AUTOSTEREOSCOPIC DISPLAY DEVICE

Abstract

An autostereoscopic display comprises a pixelated display panel comprising an array of single color pixels or an array of sub-pixels of different colors and a view forming arrangement comprising an array of lens elements. The pixels form a square (or near square) grid, and the lenses also repeat in a square (or near square) grid. A vector p is defined which relates to a mapping between the pixel grid and the lens grid. Regions in the two dimension space for this vector p are identified which give good or poor banding performance, and the better banding performance regions are selected.

Claims

1. An autostereoscopic display, comprising: a pixelated display panel, pixelated display panel comprising an array of single color pixels or an array of sub-pixels of different colors, wherein each group sub-pixels 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 sub-pixels 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 rectangular or parallelogram grid with a maximum internal angle deviation from 90 degrees of 20 degrees or less, wherein the rectangular or parallelogram grid repeats with translation vectors x and y, and the length of the translation vectors x and y 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 regular grid with translation vectors p′ and q′; wherein defining a dimensionless vector p as (p.sub.x,p.sub.y), which satisfies:
p′=p.sub.xx+p.sub.yy
q′=−p.sub.yx+p.sub.xy and defining circular regions in the space of components of p.sub.y and p.sub.x of vector p as: $P_{n,m}=\left\{p.Math.p-v.Math.<r_{n,m}.Math.\forall v\in {ℒ}_{n,m}\right\}.Math..Math.\mathrm{where}$ ${ℒ}_{n,m}=\left\{i+\frac{j}{n}i,j\in {\mathbb{Z}}^2〈j,j〉=m\right\}$ for integer values n and m, with r.sub.n,m=r.sub.0n.sup.−γ defining the radius of each circle and .sub.n,m defining the circle centers, the translation vectors x, y, p′ and q′ are selected with values such that p falls in the vector space which excludes the set P.sub.1,1 or P.sub.2,2 or P.sub.4,4 with r.sub.0=0.1 and γ=0.75.

2. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the set P.sub.1,1 with r.sub.0=0.25 and γ=0.75.

3. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the set P.sub.2,2 with r.sub.0=0.25 and γ=0.75.

4. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes in the set P.sub.4,4 with r.sub.0=0.25 and γ=0.75.

5. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the set P.sub.5,5 with r.sub.0=0.1 and γ=0.75.

6. The autostereoscopic display as claimed in claim 5, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the set P.sub.5,5 with r.sub.0=0.25 and γ=0.75.

7. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the set P.sub.8,8 with r.sub.0=0.25 and γ=0.75.

8. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p falls in the vector space which excludes the defined set or sets with r.sub.0=0.35.

9. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p is in the set P.sub.9,18 with r.sub.0=0.35 and γ=0.75.

10. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x, y, p′ and q′ have values such that p is in the set P.sub.14,26 with r.sub.0=0.35 and γ=0.75.

11. The autostereoscopic display as claimed in claim 1, wherein the translation vectors x and y of the pixel grid have an aspect ratio of the length of the shorter to the longer between 0.83 and 1.

12. The autostereoscopic display as claimed in claim 1, wherein the rectangle or parallelogram pixel grid has a maximum internal angle deviation from 90 degrees of 5 degrees or less.

13. A portable device comprising a display as claimed claim 1, wherein the portable device is configurable to operate in a portrait display mode and a landscape display mode.

14. The portable device as claimed in claim 13, wherein the portable device is a mobile telephone.

15. The portable device as claimed in claim 13, wherein the portable device is a tablet.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0052] Embodiments of the invention will now be described, purely by way of example, with reference to the accompanying drawings, in which:

[0053] FIG. 1 is a schematic perspective view of a known autostereoscopic display device;

[0054] FIG. 2 is a schematic cross sectional view of the display device shown in FIG. 1;

[0055] FIGS. 3a-e shows various possible pixel grids;

[0056] FIG. 4 shows a lens grid overlaid over a square pixel array, with a pitch vector p defining the relationship between them;

[0057] FIG. 5 is a graphical explanation for parameters used to characterize the pixel array and lens grid;

[0058] FIG. 6 shows a plot of visible banding for a given pitch vector p;

[0059] FIG. 7 shows a first possible characterization of regions from the plot of FIG. 6;

[0060] FIG. 8 shows a second possible characterization of regions from the plot of FIG. 6;

[0061] FIGS. 9a-d shows ray trace rendering simulations of the 3D pixel structure for the 2D pixel layout of FIG. 3(c) for different lens designs;

[0062] FIGS. 10a-d are a plot of the lightness (L*) as a function of the lens phases in two dimensions, for the same examples as in FIGS. 9a-d; and

[0063] FIGS. 11a-d shows the color deviation plotted for the same examples as in FIGS. 9a-d.

