A large percentage of light passes through when the filter’s axes are parallel and this is called transmission, and a smaller percentage of light passes through when the axes are at right angles and this is called extinction. The ratio of the two is called the contrast ratio or the dynamic range. For good linear (or as I said earlier, some people call it plane) sheet polarizers for stereoscopic applications, the materials used usually have transmission between 30 to 35 percent and the dynamic range is about 3000:1 for the lower transmission material. In other words, only 1/3000th of the light in transmission passes through when the axes of the polarizers are orthogonal (extinction). For circular polarization the dynamic range is about a tenth of that for good linears.
But the specification of the filters is only part of the story. That is because the polarization-conserving metallic painted screens are imperfect; and since they are imperfect, the total dynamic range of the system is reduced. Starting with linear polarizers that are capable of a 3000:1 dynamic range, the final extinction ratio for the light reflected from the screen through the analyzing eyewear filters will be more like 200:1. I have made these measurements a number of times over the years, and although I haven’t done it lately, those are the kinds of numbers I expect we are getting today with standard products (there are specialized screens that have done better). All of this is assuming measurements are taken from the center of the theater pretty much on axis. In other words the measurements are taken pretty much in line with the lens axis of the projector, or at least close to it. Still, with a dynamic range of 200:1 you can have a good picture with low cross talk between the left and right images. Such cross talk is called ghosting in the argot of 3D; or sometimes leakage.
A major characteristic of linearly polarized light can be observed if you do the experiment I will describe. You can do this with the 3-D glasses you get from the movies, if you go to an IMAX movie or a theme park where they use linearly polarized light. Take the linear polarizers out of the eyewear (or you can use two pairs of eyewear) and holding them up to the light rotate them. You will see that even a small change in rotation away from maximum extinction rapidly produces a lot of transmission. This rapid change is explained by the Law of Malus. The interesting thing about all this is that when you actually see a 3-D movie at a theme park or in IMAX the law of Malus doesn’t seem to bother anybody. Tipping your head a few degrees this way or that way the image still looks good because you’re starting off with a fairly high dynamic range and with decent photography it works fine. I’ve been deeply interested in the problem of head tipping lately and have gone to a nearby IMAX 70mm theater a couple of times and the projection is superb.
Another kind of polarized light, circularly polarized light, is used in many stereoscopic theaters, and it is created by the ZScreen® electro-optical modulator or by the MasterImage process using a spinning filter wheel.
I turned the ZScreen it into a device for polarization image selection for both monitor viewing and for projection when I ran StereoGraphics, the company that created the electronic stereoscopic industry. The idea was given to me by Jim Fergason, who suggested I could apply his concept for a push-pull phase-shifting modulator to stereoscopic image selection. I worked with Art Berman, who helped with sourcing the parts, the difficult problem of laminating large parts, and with the physics of the device; also with Lhary Meyer, who designed the circuit to drive the parts; and with Bruce Dorworth, who was my lab assistant on the project. It was circa 1985 when we started the work on this development project. Our first OEM deal was selling the device to Evens and Sutherland for their molecular modeling workstations. Later we applied it to projection and it was used by people in engineering and scientific visualization.
How the ZScreen electro-optical modulator works is going to wait for another time but it must be mentioned because the majority of digital stereoscopic projector installations use the ZScreen. So I am going to describe how circularly polarized light works.
If you have been with me this so far you have a pretty good notion of how linearly polarized light works. We need to return to the physics of light. Light, unlike other waves, a water wave or the wave on the rope described earlier, does not require a physical medium. That is because light is propagated by means of a field, the field that Michael Faraday first conceived of and that was described elegantly by Maxwell and his colleagues. When light is propagated in space it travels at its maximum velocity, which everybody knows is C from the famous equation E=MC2.
But when light travels through a medium like water or glass or air (still pretty fast in air), it is slowed down. The ratio of the speed of light in air (or a vacuum) to the speed of light in the material is called the index of refraction. The propagation of the electromagnetic field requires a reradiation of the electrons that are part of the atomic structure of whatever the light is traversing; so it takes a while, let’s say, for those electrons to reradiate the light. For the majority of materials it doesn’t matter what direction light is traveling in – the speed of light will be the same. These materials are described as being isotropic. Air is isotropic. Glass is isotropic. So if we shine linearly polarized light through one of these materials, no matter what the orientation of the plane of polarization, it will be traveling at the same speed.
There are other materials, retarders, that are birefingent (two indices of refraction) and have anisotropic properties (different optical properties in different directions and later it will be noted that these axes are at right angles). For the purposes of this discussion we are interested in one class of materials made out of plastic. These are sheets similar to the sheets that are stretched and stressed used for making the linear polarizers. You take this plastic and you stretch it – you pull on it, you yank on it. This creates a mechanical stress in the material, and it winds up with two optical axes– a fast and a slow axis. If light travels along the slow axis it travels slower than if it travels along the fast axis. If we shine linearly polarized light so that its axis is parallel to the fast axis, it will pass through the material faster than it would if the axis of the linear polarized light was parallel to the slow axis. It’s the damnedest thing; imagine a piece of plastic that has two values for the speed of light.
Now imagine what would happen if the axis of the linear polarized light bisected the fast and slow axes (remember they are orthogonal) so that it was at 45 degrees to both. You would then have, through vector analysis, two components of the electric vector. (Here’s where you had better go look at Jenkins and White.) Those vector components are orthogonal to each other and lined up with the fast and slow axes respectively. One component is parallel to the fast axis, and one component is parallel to the slow axis. When the wave that is traveling in the fast-axis direction meets the one that is traveling in the slow-axis direction as they emerge from the material into the air, these two orthogonal waves are going to be out of phase and the vector sum of these two waves is the heart of the matter.
Depending upon where the electric vectors are when they emerge from the material, that is to say their phase relationship, you will get a specific kind of polarized light emerging from the retarder. If the material is a half-wave retarder the two out of phase linear waves will combine to undergo a 90-degree phase shift and by vector summing will be toggled or flipped through 90 degrees. If you have a quarter-wave retarder the result will be circularly polarized light. You will either get left- or right-handed circularly polarized light, depending upon the orientation of the plane polarized light’s axis to the fast and slow axes.
If you could look at the electric vector in a linear polarized light beam that was headed toward you, you would see that the electric vector is traveling in a plane. The amplitude would be changing, that is to say the electric vector is going up and down, but it would be restricted to a plane. If you took a look at circularly polarized light, in the case of one kind of circularly polarized light you would see that the tip of the electric vector is describing a circle or corkscrew turning clockwise or counterclockwise as it heads towards you. If the tip of the vector is traveling clockwise it’s called right handed and if it’s going counterclockwise it’s called left handed. Or maybe it’s the other way around because having looked it up in a couple of books I suspect the standard is ambiguous.