherein:

[0007] Figure 1 shows a schematic diagram of a three-dimensional (3D) display system including a 3D display in an example of an embodiment according to principles described herein;

[0008] Figure 2 shows a front view of a display panel including an array of light emitting diodes in an example of an embodiment according to principles described herein;

[0009] Figure 3 shows a front view of a display panel including a backlight and a light valve array, in an example of an embodiment according to principles described herein;

[0010] Figure 4 shows a front view drawing of a display panel including a Pentile subpixel arrangement in an example of an embodiment according to principles described herein;

[0011] Figure 5 shows an elevation view of a periodic optical element including a lenticular lens array in an example of an embodiment according to principles described herein;

[0012] Figure 6 An example of an embodiment according to the principles described herein is shown. Figure 5 A cross-sectional view of a lenticular lens array;

[0013] Figure 7 shows an elevation view of a periodic optical element including a parallax barrier with transmissive slits, in an example of an embodiment according to principles described herein;

[0014] Figure 8 An example of an embodiment according to the principles described herein is shown. Figure 7 A cross-sectional view of a parallax barrier with transmissive slits;

[0015] Figure 9 A flowchart illustrating a method of displaying a 3D image in an example of an embodiment according to the principles described herein;

[0016] Figure 10 A flowchart illustrating a method of displaying a 3D image in an example of another embodiment according to the principles described herein is shown.

[0017] Certain examples and embodiments have other features in addition to or instead of the features shown in the above drawings. These and other features will be described in detail below with reference to the above drawings. DETAILED DESCRIPTION

[0018] In a 3D display, a display panel having a subpixel array can display images according to stereoscopically mapped coordinates associated with a viewer. A periodic optical element can direct light from the display panel toward the viewer. The periodic optical element can be constant along an optical axis that has an oblique angle relative to the display panel. A viewer tracker can determine the viewer's position. The stereoscopically mapped coordinates of a selected subpixel in the subpixel array can be a function of the viewer's position, the position of the selected subpixel, a phase function of the periodic optical element, a spacing 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.

[0019] The controller can use the stereo mapping coordinates from a particular sub-pixel to determine whether light from that sub-pixel is directed to the viewer's left or right eye. The controller can use the stereo mapping coordinates of the sub-pixel to select which image to represent with that sub-pixel, such as directing a sub-pixel of a "left image" to the viewer's left eye, a sub-pixel of a "right image" to the viewer's right eye, or a weighted combination of sub-pixels of a "left image" and sub-pixels of a "right image."

[0020] As used herein, the article "a" means its ordinary meaning in the patent art, i.e., "one or more". For example, "sub-pixel" means one or more sub-pixels, and therefore, "the sub-pixel" herein refers to "the (one or more) sub-pixels". In addition, any reference to "top", "bottom", "upper", "lower", "up", "down", "front", "back", "first", "second", "left", or "right" herein is not intended to be limiting. Unless otherwise expressly provided, the term "about" herein, when applied to a value, generally refers to within the tolerance range of the device that produces the value, or may refer to plus or minus 10%, or plus or minus 5%, or plus or minus 1%. In addition, the term "substantially" as used herein refers to most, almost all, all, or an amount in the range of about 51% to about 100%. In addition, the examples herein are intended to be illustrative only and are presented for discussion purposes and not for limitation.

[0021] Figure 1 Schematic diagram of a 3D display system 100 including a 3D display 102 is shown in an example of an embodiment according to the principles described herein. Specifically, Figure 1 An exploded view of the 3D display 102 is shown. Figure 1 The notational convention shown in and used below assumes that 3D display 102 extends in the (x, y) plane, and that the z-axis extends away from 3D display 102 and generally toward the viewer in a direction normal to the plane of 3D display 102. Other notational conventions may also be used.

[0022] like Figure 1 As shown, the 3D display 102 may include a display panel 106 having a sub-pixel array 108 configured to display an image according to stereoscopic mapping coordinates associated with the viewer 104. The sub-pixels 108 may be located at sub-pixel positions in a grid having grid axes. Each sub-pixel 108 may produce light having a specified color. For example, the sub-pixels 108 may include red sub-pixels, green sub-pixels, and blue sub-pixels that produce red light, green light, and blue light, respectively. Other color / wavelength schemes may also be used. The sub-pixels 108 may be grouped into pixels, each pixel including at least two sub-pixels 108 that produce light of different colors. Two possible configurations for the display panel 106 are described below and are described in detail in the accompanying drawings. Figure 2 and Figure 3 Other configurations may also be used.

