Autostereoscopic display device

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First Claim
1. An autostereoscopic display, comprising:
 a pixelated display panel, pixelated display panel comprising an array of single color pixels or an array of subpixels of different colors, wherein each group subpixels define full color pixels; and
a view forming arrangement, wherein the view forming arrangement is positioned over the display panel,wherein the view forming arrangement is arranged to direct light the light from different pixels or subpixels to different spatial locations, thereby enabling different views of a three dimensional scene to be displayed in different spatial locations,wherein the pixels of the display panel form a hexagonal grid, with a maximum internal angle deviation from 120 degrees of 20 degrees or less,wherein the hexagonal grid repeats with translation vectors a and b, and the lengths of the translation vectors a and b have an aspect ratio of the shorter to the longer between 0.66 and 1;
wherein the view forming arrangement comprises a two dimensional array of lenses which repeat in a hexagonal grid with translation vectors p′ and
q′
;
wherein defining a dimensionless vector p as (p_{a},p_{b}), which satisfies;
p′
=p_{a}a+p_{b}b, and defining circular regions in the space of components p_{b }and p_{a }for integer n as;
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Abstract
An autostereoscopic display comprises a pixelated display panel comprising an array of single color pixels or an array of subpixels of different colors and a view forming arrangement comprising an array of lens elements. The pixels form a hexagonal grid, and the lenses also repeat in a hexagonal grid. A vector p is defined which relates to a mapping between the pixel grid and the lens grid. Regions in the two dimensional space for this vector p are identified which give good or poor banding performance, and the better banding performance regions are selected.
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OPTICAL ARRANGEMENT AND AN AUTOSTEREOSCOPIC DISPLAY DEVICE INCORPORATING THE SAME  
Patent #
US 20110075256A1
Filed 05/27/2009

Current Assignee
Koninklijke Philips N.V.

Sponsoring Entity
Koninklijke Philips N.V.

LOWDIMENSIONAL RANK1 LATTICES IN COMPUTER IMAGE SYNTHESIS  
Patent #
US 20090244084A1
Filed 04/01/2009

Current Assignee
NVIDIA Corporation

Sponsoring Entity
NVIDIA Corporation

Lenticular Autostereoscopic Display Device and Method, and Associated Autostereoscopic Image Synthesising Method  
Patent #
US 20080291267A1
Filed 10/14/2005

Current Assignee
Artistic Images

Sponsoring Entity
Artistic Images

Lens array and display apparatus using same  
Patent #
US 20060195293A1
Filed 01/05/2006

