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Stereoscopic view via polarisation

How stereoscopic view via polarisation works and why linear polarisation is normally used.

Light Polarisation: Theory and History

When viewed through a calcite (calcium carbonate, CaCO3) crystal, text can be seen twice. Newton concluded that his light particles should also have transversal movement properties. Unfortunately he did not listen to Hooke who put forward, that Huygens' waves might be transversal rather than longitudinal. Later, Malus noticed that the light of a sunset, reflected at the windows of the Palais de Luxembourg, changes brightness when viewed through such a crystal under different angles. [1]
What he saw was the effect of using two polarising materials in the path of light: The reflection of the windows is slightly polarized (see: Brewster angle) and the double view through CaCO3 is due to differently polarized light taking different paths.

Light is a transversal wave: The vectors of the electric and magnetic field are always perpendicular to the direction of movement. The polarisation of light describes a property of the electrical field vector: If the electrical field vector of a light beam always points into the same (or opposite, i.e. anti-parallel) direction, this beam is linearly polarized.

Generally spoken, light is elliptically polarized which means that the electrical field vector does not always point into the same direction but moves around on an elliptic shape which is normal to the direction of light propagation. There are two interesting special cases: circular polarisation and linear polarisation.

"Natural" light emitted by usual light sources (lamps and other thermal light sources but not lasers) is usually "not polarized". This means that all directions of polarisation are randomly and equally distributed.

Using special filters called polarizers (or polarising filters), one can change the polarisation of a light beam which is traveling through the filter. Basically, this works by absorbing that part of the light which has undesired polarisation so that only the wanted polarisation remains.

3d Channel Separation via Linear Polarisation

[continued from above] This has the following useful consequence: Imagine you send a beam of light though a linear polarizer oriented in a way so that it changes the electrical field to be horizontal. (Note that when using an unpolarized light source, this first filter will absorb half of the intensity.) This beam of horizontally polarized light is then sent through another linear polarizer. If this second filter is oriented just like the first one (i.e. horizontally as well), it will transmit all the light. If, however, it is rotated by 90 degrees and hence vertically oriented, it will absorb all the light and transmit nothing.

In general, if the angle between the two directions is a, then the amount of transmitted light intensity I is (with I0 being the amount of incident light):

I=I0 cos2(a)       (Malus' law)

The above effect can be used to project two different images (the left and the right view) on the same image plane and then separate them again in front of the viewer's eyes using polarizing filters as goggles: The left and right images are projected with standard projection devices by sending them through a horizontal and a vertical (linear) polarizer, respectively. (In 3d cinemas, these polarizing foils are sometimes simply sitcked on the glass window which separates the projection room from the presentation room.) The viewer then looks at this image with special glasses which use a horizontal (linear) polarizer for the left and a vertical one for the right eye.

Hence, the left eye only sees the left image and the right eye only the right one. This only works as long as the spectator does not rotate his head around the viewing axis, i.e. if you lean to the right in order to whisper into you right neighbour's ear, the filters in the goggles are no longer oriented like the ones in the projector and one sees "ghost-images", which is simply due to some light from the left image being transmitted by the filter in front of the right eye and vice versa. (If you put up the goggles the wrong way (swap right and left), then the right eye sees the left image and... well, try out yourself the next time you have the chance.)

(Note that you may turn your head left and right without trouble as long as you keep sitting/standing upright.
Note also that in principal, one does not have to choose horizontal and vertical polarisation but can choose one direction freely and take the other one perpendicularly.)

Why not use Circular Polarisation

As explained above, the linear polarisation method has the disadvantage that the viewer and the projector need to be "aligned", i.e. you must sit upright and may not lean to the left or right side.

To overcome this problem, one could, in theory, use circular polarisation. The setup works exactly as described above after substituting horizontal and vertical polarisation with left-circular and right-circular polarisation. This way, a spectator may still lean to one side because (even if he stands on his head) light coming left- or right-circular will be filtered correctly in his goggles (unless s/he loses them due to too much acrobatics). However, there is not much practical use because while the right (left) image will always be seen right (left) eye, the shift axis won't tilt when the viewer lean to one side. So, both the images will typically remain hoizontally separated while a viewer having his head at 45 degrees will expect to have left and right image shifted along a 45 degree axis instead of a horizontal one.

Technically, this could be done by substituting linear polarizers with circular ones but this has several disadvantages:

  • Linear polarizing slides (Polaroid) are easy to handle and cheap. Circular polarizers (as e.g. one can buy them for photographics) actually consist of a linear polarisation filter followed by a lambda/4-plate. The latter is expensive and also makes the polarizer non-flexible. (Price is no issue for the projector but for the glasses handed to the audience.)
  • Due to the lambda/4-plate, circular polarizers only work perfectly for the wave length (light color) they were designed for. Usually, one would use 550nm which is green and the wave length at the center of the sensitivity of the eye but due to this wave length dependence, the filters do no longer work correctly for red and blue light resulting in red and blue "ghost images" in cinema. In contrast, linear polarizers work well for all visible wave lengths.

If one ignores this things, then circular polarisation could as well be used as long as one looks directly into the projection device. But the killer for cinema solutions is:

  • There exists (at least to my knowledge) no diffusively reflecting material usable for cinema screens which retains circular polarisation (in contrast to linear polarisation).
    This means that the light will no longer be left- and right-circularly polarized after being reflected at the screen and the spectators would just see both (left and right) images in both eyes.

(Note that, in case it would work, in such a cinema you could change the left and right glass without trouble as long as the temple points in your direction. If you rotate the goggles so that the temple points away from you towards the screen, the 3d effect is lost. Why? - Think a moment.
(Because now the circular light first passes the linear polarizer and then the lambda/4-plate [which both make up the circular polarizer]. The linear polarizer will transmit 50% of the incident light independent of its circular polarisation. The goggles then just act like 50% transmission "grey" filters.))

[1] Gerthsen, Physik, 20th edition, p. 534

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