WO2014173853A1

WO2014173853A1 - Auto-stereoscopic display device with a lenticular sheet slanted with respect to the column of colour sub-pixels

Info

Publication number: WO2014173853A1
Application number: PCT/EP2014/058033
Authority: WO
Inventors: Eibert Gerjan VAN PUTTEN; Bart Kroon; Mark Thomas Johnson; Olexandr Valentynovych VDOVIN
Original assignee: Koninklijke Philips N.V.
Priority date: 2013-04-25
Filing date: 2014-04-21
Publication date: 2014-10-30
Also published as: TW201447382A

Abstract

Auto-stereoscopic display device (1) comprising display pixels (5) arranged in rows and columns of different colour sub-pixels, each sub-pixel having an aspect ratio "a" being the width-to-height ratio, a lenticular sheet (9) arranged in registration with the display (1) for projecting a plurality of views towards a user in different directions, wherein said lenticular sheet (9) comprises elongated elements (11) with a long axis that is slanted (angle Θ) with respect to the general column sub-pixel direction thereby defining a slant s = tan Θ and satisfying the inequalities 0.8 s ≤ a ≤ 1.2 s with s < 1/3.

Description

AUTO-STEREOSCOPIC DISPLAY DEVICE WITH A LENTICULAR SHEET

SLANTED WITH RESPECT TO THE COLUMN OF COLOUR SUB-PIXELS

FIELD OF THE INVENTION

This invention relates to an autostereoscopic display device which comprises a display panel having an array of display pixels, and an arrangement for directing different views to different physical locations.

BACKGROUND OF THE INVENTION

A known autostereoscopic display device comprises a two-dimensional liquid crystal display panel having a row and column array of display pixels 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, which function to modify the directions of the outputs.

The lenticular lenses are provided as a sheet of lens elements, each of which comprises an elongate semi-cylindrical 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 sub-pixels.

Each lenticular lens can be associated with two columns of display sub-pixels 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 sub-pixels in the row direction. Corresponding columns of display sub-pixels in each group are arranged appropriately to provide a vertical slice from a respective two dimensional sub-image. As a user's head is moved from left to right a series of successive, different, stereoscopic views are observed creating, for example, a look-around impression.

The above described autostereoscopic display device produces a display having good levels of brightness. However, one problem associated with the device is that the views projected by the lenticular sheet are separated by dark zones caused by "imaging" of the non-emitting black matrix which typically defines the display sub-pixel array. These dark zones are readily observed by a user as brightness non-uniformities in the form of dark vertical bands spaced across the display. The bands move across the display as the user moves from left to right and the pitch of the bands changes as the user moves towards or away from the display. Another problem is that the vertically aligned lens results in a reduction in resolution in the horizontal direction only, while the resolution in the vertical direction is not altered.

Both of these issues can be at least partly addressed by the well known technique of slanting the lenticular lenses at an acute angle relative to the column direction of the display pixel array. The use of slanted lenses is thus recognised as an essential feature to produce different views with near constant brightness, and a good RGB distribution behind the lenses.

Traditionally, display panels are based on a matrix of pixels that are square in shape. In order to generate images in colour, the pixels are divided into sub-pixels.

Traditionally, each pixel is divided into 3 sub-pixels, transmitting or emitting red (R), green (G) and blue (B) light, respectively. Sub-pixels of equal colour are typically arranged in columns.

WO2010/070564 discloses an arrangement in which the lens pitch and lens slant are selected in such a way as to provide an improved pixel layout in the views created by the lenticular array, in terms of spacing of colour sub-pixels, and colour uniformity.

However, there is also a relationship between the display sub-pixel sizes and shapes and the way the 2D sub-pixels are mapped to pixels of the 3D images. This invention aims to provide designs which further take into account the display panel pixel design in optimising the way the 3D views are generated.

SUMMARY OF THE INVENTION

The invention is defined by the claims.