[0023] Figure 2A front view of display panel 106A including array 202 of light-emitting diodes 208 is shown, in an example of an embodiment according to the principles described herein. In some embodiments, light-emitting diodes 208 of array 202 may comprise organic light-emitting diodes (OLEDs). Each light-emitting diode 208 may correspond to a subpixel 108. Array 202 of light-emitting diodes 208 may include a red light-emitting diode 208R, a green light-emitting diode 208G, and a blue light-emitting diode 208B, corresponding to red, green, and blue subpixels, respectively. A controller 118 (described below) may control light-emitting diodes 208 individually or in one or more groups. Each light-emitting diode 208 may controllably generate light in response to an electrical signal provided by controller 118 or a suitable light-emitting diode driver circuit in communication with controller 118. Controller 118 may directly power a given light-emitting diode 208 with a power level that varies as a function of the intensity at the corresponding position in an image. The power delivered to light-emitting diodes 208 may optionally be pulse-width modulated at a modulation frequency higher than that perceptible to the human eye. Using pulse width modulation can simplify the design of an LED array controller because it can generate any average power level from a relatively small number of instantaneous power levels by varying the duty cycle of the power. In some examples, array 202 of LEDs 208 can be arranged in a rectangular or square repeating pattern across a surface area 210 of array 202. For example, array 202 can have grid axes 204 that are orthogonal to one another. In some examples, grid axes 204 can be parallel to edges 206 of array 202 of LEDs 208.

[0024] Figure 3 1 shows a front view of a display panel 106B including a backlight 302 and a light valve array 304, in an example of an embodiment according to the principles described herein. Figure 3While the backlight 302 and light valve array 304 are shown as separate from each other, they can be in contact with each other or placed as close together as practical. The backlight 302 can provide illumination with uniform or substantially uniform intensity across the surface area of the backlight 302. The backlight 302 can provide illumination across a broad spectrum, for example, encompassing most or all of the visible portion of the electromagnetic spectrum. The backlight 302 can provide illumination at a continuous range of propagation angles toward the light valve array 304. The backlight 302 can provide unmodulated illumination to the light valve array 304. The light valve array 304 can include light valves 308, which can be controlled individually or in one or more groups by the controller 118 (as described below). Each light valve 308 can controllably attenuate illumination from the backlight, for example, in response to an electrical signal generated by the controller 118 or by suitable light valve driver circuitry in communication with the controller 118. The light valves 308 can include color filters that allow only a portion of the electromagnetic spectrum to pass through the light valve 308. For example, the light valves 308 may include a red light valve 308R having a red filter that allows only red light to pass through the red light valve 308R; a green light valve 308G having a green filter that allows only green light to pass through the green light valve 308G; and a blue light valve 308B having a blue filter that allows only blue light to pass through the blue light valve 308B. Other color schemes and numbers of colors may also be used. Suitable light valve arrays 304 may include liquid crystal light valves, electrophoretic light valves, light valves based on electrowetting, and the like. In some examples, the light valves 308 of the light valve array 304 may be arranged in a repeating rectangular or square pattern across the surface area 312 of the light valve array 304. For example, the light valve array 304 may have grid axes 204 that are orthogonal to each other. In some examples, the grid axes 204 may be parallel to the edges 306 of the light valve array 304.

[0025] Figure 4 FIG. 1 is a diagram illustrating a front view of a display panel 106C including a Pentile arrangement of sub-pixels 408, in an example of an embodiment according to the principles described herein. Figure 2 The light emitting diodes 208 in the array 202 of light emitting diodes 208 are shown, or as shown in FIG. Figure 3Light valves 308 in light valve array 304 are shown. Compared to a conventional red-green-blue subpixel arrangement, where each pixel includes a red subpixel 408R (e.g., an LED that produces red light), a green subpixel 408G (e.g., an LED that produces green light), and a blue subpixel 408B (e.g., an LED that produces blue light), a pentile subpixel arrangement can include only two subpixels 408 (or LEDs) per pixel 402. The colors of the subpixels 408 in display panel 106C can be arranged so that the missing color of a particular pixel 402 can be found in a neighboring pixel 404. While some display panels may employ subpixel rendering in software to help smooth features in an image, the display panel 106C described herein may have subpixel rendering turned off when displaying images. For display panel 106C that turns off sub-pixel rendering when displaying an image, the position of each sub-pixel 408 (e.g., each LED) can be used to calculate the corresponding stereo mapping coordinates rather than using the center of pixel 402 (e.g., the center of a specified group of sub-pixels 408 or the center of a specified group of LEDs 208).

[0026] Reference again Figure 1 , the 3D display 102 may include a periodic optical element 110 that can direct light 112 corresponding to an image from the display panel 106 toward the viewer 104. For example, the periodic optical element 110 may include a parallax optical element or an optical element that produces parallax. Two possible configurations for the periodic optical element 110 are described below and are provided in Figure 5 and Figure 6 as well as Figure 7 and Figure 8 Other configurations may also be used. Figure 5 and Figure 6 as well as Figure 7 and Figure 8 Each configuration in Figure 2 and Figure 3 Use any combination of the configurations in .

[0027] Figure 5 1 shows a front view of a periodic optical element 110A including a lenticular lens array 502, in an example of an embodiment according to principles described herein. In some embodiments, periodic optical element 110A including a lenticular lens array 502 may be referred to as a parallax optical element or a parallax-generating optical element as defined herein. Figure 6 An example of an embodiment according to the principles described herein is shown. Figure 56. A cross-sectional view of a lenticular lens array 502. The lenticular lens array 502 may include an array of thin cylindrical lenslets 604 positioned to receive light from the display panel 106 and at least partially focus the received light to direct it toward a designated area near a viewer's eyes.