Current Assignee
Panasonic Liquid Crystal Display Company Limited

Sponsoring Entity
Hitachi Displays Limited

Lightfield display  
Patent #
US 8,416,289 B2
Filed 04/28/2009

Current Assignee
Microsoft Technology Licensing LLC

Sponsoring Entity
Microsoft Corporation

THREEDIMENSIONAL IMAGE DISPLAY PANEL STRUCTURE  
Patent #
US 20130182319A1
Filed 07/20/2011

Current Assignee
Hyunin Chung

Sponsoring Entity
Hyunin Chung

DIRECT VIEW AUGMENTED REALITY EYEGLASSTYPE DISPLAY  
Patent #
US 20130286053A1
Filed 12/19/2012

Current Assignee
Microsoft Technology Licensing LLC

Sponsoring Entity
Andreas G. Nowatzyk, John G. Bennett, Rod G. Fleck

12 Claims
 1. An autostereoscopic display, comprising:
a pixelated display panel, pixelated display panel comprising an array of single color pixels or an array of subpixels of different colors, wherein each group subpixels define full color pixels; and a view forming arrangement, wherein the view forming arrangement is positioned over the display panel, wherein the view forming arrangement is arranged to direct light the light from different pixels or subpixels to different spatial locations, thereby enabling different views of a three dimensional scene to be displayed in different spatial locations, wherein the pixels of the display panel form a hexagonal grid, with a maximum internal angle deviation from 120 degrees of 20 degrees or less, wherein the hexagonal grid repeats with translation vectors a and b, and the lengths of the translation vectors a and b have an aspect ratio of the shorter to the longer between 0.66 and 1; wherein the view forming arrangement comprises a two dimensional array of lenses which repeat in a hexagonal grid with translation vectors p′ and
q′
;wherein defining a dimensionless vector p as (p_{a},p_{b}), which satisfies;
p′
=p_{a}a+p_{b}b,and defining circular regions in the space of components p_{b }and p_{a }for integer n as;  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
1 Specification
This application is the U.S. National Phase application under 35 U.S.C. § 371 of International Application No. PCT/EP2015/080839, filed on Dec. 21, 2015, which claims the benefit of EP Patent Application No. EP 14200331.8, filed on Dec. 24, 2014. These applications are hereby incorporated by reference herein.
This invention relates to an autostereoscopic display device and a driving method for such a display device.
A known autostereoscopic display device comprises a twodimensional liquid crystal display panel having a row and column array of display pixels (wherein a “pixel” typically comprises a set of “subpixels”, and a “subpixel” is the smallest individually addressable, singlecolor, picture element) acting as an image forming means to produce a display. An array of elongated lenses extending parallel to one another overlies the display pixel array and acts as a view forming means. These are known as “lenticular lenses”. Outputs from the display pixels are projected through these lenticular lenses, whose function is to modify the directions of the outputs.
The pixel comprises the smallest set of subpixels which can be addressed to produce all possible colors. For the purposes of this description, a “unit cell” is also defined. The unit cell is defined as the smallest set of subpixels which repeat to form the full subpixel pattern. The unit cell may be the same arrangement of subpixels as a pixel. However, the unit cell may include more subpixels than a pixel. This is the case if there are pixels with different orientations of subpixels, for example. The overall subpixel pattern then repeats with a larger basic unit (the unit cell) than a pixel.
The lenticular lenses are provided as a sheet of lens elements, each of which comprises an elongate partiallycylindrical (e.g. semicylindrical) lens element. The lenticular lenses extend in the column direction of the display panel, with each lenticular lens overlying a respective group of two or more adjacent columns of display subpixels.
Each lenticular lens can be associated with two columns of display subpixels to enable a user to observe a single stereoscopic image. Instead, each lenticular lens can be associated with a group of three or more adjacent display subpixels in the row direction. Corresponding columns of display subpixels in each group are arranged appropriately to provide a vertical slice from a respective two dimensional subimage. As a user'"'"'s head is moved from left to right a series of successive, different, stereoscopic views are observed creating, for example, a lookaround impression.
The display panel 3 has an orthogonal array of rows and columns of display subpixels 5. For the sake of clarity, only a small number of display subpixels 5 are shown in the Figure. In practice, the display panel 3 might comprise about one thousand rows and several thousand columns of display subpixels 5. In a black and white display panel a subpixel in fact constitutes a full pixel. In a color display a subpixel is one color component of a full color pixel. The full color pixel, according to general terminology comprises all subpixels necessary for creating all colors of a smallest image part displayed. Thus, e.g. a full color pixel may have red (R) green (G) and blue (B) subpixels possibly augmented with a white subpixel or with one or more other elementary colored subpixels. The structure of the liquid crystal display panel 3 is entirely conventional. In particular, the panel 3 comprises a pair of spaced transparent glass substrates, between which an aligned twisted nematic or other liquid crystal material is provided. The substrates carry patterns of transparent indium tin oxide (ITO) electrodes on their facing surfaces. Polarizing layers are also provided on the outer surfaces of the substrates.