[0064] Note that FIGS. 3a-e and 4 are intended to show square pixel and lens grids, and that FIGS. 5 to 8 are intended to show circular regions. Any distortions from square and circular representations are the result of inaccurate image reproduction.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The invention provides an autostereoscopic display, comprising a pixelated display panel comprising an array of single color pixels or an array of sub-pixels of different colors and a view forming arrangement comprising an array of lens elements. The pixels form a square (or near square) grid, and the lenses also repeat in a square (or near square) grid. A vector p is defined which relates to a mapping between the pixel grid and the lens grid. Regions in the two dimension space for this vector p are identified which give good or poor banding performance, and the better banding performance regions are selected.

[0066] In the description below, display panel designs are discussed with pixels on a regular 4-fold symmetric essentially square grid, on top of which there is a light modulator that also has elements in a regular 4-fold 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.

[0067] FIG. 3 shows various possible pixel grids. Each example shows the smallest unit cell 30 (i.e. the smallest set of sub-pixels 31 which repeat to form the sub-pixel pattern, as defined above) and a pixel 32 using the definition employed in this description. A pixel 32 is the smallest square arrangement of all of the primary colors so that the pixel size and shape is the same in the two orthogonal orientations.

[0068] The sub-pixels are shown as squares. However, the actual sub-pixel 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 sub-pixels.

[0069] 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.

[0070] FIG. 3(a) shows an RGGB unit cell and an RGGB pixel, FIG. 3(b) shows an RGBGBGRG unit cell and an RGBG pixel, FIG. 3(c) shows an RGBW unit cell and an RGBW pixel, FIG. 3(d) shows an RGBWBWRG unit cell and an RGBW pixel, and FIG. 3(d) shows a W unit cell and a W pixel.

[0071] 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 sub-pixels. As shown in FIGS. 3(a) to (d), for color displays, the pixel definition most simply results in a region with 2×2 sub-pixels. When the unit cell is larger, as in FIGS. 3(b) and (d), the pixel group appears rotated or mirrored to form the larger unit cell, but also in these cases X remains a 2×2 region. For monochrome displays the pixel is the region of a single sub-pixel.

[0072] 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:

[00002]$a=\frac{.Math.x.Math.}{.Math.y.Math.}$

and the angle of the grid is:

[00003]$\theta ={\cos }^{-1}.Math.\frac{〈x,y〉}{\sqrt{〈x,x〉.Math.〈y,y〉}}.$

[0073] The sheer is then expressed as |θ−90°|. Hence for an approximately square grid it holds that a≈1 and |θ−90°|≈0°.

[0074] 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).

[0075] To define the lens grid, lens pitch vectors can be defined.

[0076] FIG. 4 shows a lens grid 42 overlaid over a square pixel array 40 with 2×2 sub-pixels 31 per pixel 32 (such as in FIGS. 3(a) and (c). One out of each pixel group of four sub-pixels 31 is highlighted (i.e. shown white). The vectors x and y are the pixel pitch vectors of that grid as explained above. The lens grid 42 comprises a microlens array with spherical lenses 44 organized on a square grid. The vectors p′ and q′ are the pitch vectors of that grid. They are formed by a linear combination of the pixel pitch vectors.

[0077] Instead of physical lens pitch vectors in units of meters, logical and dimensionless lens pitch vectors can be defined as:

p=(p.sub.x,p.sub.y) and

q=(−p.sub.y,p.sub.x)

[0078] for chosen p.sub.x and p.sub.y.

[0079] 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.sub.xx+p.sub.yy,

q′=Xq=p.sub.yx+P.sub.xy.

[0080] 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′|.

[0081] For the purposes of this description, regions are defined P.sub.n,m for integer values n and m. These regions consist of multiple circles, themselves organized on a grid of circles.

[0082] Such a region is defined by:

[00004]$P_{n,m}=\left\{p.Math.p-v.Math.<r_{n,m}.Math.\forall v\in {ℒ}_{n,m}\right\}.Math..Math.\mathrm{where}$${ℒ}_{n,m}=\left\{i+\frac{j}{n}i,j\in {\mathbb{Z}}^2〈j,j〉=m\right\}.$

[0083] The p-v term specifies the length of the vector from v top and thus the inequality defines a set of circles 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.