According to the invention, there is provided an autostereoscopic display device comprising:

a display having an array of display pixels for producing a display, wherein the display pixels are arranged in rows and columns of different colour sub-pixels, and wherein each sub-pixel has an aspect ratio "a" comprising the ratio of width to height;

a view forming arrangement arranged in registration with the display for projecting a plurality of views towards a user in different directions, wherein the view forming arrangement comprises elongate elements with a long axis which is slanted at an angle Θ to the general column sub-pixel direction thereby defining a slant s=tan Θ, wherein a = 0.8s to 1.2s and s<l/3. It is to be noticed that the general column sub-pixel direction is not necessarily orthogonal to the general row direction. This arrangement provides a low slant angle, but the corresponding design of the display pixels means that the 2D sub-pixels are efficiently used when mapping to the 3D displayed images. In preferred embodiments, the device can be arranged such that each 2D subpixel contributes to only one 3D pixel.

In a preferred arrangement a=s. This provides an optimum reduction of crosstalk in addition to providing efficient pixel mapping.

Each pixel of the display can comprise an RGB pixel with red green and blue sub-pixels each extending in the column direction and arranged side by side. The columns of pixels may be slanted with an angle to a vertical side of the display.

Some examples have a pitch between 0.9p and l .lp where: p = ^ (2M + l) (l + s²),

where M is a positive integer, and the slant is between 0.9s and 1.1s where:

1

^{5 ~} 2VM + 1

where V is the ratio of the height to width of the pixel grid of individual views projected to the user. This provides a relationship between slant and pitch as described in WO

2010/070564.

In a first example s = a = 1/5. In this case, the pitch "p" of the elongate lenses, expressed as the number of sub-pixel widths across the lens width in the row direction, can be close to p=7 4/5.

In a second example s = a = 1/6. The pitch can then be close to p=10 19/24.

In a third example s = a = 1/7. The pitch can then be close to p=10 5/7.

In a fourth example s = a = 1/9. The pitch can then be close to p=13 2/3 or close to p=10 2/3.

This set of examples provides specific solutions which give practical display designs.

The slant and aspect ratio do not have to be the exact value given, and a 10% deviation can be tolerated whilst obtaining the desired overall effect (i.e. between 0.9 and 1.1 times the value given). Similarly the pitch value can be within 10% of the value given. More preferably, the two parameters are within 5% of the values given (i.e. between 0.95 and 1.05 times the value given). These examples of 1/5, 1/7 and 1/9 satisfy (i) s=a exactly as well as the requirements from the WO 2010/070564 that give (ii) a perfect delta-nabla structure (i.e. a hexagonal lattice) of the 3D pixel distribution, and (iii) equal division of spatial resolution in3D mode. The s=a=l/6 example has (i) and (ii) but not (iii) as the pixel grid is a slightly stretched in one direction.

Changing the pitch would allow to sacrifice (ii) but keep (iii), and other designs close to the pitch values given can also be used.

Thus, these specific examples are only a selection of possible examples in accordance with the invention.

BRIEF DESCRIPTION OF THE FIGURES

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

Figure 1 is a schematic perspective view of a known autostereoscopic display device;

Figure 2 is a schematic cross sectional view of the display device shown in

Figure 1;

Figure 3 shows how the known RGB pixel is projected by the lenticular arrangement in a known display;

Figure 4 shows the known RGB pixel layout;

Figure 5 shows parameters relating to the configuration of the 2D display panel and a projected 3D view;

Figure 6 shows the known pixel configuration and two examples of pixel configuration of the invention; and

Figure 7 shows how the pixel layout is projected by the lenticular arrangement in one example of display in accordance with the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The invention provides an autostereoscopic display device with a particular design of view forming arrangement (being for example a lenticular or parallax barrier array) and display panel (in particular the slant angle and the display panel sub-pixel aspect ratio) to enable low slant angles while still enabling efficient mapping of the 2D display panel pixels to the 3D pixels. The aspect ratio of the display sub-pixels is made close to the slant value. Before describing the invention in detail, the configuration of a known autostereoscopic display will first be described.

Figure 1 is a schematic perspective view of a known multi-view autostereoscopic display device 1. The known device 1 comprises a liquid crystal display panel 3 of the active matrix type that acts as an image forming means to produce the display. The device can instead use OLED pixels.

The display panel 3 has by way of example an orthogonal array of display sub- pixels 5 arranged in rows and columns. For the sake of clarity, only a small number of display sub-pixels 5 are shown in Figure 1. In practice, the display panel 3 might comprise about one thousand rows and several thousand columns of display sub-pixels 5.