Each display subpixel 5 comprises opposing electrodes on the substrates, with the intervening liquid crystal material there between. The shape and layout of the display subpixels 5 are determined by the shape and layout of the electrodes. The display subpixels 5 are regularly spaced from one another by gaps.
Each display subpixel 5 is associated with a switching element, such as a thin film transistor (TFT) or thin film diode (TFD). The display pixels are operated to produce the display by providing addressing signals to the switching elements, and suitable addressing schemes will be known to those skilled in the art.
The display panel 3 is illuminated by a light source 7 comprising, in this case, a planar backlight extending over the area of the display pixel array. Light from the light source 7 is directed through the display panel 3, with the individual display subpixels 5 being driven to modulate the light and produce the display.
The display device 1 also comprises a lenticular sheet 9, arranged over the display side of the display panel 3, which performs a light directing function and thus a view forming function. The lenticular sheet 9 comprises a row of lenticular elements 11 extending parallel to one another, of which only one is shown with exaggerated dimensions for the sake of clarity.
The lenticular elements 11 are in the form of convex cylindrical lenses each having an elongate axis 12 extending perpendicular to the cylindrical curvature of the element, and each element acts as a light output directing means to provide different images, or views, from the display panel 3 to the eyes of a user positioned in front of the display device 1.
The display device has a controller 13 which controls the backlight and the display panel.
The autostereoscopic display device 1 shown in
The skilled person will appreciate that a light polarizing means must be used in conjunction with the above described array, since the liquid crystal material is birefringent, with the refractive index switching only applying to light of a particular polarization. The light polarizing means may be provided as part of the display panel or the view forming arrangement of the device.
In the designs above, the backlight generates a static output, and all view direction is carried out by the lenticular arrangement, which provides a spatial multiplexing approach. A similar approach is achieved using a parallax barrier.
The lenticular arrangement only provides an autostereoscopic effect with one particular orientation of the display. However, many hand held devices are rotatable between portrait and landscape viewing modes. Thus, a fixed lenticular arrangement does not allow an autostereoscopic viewing effect in different viewing modes. Future 3D displays, especially for tablets, mobile phones and other portable devices will thus have a possibility to observe 3D images from many directions and for different screen orientations. Modern LCD and OLED display panels with existing pixel designs are not suited for this application. This issue has been recognized, and there are various solutions.
A dynamic solution involves providing a switchable lens arrangement, which can be switched between different modes to activate the view forming effect in different orientations. There may essentially be two lenticular arrangements, with one acting in pass through mode and the other acting in lensing mode. The mode for each lenticular arrangement may be controlled by switching the lenticular arrangement itself (for example using an LC switchable lens array) or by controlling a polarization of the light incident on the lenticular arrangement.
A static solution involves designing a lens arrangement which functions in the different orientations. A simple example can combine a rectangular grid of square subpixels in the display with a rectangular grid of microlenses (where the lens grid directions are either slanted or nonslanted with respect to the pixel grid directions) to create multiple views in both display orientations. The subpixel shapes should be preferably close to a 1:1 aspect ratio, as this will allow avoiding a problem of different angular width for individual views in portrait/landscape orientations.
An alternative grid design can be based on tessellated hexagons, and this invention relates specifically to such designs. A hexagonal grid for the display panel pixels and for the view forming arrangement (lenses) can give additional symmetry and compact packing.
One possible disadvantage of this approach is a banding effect, in which the black matrix areas between the subpixels are projected to the viewer as a regular pattern. Partially it can be solved by slanting the lens array. Specifically, in order to reduce banding effect due to projection of periodic black pixel matrix a view forming arrangement need to be chosen with respect to the pixel addressing direction (rows/columns).
The invention is defined by the claims.
According to the invention, there is provided an autostereoscopic display, comprising:
a pixelated display panel comprising an array of single color pixels or an array of subpixels of different colors with respective groups of subpixels together defining full color pixels; and