[0028] Figure 7 804, in accordance with the principles described herein. Figure 8 An example of an embodiment according to the principles described herein is shown. Figure 7 Figure 7 is a cross-sectional view of a parallax barrier 702 with transmissive slits 804. The parallax barrier 702 may include an opaque strip 806 and an array of thin transmissive slits 804 arranged to block portions of a displayed image in left and right viewing areas. The transmissive slits 804 may be spatially arranged to ensure that left / right image portions are visible only in their intended respective left / right viewing areas. The parallax barrier 702 may be provided by a static physical layer in which the slits are precisely placed, or may be electronically generated on an adaptive intermediate liquid crystal display layer.

[0029] Periodic optical element 110 (including one of lenticular lens array 502 or parallax barrier 702 with transmissive slits 804 ) may cooperate with display panel 106 (including one of array 202 of light emitting diodes 208 or backlight 302 and light valve array 304 ).

[0030] like Figure 5 and Figure 6As shown, the periodic optical element 110 may be invariant along an optical axis (OA) at a tilt angle α relative to the grid axis 204. For example, the periodic optical element 110 may include transmissive features, such as lenslets or transmissive slits, that are invariant along the optical axis (OA) and periodic along an orthogonal axis perpendicular to the optical axis (OA). As a specific example, the periodic optical element 110 may include transmissive slits that are parallel to the optical axis (OA) and equally spaced along the orthogonal axis. As another specific example, the periodic optical element 110 may include cylindrical lenslets that are invariant along the optical axis (OA), have a curvature along the orthogonal axis, and are equally spaced (e.g., center-to-center spacing) along the orthogonal axis. The periodic optical element 110 may be tilted at an angle α relative to the grid axis 204, which may optionally be parallel to the edge 206 of the array 202 of LEDs 208 or the edge 306 of the light valve array 304. For example, the inclination angle α may be within a specified angular tolerance of forty-five degrees, such as for a tolerance of + / - one degree, the inclination angle is between forty-four and forty-six degrees; for a tolerance of + / - two degrees, the inclination angle is between forty-three and forty-seven degrees; for a tolerance of + / - three degrees, the inclination angle is between forty-two and forty-eight degrees; for a tolerance of + / - four degrees, the inclination angle is between forty-one and forty-nine degrees; for a tolerance of + / - five degrees, the inclination angle is between forty and fifty degrees, or the inclination angle is another suitable angle or angle range.

[0031] like Figure 1As shown, 3D display 102 may include material 114 disposed between display panel 106 and periodic optical element 110. In some examples, material 114 may extend completely between display panel 106 and periodic optical element 110, such that light rays originating from display panel 106 pass only through material 114 (and not through any air or unfilled volume) before reaching periodic optical element 110. In other examples, material 114 may occupy only a portion of the volume between display panel 106 and periodic optical element 110, such that light rays originating from display panel 106 pass through at least a portion of material 114 and a volume of air before reaching periodic optical element 110. Material 114 may have a refractive index denoted by n. The refractive index n may have a value between approximately 1.3 and approximately 2, although other suitable values may also be used. Suitable materials may include glass, plastic, transparent optical adhesives, and the like. In some examples, material 114 may be dispensed in liquid form and then cured in situ, for example, by exposure to ultraviolet light or heat. In other examples, material 114 can be fabricated as a solid unit and placed in its position within 3D display 102. For example, material 114 can serve as cover glass for display panel 106. In some examples, material 114 can serve as a relatively precise spacing element. For example, material 114 can be fabricated to a specified thickness with a specified thickness tolerance, and when assembling 3D display 102, the spacing between display panel 106 and periodic optical element 110 can be set to a value equal to the specified thickness.

[0032] like Figure 1 As shown, the 3D display 102 may include a viewer tracker 116 that can determine the position of the viewer 104. The viewer tracker 116 can provide a tracked position of the viewer 104 (e.g., the position of the viewer's 104 head, one or both eyes of the viewer 104, or another anatomical feature of the viewer 104). The viewer tracker 116 can be coupled to a controller 118 (as described below), such as by providing viewer position data (in a formatted format) representing a measured position or location of the viewer 104. Figure 1, as coordinates xv, yv, and zv in ). Viewer tracker 116 may provide viewer position data to controller 118 at regular or irregular intervals. Viewer tracker 116 may include a camera configured to capture images of viewer 104. Viewer tracker 116 may also include an image processor (or a general-purpose computer programmed as an image processor) configured to determine the position of viewer 104 within the captured images to provide the tracked position. In some examples, controller 118 may include the image processor of viewer tracker 116, for example by performing operations using the same processing circuitry. In other examples, controller 118 may be separate from the image processor of viewer tracker 116. Other suitable viewer trackers may also be used, including those based on lidar or other technologies, for example, using the time of flight of reflected light in the view scene to determine the distance to one or more objects in the scene (such as the viewer's head or the viewer's eyes). As described in detail below, controller 118 may use the output of viewer tracker 116, along with other data, to calculate stereo mapping coordinates.

[0033] like Figure 1 As shown, the 3D display system 100 may include a controller 118. The controller 118 may include a processor 120 and a memory 122 storing instructions executable by the processor 120. These instructions may be executed by the processor 120 to perform data processing activities. The data processing activities may include determining, for a sub-pixel 108 in the sub-pixel array 108 of the display panel 106, a stereoscopic mapping coordinate of the sub-pixel 108 and causing the display panel 106 to display an image based on the stereoscopic mapping coordinates. These data processing activities will be described in detail below.