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. Polarising layers are also provided on the outer surfaces of the substrates.

Each display sub-pixel 5 comprises opposing electrodes on the substrates, with the intervening liquid crystal material therebetween. The shape and layout of the display sub-pixels 5 are determined by the shape and layout of the electrodes and a black matrix arrangement provided on the front of the panel 3. The display sub-pixels 5 are regularly spaced from one another by gaps.

Each display sub-pixel 5 is associated with a switching element, such as a thin film transistor (TFT) or thin film diode (TFD). The display sub-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 sub-pixels 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 view forming function. The lenticular sheet 9 comprises a row of lenticular lenses 11 extending parallel to one another, of which only one is shown with exaggerated dimensions for the sake of clarity. The lenticular lenses 11 act as view forming elements to perform a view forming function. The lenticular lenses 11 are in the form of convex cylindrical elements, and they act 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 autostereoscopic display device 1 shown in Figure 1 is capable of providing several different perspective views in different directions. In particular, each lenticular lens 11 overlies a small group of display sub-pixels 5 in each row. The lenticular element 11 projects each display sub-pixel 5 of a group in a different direction, so as to form the several different views. As the user's head moves from left to right, his/her eyes will receive different ones of the several views, in turn.

Figure 2 shows the principle of operation of a lenticular type imaging arrangement as described above and shows the light source 7, display panel 3 and the lenticular sheet 9. The arrangement provides three views each projected in different directions. Each sub-pixel of the display panel 3 is driven with information for one specific view.

The above described autostereoscopic display device produces a display having good levels of brightness. It is well known to slant the lenticular lenses at an acute angle relative to the column direction of the display pixel array. This enables an improved brightness uniformity and also divides the resolution loss in the horizontal and vertical directions more equally .

Whatever the mechanism used to obtain an auto-stereoscopic display system, resolution is traded for 3D depth: the more views, the higher the loss in resolution per view. This is illustrated in Figure 3, which shows the native sub-pixel layout of the 2D display panel as well as, on the same scale, the sub-pixel layout in a 3D view obtained by putting a lenticular in front of the panel.

The sub-pixel layout shown for the 3D image represents the sub-pixel pattern as seen from one viewing direction. The same geometric sub-pixel pattern is seen from all viewing directions, but different sets of sub-pixels of the underlying 2D display are visible. For a given viewing direction as shown, a blue 3D sub-pixel is an image of one or more blue sub-pixels of the native 2D display (and the same applies for green and red).

The lenticular has a slant s = tan(9)=l/6 to the general column sub-pixel direction and a lens pitch

p_x (where p_x is the sub-pixel pitch in the general row direction) resulting in 15 views. In this case, p_x=p_y. The lens pitch is thus 7.5 when expressed as a number of sub-pixel dimensions in the row direction. The 3D image has a repeating pattern of sub-pixels, and the colours of a few sub-pixels (R, G and B) are shown so that all colours in the pattern can be understood. Each colour is output as a diamond shaped grid of sub-pixels which are interleaved with each other.

As seen in Figure 3, for the particular viewing direction shown, each 3D sub- pixel has contributions from three 2D sub-pixels (each 3D sub-pixel is divided into three sections). This is because a line parallel to the lenticular lens axis (such as the white lines shown over the 2D display panel) cross three sub-pixels of one colour, followed by three sub- pixels of the next colour, followed by three sub-pixels of the last colour. For different viewing angle directions, there can instead be two full sub-pixels for each 3D sub-pixel.

The slant angle of the lenticular as well as its pitch should be chosen such that a number of requirements are fulfilled as much as possible:

(i) A favourable distribution of sub-pixels should be obtained for each 3D view.

In each of the 3D views the sub-pixels of each colour should be distributed in a pattern that is regular and having a resolution that is similar for the horizontal and vertical direction. As shown in Figure 3, the horizontal distance between neighbouring green sub- pixels (labelled A in Figure 3) should be comparable to the vertical distance between neighbouring green sub-pixels (labelled B). This should hold for the other colours as well.

(ii) The surface area occupied by sub-pixels of the same colours should be equal for each 3D view.

(iii) Absence of moire.