a view forming arrangement comprising an array of lens elements, positioned over the display panel, for directing the light from different pixels or subpixels to different spatial locations, thereby to enable different views of a three dimensional scene to be displayed in different spatial locations,
wherein the pixels of the display panel form a hexagonal grid, with a maximum internal angle deviation from 120 degrees of 20 degrees or less, and wherein the hexagonal grid repeats with basic translation vectors a and b, and the lengths of the basic translation vectors a and b have an aspect ratio of the shorter to the longer between 0.66 and 1,
wherein the view forming arrangement comprises a two dimensional array of lenses which repeat in a hexagonal grid with basic translation vectors p′ and q′;
wherein defining a dimensionless vector p as (p_{a},p_{b}), which satisfies:
p′=p_{a}a+p_{b}b,
and defining circular regions in the space of components p_{b }and p_{a }for integer n as:
with r_{n}=r_{0}n^{−γ} defining the radius of each circle, Γ_{n }defining the circle centers, and with N comprising a vector function for two coordinate vectors defined as:
the basic translation vectors a, b, p′ and q′ are selected such that with values such that p falls in the vector space which excludes the sets E_{1}, E_{3 }or E_{4 }with r_{0}=0.1 and γ=0.75.
In words, the main equation above reads as follows:
(Line 1) E_{n }is equal to the set of values of p such that the function N applied to the difference vector from a vector v to the vector p is less than r_{n}^{2 }for all values of vector v in the set Γ_{n}. The function N is subsequently defined. This defines the circles centered on the set of values Γ_{n}.
(Line 2) Γ_{n }is the set of vector values i+j/n with i and j as vectors in the two dimensional vector space of integer values (i.e. positive and negative integers and zero) and for which function N applied to the j vector gives the answer n.
The vector p defines the spatial relationship between the pixel (or subpixel) grid and the grid of lenses. Thus, it defines a mapping between the pixels (or subpixels) and the lenses. In particular, the components of the vector p are the terms of the matrix transformation from the pixel grid vector space (defined by a and b) and the lens grid vector space (defined at least by p′). The components of the vector p in turn define how different pixels (or subpixels) contribute to different lens phases and how the black mask area is imaged by the grid of lenses. Thus, the vector p can be considered to be a most fundamental way to define the relationship between the lenses and the pixels.
By “basic translation vector” is meant a vector translation from one point within a pixel or lens area to a corresponding point in an adjacent pixel or lens area. The lens and pixel areas are two dimensional, so there are two translation vectors—one for each grid direction. For a regular hexagonal grid, the basic translation vectors are in row and column directions at 120 degrees to each other. For a skewed grid, the basic translation vectors may deviate from this 120 degree angle, but follow the row and column directions of the grid. Thus, the hexagonal grid of the lenses and/or of the pixels may be regular hexagonal or they may be of a nonregular hexagonal form, for example a skewed version of a regular hexagonal grid.
The circular regions define sets of possible values for the components of the vector p and thus define regions of related characteristics.
By excluding the regions near the centers of E_{1}, E_{3 }and E_{4}, banding problems are prevented. In particular, routine panel designs, for example with an integer array of subpixels under each lens, as well as fractional designs, correspond to values of p which fall in the center of the E_{1}, E_{3 }or E_{4 }regions.
In this way, the invention provides design parameters for display panel layouts that solve the banding problems mentioned above and enable rotatable multiview autostereoscopic 3D displays with good performance.
The basic translation vectors a, b, p′ and q′ may have values such that p is not in the set E_{1 }with r_{0}=0.25 and γ=0.75.
The basic translation vectors a, b, p′ and q′ may have values such that p is not in the set E_{3 }with r_{0}=0.25 and γ=0.75.
The basic translation vectors a, b, p′ and q′ may have values such that p is not in the set E_{4 }with r_{0}=0.25 and γ=0.75.
These different regions represent progressively better banding performance, such that by excluding progressively more areas in the design space for the vector p, the remaining design options give progressively better banding performance.
The basic translation vectors a, b, p′ and q′ may have values such that p is not in the set or sets as defined above with r_{0}=0.35.
There are also preferred regions in the vector space for the vector p. In one example, the basic translation vectors a, b, p′ and q′ have values such that p is in the set E_{7 }with r_{0}=0.35 and γ=0.75.
In another example, the basic translation vectors a, b, p′ and q′ have values such that p is in the set E_{9 }with r_{0}=0.35 and γ=0.75.
The display device may be used in a portable device, wherein the portable device is configurable to operate in a portrait display mode and a landscape display mode. It may be a mobile telephone or tablet.
Embodiments of the invention will now be described, purely by way of example, with reference to the accompanying drawings, in which:
Note that