[0034] Figure 9 A flowchart illustrating a method 900 for displaying a 3D image in an example of an embodiment according to the principles described herein is provided. According to various embodiments, method 900 for displaying a 3D image may be performed by 3D display system 100 or another suitable 3D display system. Method 900 for displaying a 3D image is only one method for displaying a 3D image. Other suitable methods may also be used.

[0035] At operation 902 , the 3D display system may determine the position of a viewer using a viewer tracker, such as viewer tracker 116 .

[0036] At operation 904 , the 3D display system may determine stereoscopic mapping coordinates associated with the viewer.

[0037] At operation 906 , the 3D display system may display an image using a display panel (such as display panel 106 ) having a sub-pixel array according to stereoscopic mapping coordinates associated with the viewer.

[0038] In operation 908, the 3D display system may direct light from the display panel toward a viewer using a periodic optical element, such as periodic optical element 110. The periodic optical element may be invariant along an optical axis having an oblique angle relative to the display panel.

[0039] The stereoscopic mapping coordinates of a selected sub-pixel in the sub-pixel array can be a function of one or more parameters, such as the viewer's position, the position of the selected sub-pixel, the phase function of the periodic optical element, the spacing between the periodic optical element and the display panel, and the refractive index of a material disposed between the periodic optical element and the display panel. Among these parameters, the viewer's position (in three dimensions) can be dynamically measured by a viewer tracker during use of the 3D display system 100, while other quantities can be known in advance without requiring measurement during use of the 3D display system 100.

[0040] The stereo mapping coordinates may determine whether light from a given sub-pixel is directed to the viewer's left or right eye. Controller 118 may use the stereo mapping coordinates of a given sub-pixel to select which image to represent using the given sub-pixel, such as directing a sub-pixel of a "left image" to the viewer's left eye, a sub-pixel of a "right image" to the viewer's right eye, or a weighted combination of the sub-pixels of the "left image" and the sub-pixels of the "right image."

[0041] Figure 10 A flowchart illustrating a method 1000 for displaying a 3D image in accordance with another example of an embodiment of the principles described herein is provided. According to various embodiments, method 1000 for displaying a 3D image may be performed by 3D display system 100 or another suitable 3D display system. Method 1000 for displaying a 3D image is merely one method for displaying a 3D image. Other suitable methods may also be used. In this example, operation 904 (e.g., determining stereoscopic mapping coordinates associated with a viewer) in method 900 may include operations 1004, 1006, and 1008.

[0042] At operation 1002 , the 3D display system may determine the position of a viewer using a viewer tracker, such as the viewer tracker described.

[0043] At operation 1004, the 3D display system may determine an intermediate position as a function of one or more parameters, such as the position of the viewer, the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel. The intermediate position may correspond to a position on the periodic optical element where light rays originating from the display panel and reaching the viewer pass through the periodic optical element.

[0044] The intermediate positions can be determined in a closed mathematical form using ray tracing and the following four assumptions. First, the volume between the display panel and the periodic optical element is assumed to be occupied by a material with a refractive index greater than 1. Second, the space between the periodic optical elements is assumed to be occupied by air with a refractive index of 1. Third, the periodic optical element is assumed to form a planar interface between the air and the material with a refractive index greater than 1. Fourth, it is assumed that light is refracted at the planar interface located at the plane of the periodic optical element.

[0045] To provide a mathematical representation, assume that the display panel extends in the (x, y) plane at a first z position, and the periodic optical element extends in the (x, y) plane at a second z position. The position of a selected subpixel at the display panel is denoted as (xs, ys). The intermediate position at the periodic optical element is denoted as (xi, yi). The (measured) position of the viewer is denoted as (xv, yv, zv).

[0046] Generally speaking, determining the intermediate position may include determining an x-coordinate of the intermediate position as a function of parameters including the position of the viewer, the x-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel. Similarly, determining the intermediate position may include determining a y-coordinate of the intermediate position as a function of parameters including the position of the viewer, the y-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel.

[0047] In mathematical terms, determining the intermediate position may involve setting the dimensionless quantity q according to equation (1)

[0048] (1)

[0049] Wherein d is the spacing between the periodic optical element and the display panel, n is the refractive index of the material disposed between the periodic optical element and the display panel, xv is the x-component of the viewer's position, yv is the y-component of the viewer's position, zv is the z-component of the viewer's position, xs is the x-component of the position of the selected sub-pixel, and ys is the y-component of the position of the selected sub-pixel.

[0050] Determining the middle position may further include setting the x-coordinate xi of the middle position according to equation (2):

[0051] (2)

[0052] Determining the middle position may further include setting the y-coordinate yi of the middle position according to equation (3):

[0053] (3)

[0054] The intermediate position (xi, yi) corresponds to the position on the periodic optical element at which light originating from the sub-pixel position (xs, ys) on the display panel and reaching the viewer at position (xv, yv, zv) passes through the periodic optical element.