The combination of a lenticular in front of a display panel is very susceptible to the occurrence of moire ('banding'). This effect is caused by the combination of the periodicity of the sub-pixel layout of the display panel and the periodicity of the lenticular. It is worsened by the fact that the sub-pixels of the display panel are surrounded by a black matrix. By means of slanting the lenticular and by choosing the lenticular to have a width that is not equal to an integer times the width of a sub-pixel (i.e. by using fractional views), this moire effect can be minimised.

Figure 4 shows a conventional RGB striped pixel layout. Each pixel has three sub-pixels, hence the subscript "3" in RGB 3. Pixel layouts using more than 3 primary colours are also known, and these are termed "multi-primary" pixel layouts. Several such multi-primary layouts have reached the market and are expected to become mainstream, and this invention can also be applied to such pixel layouts.

The invention is based on the relationship between the sub-pixels of the native 2D display and the sub-pixels of the 3D views. Depending on the way the lenticular lens is positioned on the display panel, there will be more or less 2D sub-pixels contributing to a 3D sub-pixel.

For an efficient use of the display panel sub-pixels, the ratio N between the number of 2D sub-pixels N¾ that contribute to a number of 3D sub-pixels N3D, should be close to one.

This would mean that each independently addressed sub-pixel of the display controls (on average) one sub-pixel of the 3D image, so that the maximum 3D spatial resolution can be obtained i.e., the native 2D resolution divided by the number of views.

Figure 5 shows schematically a 3D pixel layout that results from placing a lenticular lens with pitch p and slant s (where the slant is defined as the tangent of the angle to the column direction, s=tan9 ) on a striped underlying display panel. Figure 5 is an enlarged view of one 3D pixel from Figure 3. Note that the slant can be in either sense, but still with a positive slant value s. The columns of pixels may be slanted with an angle a to a vertical side of the display, the angle a preferably being equal to either 0 which has the advantage of providing a simple rectangular grid, or to the angle Θ which has the advantage that then the lenticular lenses are oriented vertically so that parallax is fully in horizontal direction.

The value N is shown in Figure 5 as the ratio of the height (in the orthogonal to the row direction) of a 3D sub-pixel to the height of a 2D sub-pixel. Thus, the value N represents how many 2D sub-pixels contribute to each 3D sub-pixel. As shown, N is not necessarily an integer value, and Figure 5 shows a value of N slightly greater than 1.

From Figure 5 it follows that:

Nh = w/s

When defining the sub-pixel aspect ratio a as

a ≡ w/h

the following expression for N results:

N = N_2D/N_3D = a/s. Eq. 1

The fraction of parallax that is projected in the horizontal direction is determined by the slant of the lenticular:

V_h/V = cos[tan^_1 (s)] Eq. 2

The views of the display are generated along the lenticular lenses. If the lenticular lenses are slanted in respect to the column direction, also the views are generated under an angle. V is the total amount of views that a display generates, V_h is the horizontal projection of these (V*cos(0)).

In the table below this fraction is shown for some slant values. Slant, s Fraction of views projected horizontally, VyJV

1/3 0.949

1/6 0.986

1/9 0.994

This analysis shows that the quality of the display is influenced in several ways by the actual value of the slant:

1. In order to make efficient use of the display sub-pixels in the generation of the views, one 2D sub-pixel should contribute to each 3D sub-pixel. Therefore the slant has to be close to the inverse of the aspect ratio, as can be seen in Eq. 1. For a regular RGB-striped display as in Figure 4, this means the slant should be close to 1/3.

2. In order to have the views directed mostly in the horizontal direction, the slant has to be as small as possible (see Eq. 2). Therefore the preferred slant should be smaller than 1/3. Two examples of practical values are s = 1/6 and s = 1/9.

3. For a display which is to be used in a 2D mode (as well as a 3D mode) the sub-pixel triplet should be close to a square, so that black or white lines are equally thick in both directions in the 2D mode.

For current display panels there is always a trade-off between these three points when choosing the slant.

The invention provides a panel design for which a slant value can be chosen so that efficient use of the available sub-pixels is made, and a large fraction of the views are directed in the horizontal direction.

The invention is based on a change to the aspect ratio of the sub-pixels such that a small slant is possible (e.g. 1/6 or 1/9) while still having an efficient use of the sub- pixels (N close to 1).