The invention provides an autostereoscopic display, comprising a pixelated display panel comprising an array of single color pixels or an array of subpixels of different colors and a view forming arrangement comprising an array of lens elements. The pixels form a hexagonal grid, and the lenses also repeat in a hexagonal grid. A vector p is defined which relates to a mapping between the pixel grid and the lens grid. Regions in the two dimensional space for this vector p are identified which give good or poor banding performance, and the better banding performance regions are selected.
The invention is based on an analysis of the effect of the relationship between the pixel grid and the lens grid on the banding performance. The banding analysis can be applied to different pixel and lens designs. Note that the term “pixel grid” is used to indicate the grid of pixels (if each pixel has only one addressable element), or the grid of subpixels (if each pixel has multiple independently addressable subpixels).
To illustrate the analytical approach, a first example will be presented based on square (or near square) pixel grids and lens grids. This invention relates specifically to hexagonal pixel and lens grids, for which an analysis is provided as a second example.
For the first example of a square pixel grid and lens grid, display panel designs are discussed with pixels on a regular 4fold symmetric essentially square grid, on top of which there is a light modulator that also has elements in a regular 4fold symmetric grid. For the purposes of explanation, some definitions are needed. In particular, a coordinate system of the panel (i.e. the pixel grid) needs to be defined, and a coordinate system of the view forming arrangement needs to be defined in terms of geometric (physical) coordinates and logical coordinates that are relative to the coordinate system of the panel.
The subpixels are shown as squares. However, the actual subpixel shape may be different. For example the actual pixel aperture will typically be an irregular shape as it may for example depend on the size and position of pixel circuit elements, such as the switching transistor in the case of an active matrix display panel. It is the pixel grid shape that is important rather than the precise shape of individual pixels or subpixels. The same reasoning applies to the hexagonal pixel grid discussed further below.
Pixel pitch vectors x and y are also shown. These are translation vectors between adjacent pixel centers in the row direction and the column direction, respectively. The letters in the smallest unit cell 30 indicate the primary colors: R=red, G=green, B=blue, W=white.
A pixel grid is defined based on the two vectors x and y, hereafter referred to as pixel pitch vectors. The vectors form a lattice matrix X=[x y] with length units (e.g. meters). There are multiple possible definitions of a pixel including the smallest unit cell, however for this description, the pixel is approximately square. Therefore X should be chosen to form an approximately square region of subpixels. As shown in
The pixels do not need to be perfectly square. They may be approximately square, which is taken to mean that a rotation over any angle, a limited sheer or limited elongation is within scope. The aspect ratio is defined as:
and the angle of the grid is:
The sheer is then expressed as θ−90°. Hence for an approximately square grid it holds that a≈1 and θ−90°≈0°.
For example, a is preferably between 0.9 and 1.1 and θ is between 80 and 100 degrees (of course, if one pair of corner angles is at 80 degrees, then the other pair will be at 100 degrees).
To define the lens grid, lens pitch vectors can be defined.
Instead of physical lens pitch vectors in units of meters, logical and dimensionless lens pitch vectors can be defined as:
p=(p_{x},p_{y}) and
q=(−p_{y},p_{x})
for chosen p_{x }and p_{y}.
The geometric (physical) pitch vectors p′ and q′ (e.g. in meters) are defined in terms of the logical lens pitch vectors as:
p′=Xp=p_{x}x+p_{y}y,
q′=Xq=−p_{y}x+p_{x}Y.
Deformations in the pixel grid should be reflected in equal deformations of the lens grid. Notice that p,q=0 but not necessarily p′,q′=0 as we do not require x,y=0. Similarly p=q but not necessarily p′=q′.
For the purposes of this description, regions are defined P_{n,m }for integer values n and m. These regions consist of multiple circles, themselves organized on a grid of circles.
Such a region is defined by:
The pv term specifies the length of the vector from v to p and thus the inequality defines a set of circles centered with a center defined by v. v is itself a set of vectors defined by the set of L terms. This has a discrete number of members as a result of the conditions placed on the integer values which make up the two dimensional vectors i and j.
Here r_{n,m}=r_{0}n^{−γ} is the radius of each circle. This radius thus decreases with increasing n. _{n,m }is the set of centers, and i,i denotes the inner product, such that when i=[i j]^{T }then i,i=i^{2}+j^{2}. A shorthand P_{n}=P_{n,n }is used in this description. Note that there are integers k for which there are no possible combinations of integers i and j for which j,j=k holds. As a consequence, the P_{3}, P_{6 }and P_{7 }sets are empty.
As an example, the set P_{5 }can be explored starting with _{5,5}.
With i∈^{2 }we indicate all i=[i j]^{T }where i and j are integers (negative, zero or positive). The set of solutions to j∈^{2}j,j=5 is:
There is a graphical explanation of j and j/n as Gaussian integers and the reciprocal lattice thereof respectively shown in
Each point in
Any combination
from the set of solutions for j shown above is in _{5,5}. Two examples are
The region P_{5 }then consists of circular regions with those centers and radius r_{5}=r_{0}5^{−γ}. Note that there are eight P_{5 }circles around each P_{1 }circle because there are eight solutions to j∈^{2}j,j=5.
In order to minimize the problems of banding for rotatable displays with pixels on an approximately square grid a display design is presented in which an array of view forming arrangements (typically a microlens array) forms a square grid that can be described by the direction p in terms of pixel coordinates where p is chosen outside of regions P_{n }that give rise to banding.
To analyze the banding problem, two models have been used. The first model is based on an analysis of the spatial frequencies in both the pixel structure and the lens structure and the second one is based on ray tracing.
The first model uses moiré equations and a visibility function to estimate the amount of visible banding for a given pitch vector p.
This model results in a map such as
As a consequence of the PSF scaling more banding components are visible for smaller p (in the top left part of
The analysis is based in part of the recognition that most of the structure in this banding map can be explained using the P_{n }areas where P_{n }with higher n correspond to smaller areas. Most of the areas with significant banding are explained by P_{1 }. . . P_{8}.
By fitting a radius r_{0}=0.35 and γ=0.75 to this map, the image shown in
In
The approach of this invention is based on avoiding the zones that give rise to banding, namely avoiding certain ranges of values of the vector p=(p_{x},p_{y}).
The first zones to avoid are the regions P_{1 }(i.e. P_{1,1}) which give rise to the greatest banding. In
The zones to exclude when designing the relationship between the pixel grid and the lens grid for this square example are:
1. p∉P_{1 }with radius r_{0}=0.25 and γ=0.75,
2. As directly above and also p∉P_{2},
3. As directly above and also p∉P_{4},
4. As directly above and also p∉P_{5},
5. As directly above and also p∉P_{8},
6. Any of the above but with radius r_{0}=0.35.
Within the space that is left by excluding the regions, there are some regions that are of particular interest because banding is especially low for a wide range of parameters. These regions are:
1. p∈P_{9,18 }with radius r_{0}=0.35,
2. p∈P_{14,26 }with radius r_{0}=0.35.
Preferably, for the square grid example, the subpixels are on a perfectly square grid but small variations are possible. The aspect ratio is preferably limited to
or more preferably to
The sneer of me grid from a square/rectangle to a rhombus/parallelogram is preferably to θ−90°≤20°, or even to θ−90°≤5°.
An alternative for moiré equations to illustrate the approach is to ray trace a model of a display with a lens that displays a fully white image.
A patch such as shown in
In this perceptual color space the L_{2 }distance between two color values (denoted ΔE below) is indicative of the perceived difference between those colors.
The target is white corresponding to (L*, a*, b*)=(100, 0, 0).
In
In
Depending on the situation ΔE≈1 is just visible. The bandingfree example in
Because the display uses a 2D microlens array, the lens phase itself is also 2D.
The plots can be summarized by taking the rootmeansquare (RMS) value of ΔE over the entire phase space.
In the table below, this has been done for a list of points that correspond to regions that according to the banding model explained above should be excluded or included.
From this table it is clear that the two models are largely consistent in terms of banding prediction. The positive areas have low ΔE_{RMS }values, and the biggest negative areas (with lowest ordinals) have the highest ΔE_{RMS }values.
The first model above provides an overview of the banding effect, while the second model provides more details and visualization.
An analogous analysis will now be presented for the example of a hexagonal pixel grid.
This invention relates specifically to panels with pixels (or subpixels) on a hexagonal grid (which is preferably a regular hexagonal grid, although it may deviate from a regular grid) on top of which there is a view forming arrangement that also has elements on a hexagonal grid.
As in the example above, the coordinate system of the panel is defined, then the coordinate system of the view forming arrangement is defined in terms of geometric (physical) coordinates and logical coordinates that are relative to the coordinate system of the panel. Parametric regions in the parameter space are again defined which can be selected to achieve desired performance, for example with respect to banding.
Pixel pitch vectors are again defined and for this example vectors a and b are defined, analogous to the vectors x and y in the example above.
Vectors a and b, are the pixel pitch vectors which form a lattice matrix X=[a b] with length units (e.g. meters). There are multiple possible definitions of a pixel including the smallest unit cell, however for this invention the pixel grid is hexagonal, for example at least approximately regular hexagonal. Therefore X should be chosen to form an hexagonal region of subpixels.
Examples are shown in