[0084] Here r.sub.n,m=r.sub.0n.sup.−γ is the radius of each circle. This radius thus decreases with increasing n. .sub.n,m defines the set of centers, and i, i denotes the inner product, such that when i=[i j].sup.T then i,i=i.sup.2+j.sup.2. We also define the shorthand P.sub.n=P.sub.n,n. 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.sub.3, P.sub.6 and P.sub.7 sets are empty.

[0085] As an example, the set P.sub.5 can be explored starting with .sub.5,5.

[0086] With i∈.sup.2 we indicate all i=[i j].sup.T where i and j are integers (negative, zero or positive). The set of solutions to j∈.sup.2j,j=5 is:

[00005]$j\in \left\{\left[\begin{array}{c}-2\\ -1\end{array}\right],\left[\begin{array}{c}-2\\ 1\end{array}\right],\left[\begin{array}{c}-1\\ -2\end{array}\right],\left[\begin{array}{c}-1\\ 2\end{array}\right],\left[\begin{array}{c}1\\ -2\end{array}\right],\left[\begin{array}{c}1\\ 2\end{array}\right],\left[\begin{array}{c}2\\ -1\end{array}\right],\left[\begin{array}{c}2\\ 1\end{array}\right]\right\}.$

[0087] There is a graphical explanation of j and j/n as Gaussian integers and the reciprocal lattice thereof respectively shown in FIG. 5.

[0088] Each point in FIG. 5(a) is marked with the coordinate of the Gaussian integer g=a+b where .sup.2=−1 and the norm N(g)=a.sup.2+b.sup.2. FIG. 5(b) consists of the same points but the coordinates of the points are divided by their norm, thus corresponding to j/n instead of j.

[0089] Any combination

[00006]$i+\frac{j}{n}$

from the set of solutions for j shown above is in .sub.5,5. Two examples are

[00007]${\left[\begin{array}{cc}3.Math.\frac{2}{5}& 2.Math.\frac{1}{5}\end{array}\right]}^T.Math..Math.{\mathrm{and}.Math.\left[\begin{array}{cc}1.Math.\frac{4}{5}& \frac{2}{5}\end{array}\right]}^T.$

The region P.sub.5 then consists of circular regions with those centers and radius r.sub.5=r.sub.05.sup.−γ. Note that there are eight P.sub.5 circles around each P.sub.1 circle because there are eight solutions to j∈.sup.2j,j=5.

[0090] 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 micro-lens 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.sub.n that give rise to banding.

[0091] 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.

[0092] The first model uses moiré equations and a visibility function to estimate the amount of visible banding for a given pitch vector p.

[0093] This model results in a map such as FIG. 6 where brighter areas indicate more banding (on a log scale). FIG. 6 plots the p.sub.y versus P.sub.x. 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 FIG. 6 is generated for the case of a pixel with a single emitting area with aperture ⅛ of the whole pixel surface, a Gaussian lens point spread function (PSF) that scales with the lens aperture, and a constant lens visual angle of 20 arcsec.

[0094] As a consequence of the PSF scaling more banding components are visible for smaller |p| (in the top left part of FIG. 6) because of the more accurate focus. It has been observed that the strength of various banding “blobs” depends on the actual pixel structure (see FIG. 3) but the position of the blobs is always the same.

[0095] The invention is based in part of the recognition that most of the structure in this banding map can be explained using the P.sub.n areas where P.sub.n with higher n correspond to smaller areas. Most of the areas with significant banding are explained by P.sub.1 . . . P.sub.8.

[0096] By fitting a radius r.sub.0=0.35 and γ=0.75 to this map, the image shown in FIG. 7 results. In other situations there might be less banding and as a consequence r.sub.0=0.25 is sufficiently stringent. FIG. 8 shows the results of fitting a radius r.sub.0=0.25 to the map of FIG. 5.

[0097] In FIGS. 7 and 8, preferred regions are also plotted, namely P.sub.9,18 and P.sub.14,26. These regions are best described by r.sub.0=0.35.

[0098] The invention is based on avoiding the zones that give rise to banding, namely avoiding certain ranges of values of the vector p=(p.sub.x,p.sub.y).

[0099] The first zones to avoid are the regions P.sub.1 (i.e. P.sub.1,1) which give rise to the greatest banding. In FIG. 8, with smaller radius values, the excluded zone is smaller. Thus, a first zone to exclude is based on r.sub.0=0.25.

[0100] The zones to exclude when designing the relationship between the pixel grid and the lens grid are:

1. p.Math.P.sub.1 with radius r.sub.0=0.25 and γ=0.75,
2. As directly above and also p.Math.P.sub.2,
3. As directly above and also p.Math.P.sub.4,
4. As directly above and also p.Math.P.sub.5,
5. As directly above and also p.Math.P.sub.8,
6 Any of the above but with radius r.sub.0=0.35.