These requirements are fulfilled by choosing the aspect ratio a of the sub- pixels close to the desired slant Sdesired:

^ ^desired Eq. 3

Furthermore, the distribution of horizontal and vertical resolution should be approximately equal in the 3D mode.

Figure 6 shows three different RGB-striped panel designs with sub-pixel aspect ratios a = 1/3, a = 1/6, and a = 1/9. These designs are optimized for slants of respectively s = 1/3, s = 1/6, and s = 1/9.

The use of slant 1/3 in combination with aspect ratio 1/3 is known. The invention provides aspect ratios less than 1/3, and thus including the examples of 1/6 and 1/9 shown in Figure 6.

Figure 7 shows a simulation of the 3D pixel pattern based on a panel design with a = 1/9 as a basis for an autostereoscopic display. The lenticular lens is placed under a slant s = 1/9 and a pitch p = 10 2/3 (i.e. 10 2/3 times the display panel sub-pixel width).This gives an effective number of views of 10 2/3, but 32 fractional views.

Figure 7 presents information in the same form as Figure 3.

For the particular viewing angle, different 3D sub-pixel columns have their 3D sub-pixels formed from different configurations of 2D sub-pixels. This is the result of the non-integer pitch of the lenticular lens. As shown, some 3D sub-pixel columns have each 3D sub-pixel formed from a single 2D sub-pixel, whereas others have each 3D sub-pixel formed from two 2D sub-pixels. The pattern repeats every three columns (because 3 x 10.66 is an integer value 32 giving the 32 fractional views).

Overall, the value N is 1 as a result of the equality of the slant angle and aspect ratio.

With N=l , on average one 2D sub-pixel is imaged to one 3D sub-pixel.

However, when multiple 2D sub-pixels are needed to make up one 3D sub-pixel (as can be seen in Figure 7), this loss of direct correspondence is manifested as crosstalk. Setting s=a gives the optimum performance in terms of reduction of crosstalk.

In WO 2010/070564 referenced above, it is described how to obtain good pixel structures for RGB striped designs. To obtain a delta-nabla pattern of 3D pixel distribution given a sub-pixel aspect ratio a, a slant s, the pitch should be close to: p = ^ (2M + l) (l + s²), where M is an integer, preferably M>=1. To obtain a good distribution of spatial resolution among horizontal and vertical direction, according to WO 2010/070564, the slant should be chosen as:

1

^{5 ~} 2VM + 1'

Where V is the ratio of the height to width of the pixel grid of individual views projected to the user. Thus, looking at the grid of sub-pixels which make up an individual 3D view, W is the width (in the direction perpendicular to the lens axis) between same colour sub-pixels and H is the height (in the lens axis direction) between same colour sub-pixels. H and W are shown for blue sub-pixels in Figure 7, and V=H/W. It is desirable to set V=l . When applying the rule a = s as derived above, then the value M can be chosen that matches slant with sub-pixel aspect ratio, or the sub-pixel aspect ratio can be selected based on the slant. In the latter case, this gives the following designs with different trade-offs between 3D and spatial resolution.

To maintain the overall desired aspect ratio, with more elongated sub-pixels, more columns and fewer rows will be used. All rows in the table below correspond to 24.9 MP (e.g. QFHD equivalent) and 16:9 display aspect ratio. For s=a=l/3 the number of sub- pixel rows and columns corresponds to QFHD.

The number of rows and columns (the last two columns) corresponds to the number of sub-pixels in the native display. For example, 3840x2160 =8294400 pixels.

8294400 x 3 =24.88 MP (number of sub-pixels). As the sub-pixels become taller, there are less rows to achieve the same physical dimension 16:9 aspect ratio. The AR figure is the aspect ratio expressed as the ratio of the number of sub-pixel columns to the number of sub- pixel rows. For example, for the last row in the table, the sub-pixels are 9 times taller than wide. Thus, the physical display aspect ratio is 6651x3: 1247x9 = 1.7778.

The PAR column in the table above is the pixel aspect ratio, i.e. the ratio of the width to height of a pixel triplet in the native display.

The numbers in the table above can be considered to be targets and in practice a design that is close in slant, pitch, rows and columns will be selected. Especially the rows and columns should preferably be smooth numbers to simplify image scaling.