For color displays the pixel area 32 is most likely a triangular region with 3 or maybe 4 subpixels 31. Sometimes such a group appears rotated or mirrored to form a larger and possibly elongated unit cell, but also in that case X is a region with 3 or 4 subpixels 31. For monochrome displays, the unit cell 30 is the region of a single pixel 32. Important is the grid of pixels 32 rather than the shape or grid of subpixels 31.
The layout of
As in the example above, the invention does not require perfectly hexagonal grids nor is the angular orientation relevant. A rotation over any angle, a limited sheer or limited elongation is also possible.
The aspect ratio for the hexagonal pixel grid is defined as
and the angle of the grid is:
An interior angle of 120 corresponds to a regular hexagonal grid. An amount of sheer can thus be expressed as θ−120°. Hence for an approximately regular hexagonal grid it holds that β≈1 and θ−120°≈0°.
As in the example above, lens pitch vectors are also defined. The definition of the logical and dimensionless lens pitch vectors are p=(p_{a}, p_{b}) for chosen p_{a }and p_{b }
The vectors relevant to the hexagonal case are shown in
The vectors p′ and q′ have the same length and the angle between p′ and q′ is 120°. The geometric (physical) pitch vectors p′ and q′ (e.g. in meters) are defined in terms of the logical lens pitch vectors where deformations (e.g. rotation, sheer, scaling) in the pixel grid should be reflected in equal deformations of the lens grid. This can be understood by considering a flexible autostereoscopic display being stretched.
The dimensionless pitch vector p again defines a mapping between the pixel grid and the lens grid and in this case is defined by:
p′=p_{a}a+p_{b}b,
For this example regions E_{n }are defined for integers n that consist of multiple circles, themselves organized on a grid of circles. Such regions are defined by:
Again r_{n}=r_{0}n^{−γ} is the radius of each circle, Γ_{n }is the set of centers, and N(j) is the norm akin the Eisenstein integer norm defined as:
This defines a hexagonal lattice of centers. As in the example above, the pv term specifies the vector from v to p and thus the inequality, which is essentially based on the norm of the space (distance squared), This defines a set of circles with a center defined by v. v is itself a set of vectors defined by the set of Γ_{n }terms. This has a discrete number of members as a result of the conditions placed on the integer values which make up the two dimensional vectors i and j.
As an example, explore E_{4 }is considered, starting with Γ_{4}. The set of solutions to j∈^{2}N(j)=4 is:
Any combination
is in Γ_{4}. Two examples are
The region E_{4 }then consists of circular regions with those centers and radius r_{4}=r_{0}4^{−γ}. There is a graphical explanation of j and j/n as Eisenstein integers (that form a hexagonal lattice in the complex plane) and the reciprocal lattice thereof respectively as shown in
Each point in the left subfigure is marked with the coordinate of the Eisenstein integer c=a+ωb, and the norm N([a b]^{T}). The right subfigure consists of the same points but divided by their norm, thus corresponding to j/n instead of j.
Again there are integers k for which there are no j for which N(j)=k holds. As a consequence, the E_{2}, E_{5 }and E_{6 }sets are empty.
In the example above based on square grids, a Cartesian norm is used, namely j,j=j^{T}j and in a graphical explanation Gaussian integers are used that from a square lattice in the complex plane, instead of Eisenstein integers.
The approach explained above is used to analyze the banding effect of different designs. The resulting map, again based on moiré equations and a visibility function to estimate the amount of visible banding for a given pitch vector p, is shown in
It should be understood that the actual map depends on parameters such as the visual angle of the microlenses and the pixel structure. The map in
Most of the structure in this banding map can be explained using the E_{n }areas where E_{n }with higher n correspond to smaller areas. Most of the areas with significant banding are explained by E_{1 }. . . E_{4}.
As in the examples above, r_{0}=0.35 and γ=0.75 are used to generate the image of
Note that in
In
The invention is based on avoiding the zones that give rise to banding, namely the value of the vector p=(p_{a},p_{b}).
The first zones to avoid are the regions E_{1 }which give rise to the greatest banding. In
The zones to exclude when designing the relationship between the pixel grid and the lens grid are:
1. p∉E_{1 }with radius r_{0}=0.25 and γ=0.75,
2. As directly above and also p∉E_{3},
3. As directly above and also p∉E_{4},
4. Any of the above but with radius r_{0}=0.35.
Within the space that is left by excluding the regions, there are some regions that are of particular interest because banding is especially low for a wide range of parameters. These regions are:
1. p∈E_{7 }with radius r_{0}=0.35,
2. p∈E_{9 }with radius r_{0}=0.35.
Preferably, subpixels are on a regular hexagonal grid but small variations are within the scope of the invention: The aspect ratio is preferably limited to
or more preferably to
The sheer of the grid away from a regular hexagon is preferably limited to θ−120°≤20°, or even to θ−120°≤5°.
The invention is applicable to the field of autostereoscopic 3D displays, more specifically to fullparallax rotatable multiview autostereoscopic displays.
The invention relates to the relationship between the pixel grid and the lens grid. It can be applied to any display technology.
Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.