[0101] 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.sub.9,18 with radius r.sub.0=0.35,
2. p∈P.sub.14,26 with radius r.sub.0=0.35.

[0102] Preferably, sub-pixels are on a square grid but small variations are possible.

[0103] The aspect ratio is preferably limited to 2/3≦a≦3/2, or more preferably to 5/6≦a≦6/5. The sheer of the grid from a square/rectangle to a rhombus/parallelogram is preferably to |θ−90°|≦20°, or even to |θ−90°|≦5°.

[0104] An alternative for moiré equations to illustrate the invention is to ray trace a model of a display with a lens that displays a fully white image.

[0105] FIG. 9 shows such rendering for the 2D pixel layout as of FIG. 3(c). Any rendering of a banding-free design would appear to be on average white, while for a design with banding, the intensity and/or color depend on the viewer position (i.e. the lens phase).

[0106] FIG. 9(a) shows renderings for a lens design in a P.sub.1 region for a lens phase. Although not shown in the rendition of FIG. 9(a), the white and most of the blue primary is missing. FIG. 9(b) shows renderings for a lens design in a P.sub.2 region for a lens phase where more than average amount of black matrix is visible. FIG. 9(c) shows renderings for a lens design in a P.sub.4 region for a lens phase where almost no black matrix is visible. FIG. 9(d) shows renderings for a lens design at a P.sub.14,26 center with (virtually) equal distribution of primaries within this patch for this and all other phases.

[0107] A patch such as shown in FIG. 9 can be rendered for various lens phases, since different lens phases (by which is meant lens position which is responsible for generating the view to a particular viewing location) give rise to different distributions of sub-pixels. More effective is to compute the mean CIE 1931 XYZ color value for each such patch. From that mean, the CIE L*a*b* color value can be computed which gives quantitative means of comparing perceptual banding effects.

[0108] In this perceptual color space the L.sub.2 distance between two color values (denoted ΔE below) is indicative of the perceived difference between those colors.

[0109] The target is white corresponding to (L*, a*, b*)=(100, 0, 0).

[0110] In FIG. 10 the lightness (L*) is plotted as a function of the lens phases in two dimensions, corresponding to different views projected by the lenses to different viewer positions, for the same examples as in FIG. 9. The dimensionless lens phase variable has values in the range of (0,1). Due to the periodicity of the pixel grid and the lens grid, lens phases 0 and 1 correspond to the same generated views. Because the display uses a 2D microlens array, the lens phase itself is also 2D.

[0111] In FIG. 11, the color error (ΔE) is plotted again for the same examples.

[0112] Depending on the situation ΔE≈1 is just visible. The banding-free example in FIGS. 10(d) and 11(d) appears as uniform L*=100 and ΔE≈0 respectively, while the other examples clearly have banding as the color varies with the viewer position (i.e. lens phase).

[0113] Because the display uses a 2D microlens array, the lens phase itself is also 2D.

[0114] The plots can be summarized by taking the root-mean-square (RMS) value of ΔE over the entire phase space.

[0115] 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.

TABLE-US-00001 Region p.sub.x p.sub.y ΔE.sub.RMS P.sub.1 6.000 2.000 111.576 P.sub.2 7.000 3.000 63.375 P.sub.4 6.000 3.000 12.723 P.sub.5 7.200 3.600 3.609 P.sub.5 7.600 3.200 5.738 P.sub.8 6.500 2.500 2.289 P.sub.8 4.500 4.500 1.495 P.sub.9,18 7.333 3.333 0.467 P.sub.9,18 2.600 2.600 1.308 P.sub.9,18 3.350 3.350 0.796 P.sub.9,18 3.400 3.400 0.871 P.sub.14,26 6.143 3.286 0.180 P.sub.14,26 7.286 2.143 0.185 In between two P.sub.14,26 circles 6.000 3.286 0.155 In between two P.sub.5 circles 7.000 3.600 0.611 In between two P.sub.5 circles 5.000 3.400 0.289

[0116] From this table it is clear that the two models are largely consistent in terms of banding prediction. The positive areas have low ΔE.sub.RMS values, and the biggest negative areas (with lowest ordinals) have the highest ΔE.sub.RMS values.

[0117] The first model above provides an overview of the banding effect, while the second model provides more details and visualization.

[0118] The invention is applicable to the field of autostereoscopic 3D displays, more specifically to full-parallax rotatable multi-view auto-stereoscopic displays.

[0119] The invention relates to the relationship between the pixel grid and the lens grid. It can be applied to any display technology.

[0120] 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.