Popims HEXA Technologies for 3D Television

Why we recommend spherical lenses

There are two main reasons. The first one is that, if you want the surface of a lenticular screen to display the color of one specific pixel, the logical solution is to focus on that pixel and not simultaneously on neighboring pixels. This is the known difference between a spherical lens – focusing on a point – and a cylindrical lens – focusing on a line.

There is a second reason which is that a spherical lens surface corresponds to a smaller zone of an "interweaved" image than any other type of lens, and that using such lenses leads to more possible solutions (more views).

It is true that, in certain conditions, the line on which a cylindrical lens focuses can be pixels originating from the same image. In that case, spherical lenses can be replaced by cylindrical lenses. For example, using vertical cylindrical lenses, each focusing on a column of sub-pixels causes no problem.

When using cylindrical lenses that are slanted with respect to the display pixel columns, it normally does not work because the focusing line crosses pixels that are horizontal and/or vertical neighbors, except in a position where that line crosses the pixels separations at the rectangle angles. This is possible for only a very limited number of the spectator’s position.

However, using cylindrical lenses that are slanted with respect to the display pixel columns may work properly because, to a certain extent, it is possible to play with the shape of the physical pixels of the LCD.

This will work only if pixels are direct neighbors (one angle of the parallelogram in common), and if the side of parallelograms are parallel to the axis of the cylindrical lenses. It quickly becomes difficult to do that as it is not possible or recommended to have pixels of too funny shapes.

The MiniPopims and A6 Popims screens have a similar mapping which is close to the ones used on some screens with cylindrical lenses, but do not respect that limit of parallelograms having angles in common:

Represented in colors are the pixels corresponding to the center of the lenses. This convention is kept in all following diagrams.

As you can see, the main advantage of spherical lenses becomes very important comes when the lines of lenses are highly slanted with respect to the display pixel columns. We call “A” this angle between the lens lines and the vertical.

In that case, the resolution of the screen - equivalent to the pitch of a cylindrical lens array (equal to 1/blue arrow) becomes much higher for a given number of images (red arrow). The perceived resolution is R = 1 / [N x P x COS(A)] where N is the number of images and P the with of a pixel.

It does not seem possible to use such pixels mappings with cylindrical lenses, as the side of pixels that would have the shape of parallelograms could not be parallel to the axis of the cylindrical lenses.

Why Popims main patent seems to us being the perfect answer to the problem.

The Popims mapping used for MiniPopims and Popims A6 screens would work all the same with RGB sub-pixels, as represented below.

The fact that RGB sub-pixels are usually 3 times higher than the square pixels makes the A angle smaller than with the square pixels, and that is why we do recommend to use a bigger A angle.

The ATAN(2) = 63.43° angle used for the MiniPopims and Popims A6 screens have proven their quality, and could probably be used also for RGB .

Why the HEXA formula brings even more advantages

The diagram below uses a lower angle than the one used for the MiniPopims and Popims A6 screens: ATAN(5/6) = 39.81° which should give very good results.

This angle has been chosen because it also matches the HEXA rule : triangles have summits of different colors in order to get a better white synthesis inside each triangle.

An interesting point is that the HEXA mapping advantage increases with the number of images.

Here is HEXA 80. The value of 80 may seem very high, but 80 images becomes a possible value for Quad Full High Definition of 3840 x 2160 pixels.

We still have a nearly perfect honeycomb, which means very good white synthesis between the lenses.

The resolution of the screen (equal to 1/blue arrow) is here about 5 times better than what it would be with classical slanted cylindrical lenses (equal to 1/red dotted arrow) – the lines of black squares representing the cylindrical lenses axis.

The limits of the HEXA method

There is a limit to the HEXA method, about the maximum pixel offset between lines of pixels.

In the previous example, a vertical movement of the spectator leads to a change of image representing 15 images out of 80. The image changes 5 times faster for a vertical movement of the spectator than for his horizontal movement. This factor should not be too high, because when a spectator is not exactly at the right distance from the screen, he views on different zones of the screens portions of images that do not correspond to the same views, and if there is a too important difference between views, this difference will be seen and become uncomfortable.

The problem has to be thought of taking into account that the difference between images is mostly horizontal, because the camera positions corresponding to different views vary horizontally and not vertically. However, trials made with previous Popims Screens led to the conclusion that one should not go too far in the HEXA method.

This is why we recommend the below diagram. It still represents an 80 views mapping, but the image change for a vertical movement of the spectator is only 3 times faster than it is for a horizontal movement of the spectator. The benefit compared to the cylindrical lenses arrays remains extremely high.

Why Popims technology is the key to resolution, 3D effect and viewing angle.

Popims technology enables a considerable enhancement of the perceived resolution for a given number of images, whatever the number of images.

This means that:

1. for a given resolution to be perceived by the spectator, it enables to increase very significantly the number of images, which has a consequence of a much higher 3D effect and or a wider viewing angle,
    
2. for a given viewing angle, it is possible to have either a better resolution and/or a stronger 3D effect,
    
3. for a given 3D effect, it is possible to have either a better resolution and/or a wider viewing angle.

About future screens that would not use RGB components.

In that case, the problems will be exactly the same as the one which is to be solved with printed interweaved images, and the MiniPopims and A6 Popims screens show that the increase of the number of images is around 2.4.

HEXA Technology: main versions dedicated to 3D television

• HEXA 2: enhances resolution and brings 2 vues 3D to all small sizes screens (cell. phones, video games, organizers, camera viewers, surveilance, etc.)
  An important characteristic of HEXA 2 is that the lenticular array remains in place for the 3 different available modes:
  
  
  • Uncoded - the lenticular array does not diminish the perceived resolution of the screen with uncoded images.
     
  • HEXA 2 - 2D coded - the lenticular enhances significantly the perceived resolution of the screen through a very simple coding algorithm.
     
  • HEXA 2 - 3D coded - Of course, 3D is obtained only at the right distance from the screen, and one half of the positions are "inverted 3D", but face tracking software can be used to swich vues when the viewer changes position.
  
   
• HEXA 4: brings 4 vues 3D to all medium sizes screens : mainly LCD type PC screens
   
• HEXA 9: brings 9 vues 3D to large sizes screens
   
• HEXA N: brings an unlimited number of vues 3D to large sizes HDTV screens.