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be capable of designing many alternative embodiments without departing from the scope of the invention as defined by the appended claims. The examples above show the invention applied to lenticular lens displays. However, the concepts of the invention can be applied equally to autostereoscopic displays based on slanted barriers. In a barrier display, the barrier opening can be considered to be the "view forming element". Furthermore, it is the relative slant between sub-pixel columns and the lenticular (or barrier) axis which is important. Thus, the lenticulars or barriers can be slanted over a regular rectangular sub-pixel grid, or else the sub-pixel grid may be slanted, beneath a vertical set of lenticulars or barriers.

The example above uses striped RGB pixels. The invention can however be applied to pixels with more than three different colour sub-pixels, for example RGBY (red, green, blue, yellow) or RGBW (red, green, blue, white) pixels. Thus, a striped sub-pixel arrangement with four primary colours per pixel can also be used. It is to be understood that by introducing slant angles Θ and a the eventual views towards the viewer are not rotated because this will be compensated for by the rendering of the pixels. The techniques of rendering is not necessary to explain in this application since it is not particularly a part of the present invention and is further also well-known to the person skilled in the art of rendering 3D images on a display panel.

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.

Claims

CLAIMS:

1. An autostereoscopic display device comprising:

a display (3) having an array of display pixels (5) for producing a display, wherein the display pixels are arranged in rows and columns of different colour sub-pixels, and wherein each sub-pixel has an aspect ratio "a" comprising the ratio of width to height;

a view forming arrangement (9) arranged in registration with the display for projecting a plurality of views towards a user in different directions, wherein the view forming arrangement comprises elongate elements with a long axis which is slanted at an angle Θ to the general column sub-pixel direction thereby defining a slant s=tan Θ,

wherein a = 0.8s to 1.2s and s<l/3.

2. A device as claimed in claim 1, wherein a = 0.95s to 1.05s, more preferably a = s.

3. A device as claimed in claim 1 or 2, wherein the elongate elements of the view forming arrangement comprise lenses.

4. A device as claimed in any preceding claim, wherein each pixel (5) of the display comprises an RGB pixel with red green and blue sub-pixels each extending in the column direction and arranged side by side.

5. A device as claimed in any preceding claim, wherein the columns of pixels are parallel to a side edge of the display.

6. A device as claimed in any preceding claim, wherein the pitch is between 0.9p and 1.1 p where: p = ^ (2M + l) (l + s²), where M is a positive integer, and the slant is between 0.9s and 1,1s where:

1

^{5 ~} 2VM + 1 where V is the ratio of the height to width of the pixel grid of individual views projected to the user.

7. A display as claimed in any preceding claim, wherein s = a and is between 0.9 and 1.1 times 1/5.

8. A display as claimed in claim 7, wherein the pitch "p" of the elongate elements, expressed as the number of sub-pixel widths across the lens width in the row direction is between 0.9 and 1.1 times 7 + 4/5.

9. A display as claimed in any one of claims 1 to 6, wherein s = a and is between 0.9 and 1.1 times 1/6.

10. A display as claimed in claim 9, wherein the pitch "p" of the elongate elements, expressed as the number of sub-pixel widths across the lens width in the row direction is between 0.9 and 1.1 times 10 + 19/24.

11. A display as claimed in any one of claims 1 to 6, wherein s = a and is between 0.9 and 1.1 times 1/7.

12. A display as claimed in claim 11, wherein the pitch "p" of the elongate elements, expressed as the number of sub-pixel widths across the lens width in the row direction is between 0.9 and 1.1 times 10 + 5/7.

13. A display as claimed in any one of claims 1 to 6, wherein s = a and is between

0.9 and 1.1 times 1/9.

14. A display as claimed in claim 13, wherein the pitch "p" of the elongate elements, expressed as the number of sub-pixel widths across the lens width in the row direction is between 0.9 and 1.1 times 13 + 2/3.

15. A display as claimed in claim 13, wherein the pitch "p" of the elongate elements, expressed as the number of sub-pixel widths across the lens width in the row direction is between 0.9 and 1.1 times 10 + 2/3.

16. A display as claimed in any preceding claim, wherein the general column sub- pixel direction is slanted with an angle a to a vertical side of the display, the angle a preferably being equal to either 0 or to the angle Θ.