[0055] Back to Figure 10 At operation 1006 , the 3D display system may apply a phase function to the intermediate position to generate a phase value.

[0056] The phase function is linear with respect to the position on the periodic optical element in a direction at a certain angle relative to the optical axis. The phase function may receive as input the intermediate position determined in operation 1004. The phase function may generate a single phase value as a function of the intermediate position.

[0057] For example, along the extent of a first lenticular lens or a first transmission slit, the phase value may have a first value, such as 0. The phase value may increase linearly between the first lenticular lens or the first transmission slit and the adjacent second lenticular lens or the second transmission slit. Along the extent of the second lenticular lens or the second transmission slit, the phase value may have a second value, such as 1. The phase value may be linear in this manner, having a fixed value along each lenticular lens or each transmission slit and linearly increasing in the region between adjacent lenticular lenses or adjacent transmission slits.

[0058] In some examples, the phase function can effectively "number" the lenticular lenses or transmission slits in sequence by having integer values at the lenticular lenses or transmission slits and linearly increasing fractional values between the lenticular lenses or transmission slits.

[0059] Generally speaking, applying the phase function to the intermediate position to generate a phase value may include adding a first quantity, a second quantity, and a third quantity to form the phase value. The first quantity may represent the phase at a specified location on the display panel, such as the center of the display panel or the center of a periodic optical element. The second quantity may be the x-coordinate of the intermediate position divided by the period of the periodic optical element in the x-direction. The third quantity may be the y-coordinate of the intermediate position divided by the period of the periodic optical element in the y-direction.

[0060] In mathematical terms, applying the phase function to the intermediate position to generate a phase value may include setting the phase value according to equation (4) :.

[0061] (4)

[0062] in, is the phase value at the center of the periodic optical element (or other specified position on the periodic optical element or display panel), is the x component of the middle position, is the y component of the middle position, is the tilt angle, and is the period of the periodic optical element along the x direction (see Figure 5 and Figure 6 ). Note the tilt angle The tangent of the periodic element is equal to the period in the x direction Divide by the period of the periodic element in the y direction (See Figure 5 and Figure 6 ).

[0063] Back to Figure 10 At operation 1008 , the 3D display system may use the phase values to form stereoscopic mapping coordinates associated with the viewer.

[0064] Generally speaking, using the phase value to form the stereo mapping coordinate may include taking a modulo of the phase value to form the stereo mapping coordinate.

[0065] In mathematical terms, for a phase function that assigns continuous integers to a biconvex lens or a transmission slit, using the phase values to form stereo mapping coordinates may include setting the stereo mapping coordinates according to equation (5)

[0066] (5)

[0067] in is the phase value. For example, for a given sub-pixel, if the phase value Equal to 5.7, the corresponding stereo mapping coordinates Equal to 0.7.

[0068] In some configurations, a 3D display system can display two adjacent views of a multi-view image. For example, a 3D display system can display two adjacent views of a multi-view image by mapping a view k of N views to a phase band To allocate more than two views, other suitable configurations may also be used.

[0069] At operation 1010, a 3D display system may display an image using a display panel having a sub-pixel array (e.g., display panel 106) according to stereoscopic mapping coordinates associated with a viewer. Controller 118 may cause the display panel to display the image according to the stereoscopic mapping coordinates of the sub-pixels of the display panel. Two configurations for displaying images according to stereoscopic coordinates are described below.

[0070] In a first configuration, displaying an image based on the stereoscopic mapping coordinates of a selected subpixel may include comparing the stereoscopic mapping coordinates to a specified threshold. In some examples, the specified threshold may be the midpoint (e.g., 0.5) of a specified range (e.g., between 0 and 1) of the stereoscopic mapping coordinates. In response to the comparison, the controller 118 may cause the display panel to display one of the following on the selected subpixel: a portion of the image corresponding to the viewer's left eye or a portion of the image corresponding to the viewer's right eye. For the example of assigning consecutive integers to a phase function of a lenticular lens or a transmission slit, the specified threshold may be equal to 0.5. If the stereoscopic mapping coordinates are between 0 and 0.5, the designated subpixel is positioned to direct light to the viewer's left eye (or right eye). If the stereoscopic mapping coordinates are between 0.5 and 1, the designated subpixel is positioned to direct light to the viewer's right eye (or left eye).

[0071] In a second configuration, displaying an image based on the stereo mapping coordinates of the selected sub-pixels may include combining an image portion corresponding to a viewer's left eye and an image portion corresponding to a viewer's right eye in a ratio that depends on the value of the stereo mapping coordinates to form a blended portion of the image, and displaying the blended portion of the image on the selected sub-pixels. The ratio may be varied based on a nonlinear smoothing function. The nonlinear smoothing function may form the blended portion of the image in a linear color space. This blending of the images may smooth transitions between images that may occur at specific values of the stereo mapping coordinates (e.g., values equal to or close to 0, 0.5, and 1).

[0072] At operation 1012, the 3D display system may direct light from the display panel toward a viewer using a periodic optical element, such as periodic optical element 110. The periodic optical element may be invariant along an optical axis having an oblique angle relative to the display panel.

