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The below article is a two part series taken from Lenny Lipton (Real-D Inventor) blog. You can follow his blog here http://lennylipton.wordpress.com/

POLARIZED LIGHT AND 3-D MOVIES, PART 1
By lennylipton

From the time I was kid to my student days as an undergraduate in physics my abiding passion was light and vision.  Since my earliest years I have been interested in creating images and in understanding the role that light plays in image creation.  As a student no other part of physics engaged me as much as the study of light.
The study of light, and polarized light in particular, turns out to be of great importance in understanding how the most important stereoscopic moving image systems function.  It’s a subject of great interest to people in the field or for those who have an intellectual interest in the making and projection of 3D movies.  This article is about polarized light and how it is applied to image selection for stereoscopic movies.  The term “image selection” means: how one gets the left image to the left eye and blocks the unwanted right image from the left eye, and vice versa.  If you have a high school education through trigonometry and physics you have the background to understand a lot of what you need to know about polarized light.  If you are motivated to know more I recommend that you look at a basic physics text like Fundamentals of Optics by Jenkins and White.    On the other hand, you don’t have to know anything about polarized light to enjoy or make 3D movies.  You can consider polarized light image selection to be a black box and stop worrying about it.  Since you’re reading this, you probably want to know more.  This is not going to be a complete description and I am only going to focus on what I need to sketch in the story about how polarized light works for the stereoscopic cinema.
Physicists use the construct that light phenomena can be explained by considering it to be a longitudinal or transverse wave.  From the time of Newton, people who have thought about such things have thought that light could be explained as its being either a particle or a wave, but early on experimental evidence pointed in the direction of light being a wave phenomenon.  This idea was cemented along the way by the work of various smart people.  A lot of work was done after Newton to explain observed phenomenon in terms of waves without understanding their physic nature but it was Michael Faraday who conceived the idea of electric and magnetic fields.  James Maxwell took Faradays’ ideas about fields and used them as the basis for the creation of a set of equations that explains light in terms of it being an electromagnetic phenomenon.  He provided a basis for understanding and predicating how light worked in terms of it being a combination of electric and magnetic fields and he predicted the existence of radio waves.
To understand what follows you have to accept the fact that light is an electromagnetic phenomenon and that it behaves like a wave.  When I wrote earlier that it’s a longitudinal or transverse wave, I’m talking about the kind of wave that you can produce in a string like so: If you tie a string a few feet long to a doorknob and flick your wrist in an up-and-down motion you will produce a longitudinal wave.  You’ll observe that the amplitude or the height of the wave is perpendicular to the direction in which the wave travels – toward the doorknob.  That is what is meant by a longitudinal wave. It’s also a plane polarized wave because the wave resides within a plane.
Light can be thought of as being made up of a field with longitudinal waves described by electric and magnetic vectors. These two fields are in phase and at right angles to each other. We are going to forget about the magnetic vector because the eye is sensitive to the electric component and it’s simpler to continue this explanation by ignoring the magnetic component of light.  The light that you see reflected from surfaces or emitted by the sun, a candle, or a light bulb is unpolarized.  Assuming you could see the structure of the light leaving emissive surfaces or being reflected from many other surfaces, the planes in which the electric vectors reside are randomly oriented so there is no favored direction to their orientation. In plane (sometimes called linear) polarized light (there are other kinds), the wave is restricted to a plane, which is, as noted, exactly what happens when you try the experiment with the string.
Polarized light can be produced by a number of means.  The way we are concerned with as used in stereoscopic projection is by means of the kinds of sheet polarizers that Land and Bernauer produced in the 1920s and early 1930s.  Sheet polarizer is made of a substrate or base of a stretched sheet of plastic, usually polyvinyl alcohol, into which has been infused a dye like iodine, a kind of polymer that has long chains.  These long molecular chains are oriented to follow the stretch pattern.  The base is stretched, the dye is introduced into the material, and the long chain molecules of the dye line up and follow the direction of the stress of the plastic.  This creates a microscopic or molecular structure that favors the passage of light whose waves are oriented in only one plane.  (We are not going to talk about how that is accomplished.) That means that the light that is passing through a sheet polarizing filter will have the electric vectors of its waves all having the same parallel orientation.
Since these electric vectors are aligned in a plane that plane can be marked on the sheet polarizer with a straight line and it’s called an axis, in particular it is called the transmission axis.  The other axis, at right angles to the transmission axis, is called the absorption axis.  If you have a second polarizing filter just like the first one, and you place it on top of the first polarizer and you rotate it (say they are on a light box), what you will see is that the transmission of light goes through maxima and minima every ninety degrees.  When the transmission axes of the polarizers are crossed you get a minimum and little light passes through and when these axes are parallel you get a lot of light passing through.  The polarizers don’t have to be in contact in order for this work.  You can project a beam of polarized light onto a polarization-conserving projection screen (usually painted with aluminum metal) and observe the same phenomenon when looking through a polarizing analyzer.  In physics the second polarizer is called the analyzer so the polarizers in stereoscopic eyewear are analyzers.
There are two kinds of materials that we need to think about: conductors and dielectrics (or insulators).  Conductors conduct heat and electricity well, and they do this because they have free electrons.  Usually conductors are metals.  Non-conductors or dielectrics don’t have free electrons. Polarization-conserving screens have a metallic coating or they’re painted with metal, so they have free electrons on the surface.  It is these free electrons which reradiate the polarized light or reflect it back in a way that conserves the properties of polarization.  That is why a matte screen, which has a dielectric surface, cannot work for polarization image selection:  It doesn’t have free electrons.
If you have two projectors, that have linear polarizers over their lenses. whose axes are at right angles to each other – and you project them overlapping on this metallic screen, and you wear eyewear that have analyzers whose axes are lined up just like the ones on the projectors, one eye will see the reflected beam from one projector and the other eye will see the beam from the other projector, but each eye can only see the beam from its projector.  That’s perfect for projecting stereoscopic movies, because we can transmit one perspective for one eye and block the unwanted image for that eye, and so on.

POLARIZED LIGHT AND 3-D MOVIES, PART 2
By lennylipton

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 planar) 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 note 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 to be 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 axis.
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 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.