[0073] At a viewing distance D from the 3D display, the spatial extent of the stereoscopic viewing window (e.g., the phase value of a given subpixel varies across its range, such as from 0 to 1) can be n*D*px / d. In some examples, the viewing window can cover twice the interocular distance 10 of the viewer. For these examples, the period px of the periodic element in the x-direction can be selected to be equal to (or approximately equal to) (2*10*d) / (n*D).

[0074] To further illustrate the systems and related methods disclosed herein, a non-limiting list of examples is provided below. Each of the following non-limiting examples can exist independently or can be combined with any one or more of the other examples in any arrangement or combination.

[0075] In Example 1, a method for displaying a three-dimensional (3D) image may include: determining a position of a viewer using a viewer tracker; determining stereo mapping coordinates associated with the viewer; displaying an image using a display panel having a sub-pixel array based on the stereo mapping coordinates associated with the viewer; and directing light from the display panel toward the viewer using a periodic optical element, the periodic optical element being invariant along an optical axis having an oblique angle relative to the display panel, the stereo mapping coordinates of a selected sub-pixel in the sub-pixel array being a function of the position of the viewer, the position of the selected sub-pixel, a phase function of the periodic optical element, a spacing 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.

[0076] In Example 2, the method of Example 1 can optionally be configured such that determining the stereo mapping coordinates of the selected sub-pixel includes: determining an intermediate position as a function of the position of the viewer, the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel; applying a phase function to the intermediate position to generate a phase value; and forming the stereo mapping coordinates using the phase value.

[0077] In Example 3, the method of any one of Examples 1-2 can optionally be configured such that the intermediate position corresponds to a position on the periodic optical element where light rays originating from the display panel and reaching the viewer pass through the periodic optical element.

[0078] In Example 4, the method of any one of Examples 1-3 can optionally be configured such that determining the intermediate position includes: determining the x-coordinate of the intermediate position as a function of the position of the viewer, the x-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel; and determining the y-coordinate of the intermediate position as a function of the position of the viewer, the y-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel.

[0079] In Example 5, the method of any one of Examples 1-4 may optionally be configured such that determining the intermediate position includes setting the dimensionless quantity , which is given by:

[0080]

[0081] in, is the spacing between the periodic optical element and the display panel, is the refractive index of the material disposed between the periodic optical element and the display panel, is the x-component of the viewer's position, is the y component of the viewer's position, is the z component of the viewer's position, is the x-component of the position of the selected sub-pixel, and is the y component of the position of the selected sub-pixel; the x coordinate of the middle position Set to ; and the y coordinate of the middle position Set to .

[0082] In Example 6, the method of any one of Examples 1-5 can optionally be configured such that the phase function is linear with respect to a position on the periodic optical element in a direction at a certain angle relative to the optical axis.

[0083] In Example 7, the method of any one of Examples 1-6 can optionally be configured such that applying the phase function to the intermediate position to generate a phase value includes: summing a first quantity, a second quantity, and a third quantity to form the phase value, the first quantity representing the phase of a specified position on the display panel, the second quantity being the x-coordinate of the intermediate position divided by the period of the periodic optical element along the x-direction, and the third quantity being the y-coordinate of the intermediate position divided by the period of the periodic optical element along the y-direction.

[0084] In Example 8, the method of any one of Examples 1-7 may optionally be configured such that applying the phase function to the intermediate position to generate the phase value includes setting the phase value to a phase value given by :

[0085]

[0086] in is the phase value at the center of the periodic optical element, is the x-component of the middle position, is the y component of the middle position, is the tilt angle, and is the period of the periodic optical element along the x direction.

[0087] In Example 9, the method of any one of Examples 1-8 may optionally be configured such that forming the stereo mapping coordinates using the phase values comprises taking a modulo of the phase values to form the stereo mapping coordinates.

[0088] In Example 10, the method of any one of Examples 1 to 9 may optionally be configured such that forming stereo mapping coordinates using the phase values includes: setting the stereo mapping coordinates to Set to ,in is the phase value.

[0089] In Example 11, the method of any one of Examples 1-10 can optionally be configured such that displaying an image according to the stereo mapping coordinates of a selected sub-pixel includes: comparing the stereo mapping coordinates with a specified threshold; and in response to the comparison, displaying one of the image portion corresponding to the viewer's left eye or the image portion corresponding to the viewer's right eye on the selected sub-pixel.

[0090] In Example 12, the method of any one of Examples 1-11 can optionally be configured such that displaying an image according to the stereo mapping coordinates of a selected sub-pixel includes: combining an image portion corresponding to a viewer's left eye and an image portion corresponding to a viewer's right eye in a ratio that depends on the stereo mapping coordinate values to form a mixed portion of the image, and displaying the mixed portion of the image on the selected sub-pixel.

[0091] In Example 13, the method of any one of Examples 1-12 may optionally be configured such that the ratio is configured to vary according to a nonlinear smoothing function configured to form the mixed portion of the image in a linear color space.

[0092] In Example 14, a 3D display may include: a display panel having a sub-pixel array 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 toward the viewer, the periodic optical element being invariant along an optical axis having a tilt angle relative to the display panel; and a viewer tracker configured to determine a position of a viewer, the stereo mapping coordinates of a selected sub-pixel in the sub-pixel array being a function of the viewer's position, the position of the selected sub-pixel, a phase function of the periodic optical element, a spacing 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.

[0093] In Example 15, the 3D display of Example 14 may optionally be configured such that the periodic optical element includes one of a lenticular lens array or a parallax barrier having transmissive slits.

[0094] In Example 16, the 3D display of any one of Examples 14-15 may optionally be configured such that the display panel is an organic light emitting diode array having a Pentile sub-pixel arrangement, and the display panel is configured to turn off sub-pixel rendering when displaying an image.

[0095] In Example 17, the 3D display of any one of Examples 14-16 may optionally be configured such that the tilt angle is within a specified angular tolerance of 45 degrees.

[0096] In Example 18, a 3D display system may include: 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 positions in a grid having grid axes; a periodic optical element configured to direct light from the display panel corresponding to the image toward the viewer, the periodic optical element being invariant along an optical axis having an oblique angle relative to the grid axes; a viewer tracker configured to determine a position of the viewer; and a controller including a processor and a memory storing instructions executable by the processor, the instructions executable by the processor to perform data processing activities, the data processing activities comprising, for selected subpixels in the array of subpixels: setting a dimensionless quantity , is given by:

[0097]

[0098] in is the distance between the periodic optical element and the display panel, is the refractive index of the material disposed between the periodic optical element and the display panel, is the x component of the viewer's position, is the y component of the viewer's position, is the z component of the viewer's position, is the x component of the position of the selected sub-pixel, is the y component of the position of the selected sub-pixel; the x coordinate of the middle position Set to ; Set the y coordinate of the middle position Set to ; and sets the phase value to the phase value given by :

[0099]

[0100] in is the phase value at a specified position of the periodic optical element, is the tilt angle, and is the period of the periodic optical element along the x direction, and the stereo mapping coordinates Set to .

[0101] In Example 19, the 3D display system of Example 18 can optionally be configured such that the data processing activity further includes: comparing the stereo mapping coordinates with a specified threshold value, which is the midpoint of a specified range of stereo mapping coordinates; and in response to the comparison, causing selected sub-pixels of the display panel to display one of the image portion corresponding to the viewer's left eye or the image portion corresponding to the viewer's right eye.

[0102] In Example 20, the 3D display system of any one of Examples 18-19 can optionally be configured so that the data processing activity further includes: combining the image portion corresponding to the viewer's left eye and the image portion corresponding to the viewer's right eye in a ratio that depends on the stereo mapping coordinate value to form a mixed portion of the image; and causing the display panel to display the mixed portion of the image on selected sub-pixels, the ratio being configured to vary according to a nonlinear smooth function that is configured to form the mixed portion of the image in a linear color space.

[0103] Thus, examples and embodiments of 3D display systems and methods that can display images based on stereoscopic mapping coordinates associated with a viewer have been described herein. The above examples illustrate only a few of the many specific examples that demonstrate the principles described herein. Clearly, those skilled in the art can readily devise numerous other arrangements without departing from the scope of the following claims.

Claims

1. A method for displaying a three-dimensional (3D) image, the method comprising: Use viewer trackers to determine the viewer's location; determining stereo mapping coordinates associated with the viewer; displaying an image according to the stereoscopic mapping coordinates associated with the viewer using a display panel having a sub-pixel array; as well as directing light from the display panel toward the viewer using a periodic optical element, the periodic optical element being invariant along an optical axis having an oblique angle relative to the display panel, The stereo mapping coordinates of a selected sub-pixel in the sub-pixel array are a function of the position of the viewer, the position of the selected sub-pixel, the phase function of the periodic optical element, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel.

2. The method for displaying a 3D image according to claim 1, wherein: Determining the stereo mapping coordinates of the selected sub-pixel includes: determining an intermediate position as a function of a position of the viewer, a position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and a refractive index of the material disposed between the periodic optical element and the display panel; applying the phase function to the intermediate position to generate a phase value; and The stereo mapping coordinates are formed using the phase values.

3. The method for displaying a 3D image according to claim 2, wherein: The intermediate position corresponds to a position on the periodic optical element where light rays originating from the display panel and reaching the viewer pass through the periodic optical element.

4. The method for displaying a 3D image according to claim 2, wherein: Determining the intermediate position includes: determining an x-coordinate of the intermediate position as a function of the position of the viewer, the x-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and a refractive index of the material disposed between the periodic optical element and the display panel; and The y-coordinate of the intermediate position is determined as a function of the position of the viewer, the y-coordinate of the position of the selected sub-pixel, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel.

5. The method for displaying a 3D image according to claim 2, wherein: Determining the intermediate position includes: Set the dimensionless quantity given by : ， in, is the spacing between the periodic optical element and the display panel, is the refractive index of the material disposed between the periodic optical element and the display panel, is the x-component of the viewer's position, is the y component of the viewer's position, is the z component of the viewer's position, is the x-component of the position of the selected sub-pixel, and is the y component of the position of the selected sub-pixel; The x coordinate of the middle position Set to ;and The y coordinate of the middle position Set to .

6. The method for displaying a 3D image according to claim 2, wherein: The phase function is linear with respect to a position on the periodic optical element in a direction angularly relative to the optical axis.

7. The method for displaying a 3D image according to claim 2, wherein: Applying the phase function to the intermediate position to generate the phase value comprises: The phase value is formed by summing the first quantity, the second quantity and the third quantity, The first quantity represents the phase at a specified position on the display panel, The second quantity is the x-coordinate of the intermediate position divided by the period of the periodic optical element along the x-direction, The third quantity is the y-coordinate of the intermediate position divided by the period of the periodic optical element along the y-direction.

8. The method for displaying a 3D image according to claim 2, wherein: Applying the phase function to the intermediate position to generate a phase value comprises: The phase value is set to the phase value given by : ， in, is the phase value at the center of the periodic optical element, is the x-component of the mid-position, is the y component of the middle position, is the tilt angle, and is the period of the periodic optical element along the x direction.

9. The method for displaying a 3D image according to claim 2, wherein: Forming the stereo mapping coordinates using the phase value includes taking a modulo operation on the phase value to form the stereo mapping coordinates.

10. The method for displaying a 3D image according to claim 2, wherein: Using the phase value to form the stereo mapping coordinates includes: Set to ,in is the phase value.

11. The method for displaying a 3D image according to claim 1, wherein: Displaying an image according to the stereoscopic mapping coordinates of the selected sub-pixels comprises: comparing the stereo mapping coordinates to a specified threshold; and In response to the comparison, one of a portion of the image corresponding to the viewer's left eye or a portion of the image corresponding to the viewer's right eye is displayed on the selected sub-pixel.

12. The method for displaying a 3D image according to claim 1, wherein: Displaying an image according to the stereoscopic mapping coordinates of the selected sub-pixels comprises: combining a portion of the image corresponding to the viewer's left eye and a portion of the image corresponding to the viewer's right eye in a ratio that depends on the values of the stereo mapping coordinates to form a mixed portion of the image; and The mixed portion of the image is displayed on the selected sub-pixels.

13. The method of claim 12, wherein: The ratio is configured to vary according to a non-linear smoothing function configured to form the mixed portion of the image in a linear color space.

14. A three-dimensional (3D) display, comprising: a display panel having an array of subpixels configured to display an image according to stereoscopic mapping coordinates associated with a viewer; a periodic optical element configured to direct light from the display panel toward the viewer, the periodic optical element being invariant along an optical axis having an oblique angle relative to the display panel; as well as a viewer tracker configured to determine a location of the viewer, The stereo mapping coordinates of a selected sub-pixel in the sub-pixel array are a function of the position of the viewer, the position of the selected sub-pixel, the phase function of the periodic optical element, the spacing between the periodic optical element and the display panel, and the refractive index of the material disposed between the periodic optical element and the display panel.

15. The 3D display according to claim 14, wherein: The periodic optical element includes one of a lenticular lens array or a parallax barrier having transmissive slits.

16. The 3D display according to claim 14, wherein: The display panel is an organic light emitting diode array having a Pentile sub-pixel arrangement, and the display panel is configured to turn off sub-pixel rendering when displaying the image.

17. The 3D display according to claim 14, wherein: The tilt angle is within a specified angular tolerance of forty-five degrees.

18. A three-dimensional (3D) display system, comprising: a display panel having an array of subpixels configured to display an image according to stereoscopic mapping coordinates associated with a viewer, the subpixels being located at subpixel positions in a grid having grid axes; a periodic optical element configured to direct light corresponding to the image from the display panel toward the viewer, the periodic optical element being invariant along an optical axis having an oblique angle relative to the grid axis; a viewer tracker configured to determine a location of the viewer; as well as a controller comprising a processor and a memory storing instructions executable by the processor, the instructions executable by the processor to perform data processing activities, the data processing activities comprising, for selected sub-pixels in the sub-pixel array: Set the dimensionless quantity given by : ， in is the distance between the periodic optical element and the display panel, is the refractive index of the material disposed between the periodic optical element and the display panel, is the x-component of the viewer's position, is the y component of the viewer's position, is the z component of the viewer's position, is the x-component of the position of the selected sub-pixel, and is the y component of the position of the selected sub-pixel; The x coordinate of the middle position Set to ; The y coordinate of the middle position Set to , and sets the phase value to the phase value given by : ， in, is the phase value at a specified position of the periodic optical element, is the tilt angle, and is the period of the periodic optical element along the x direction; and The stereo mapping coordinates Set to .

19. The 3D display system according to claim 18, wherein: The data processing activities also include: comparing the stereo mapping coordinates to a specified threshold value, the specified threshold value being a midpoint of a specified range of the stereo mapping coordinates; and In response to the comparison, the selected subpixels of the display panel are caused to display one of a portion of the image corresponding to the viewer's left eye or a portion of the image corresponding to the viewer's right eye.

20. The 3D display system according to claim 18, wherein: The data processing activities also include: combining a portion of the image corresponding to the viewer's left eye and a portion of the image corresponding to the viewer's right eye in a ratio that depends on the values of the stereo mapping coordinates to form a mixed portion of the image; and The display panel is caused to display the mixed portion of the image on the selected sub-pixels, the ratio being configured to vary according to a nonlinear smoothing function configured to form the mixed portion of the image in a linear color space.

Images