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This page briefly explains a few things:

Polarized light

All light is an electromagnetic wave. That means it is a wave with an electric field oscillating up and down in one plane, and a magnetic field oscillating up and down in a plane perpendicular to the electric field. The line where those planes cross is the axis along which the wave propagates. A picture would certainly help here, but I'm not up to that right now. Just remember that there's an electric field oscillating in a particular plane. That plane is the plane of polarization of the wave. In essence, that is all there is to polarization -- a particular electromagnetic wave has its electric field oriented in a single plane. Sounds simple enough, and in fact, when you think about it, it is unpolarized light that is kind of hard to imagine. If light is an electromagnetic wave, and electromagnetic waves have their electric fields oscillating in one single plane, then what is unpolarized light?

All sources of light fundamentally involve lots of atoms with electrons in excited energy levels that drop back down to their normal energy level. When they do this, they emit a single photon. That photon has, in a loose sense, a particular polarization -- its electric field is oriented in a particular plane and is totally polarized. But because most light sources, like hot wire filaments or gas tubes, are composed of a huge number of atoms, the light they emit is a composition of a huge number of randomly polarized photons. In effect, it is unpolarized, since every possible orientation is present in the large group of photons coming out of it. Any light source that has a large number of atoms will emit light that is a mixture of different polarizations, each one randomly oriented at any instant in time (one exception to this is a laser, where all the atoms sort of cooperate to emit "coherent" light beams, but that's another topic).

So all "normal" sources of light -- flash bulbs, tungsten light filaments, fluorescent bulbs, LEDs, the sun, candles, etc. -- are unpolarized. They are composed of a huge number of atoms, each of which emits a photon with a different polarization plane. Although each individual photon is polarized, there are so many coming out that the light appears to have electric fields oscillating in all directions. It is unpolarized.

How polarizers work

A polarizer is anything that allows only light with its electric field in a certain orientation to pass through it. There are a couple of ways to do this. The method that is used in photographic polarizing filters is to make a gel of really long, skinny molecules that absorb light with its electric field in one direction but allow it to pass in the other direction. It is a lot like a grate of bars very closely spaced. Imagine a rope passing through the bars, representing an electromagnetic wave. It you grab one end of the rope and try to shake it parallel to the orientation of the bars, the wave you put on the rope will be able to pass through. But if you shake it perpendicular to the direction of the bars, the bars will stop the wave.

Another way to polarize light is to reflect it off something. It turns out that when light is reflected off a surface -- any surface, whether it is metal, water, glass, or anything else, as long as it is smooth -- the reflected light is partially polarized in the plane parallel to the surface. The sharper the angle that the light hits the surface, the more strongly polarized the light is. All materials preferentially absorb light that is polarized perpendicular to their surface and preferentially reflect light that is polarized parallel to their surface. The next section explains why this is important.

That's the basics, but there are a couple of things that need to be pointed out here. At the beginning of this section, we said a polarizer only allows light with a certain polarization to pass through. That implies that the light coming out of the polarizer has all its electric field in exactly one plane. Well, nothing is ever absolutely perfect like that, so there's going to be a small spread in the polarization of the light coming out. Most polarizers are very good and actually have a very small output angular spread, so this can be ignored for most photographic purposes.

The other point is a bit tricky and may be kind of counterintuitive. Consider this -- why does a polarizer block half the intensity of incoming unpolarized light rather than almost all of it? Looking back at the description of a polarizer at the beginning of this section, it sounds like a polarizer would reject all light except light that is exactly aligned with the polarizer's axis. In other words, if we call the polarizer's axis "0 degrees", then only light polarized in the 0-degree plane would pass through, and light at, say, 10, 35, 50, or 90 degrees would be totally blocked. We would expect to see only a very small fraction of the incoming light making it out of the polarizer, maybe 1% or 0.1% or something like that. Instead we see 50%. Why? What happens is that the component of any incoming light beam that is parallel to the polarizer's axis passes through. The orientation of any incoming beam can be broken down into two components, one parallel to the polarizer's axis and one perpendicular to it. For example, light polarized at, say, 45 degrees relative to the polarizer has a component parallel to the polarizer's axis and an equal component perpendicular to the polarizer's axis. The parallel component passes through and the perpendicular component gets rejected. A light ray polarized at, say, 10 degrees will almost totally pass through, and a light ray polarized at 85 degrees will be almost totally blocked. If you add up all the contributions from all possible angles mathematically, it turns out that 50% of randomly polarized (or unpolarized, same thing) light will pass through.

Why polarizers are useful

The previous section mentioned that light reflecting off a surface is partially polarized parallel to that surface. This effect is what makes a polarizing filter have a useful role in photography. A filter that blocks light with a certain polarization can block the partially polarized light that is reflected from a surface. For example, light reflecting from a swimming pool will be partially polarized with its electric field oscillating horizontally. A polarizing filter that is oriented perpendicular to that will block that light, so some of the light  reflected from the surface of the pool will be filtered out. The result will be that a greater fraction of the light reaching the film or image sensor will be light that came from underneath the water surface, and there will be less glare from the reflection off the surface. The effect is greater for light hitting the surface at a shallow angle, nearer the ground, than it is for light coming in nearly perpendicular to the pool's surface because light reflecting off a surface nearly parallel to that surface will be more strongly polarized.

Polarizers can also block light reflecting from windows. These reflections will be polarized in a vertical plane, so orienting the polarizer horizontally will block most of the reflections. Again, the amount of light blocked will depend on the angle at which the light is coming into the window.

Why linear polarizers cause problems

It is very nice to be able to block unwanted reflections from objects in our photographic composition, but some problems develop when using a linear polarizer in most modern cameras. Remember that reflecting surfaces will tend to reflect mainly light that is polarized parallel to their surface and to absorb light that is polarized perpendicular to their surface. This is not a problem for a simple camera where the film or image sensor is right behind the lens and nothing else is in between. But most modern cameras have some internal beam splitters, mirrors, or prisms that rely on reflections in some way or another, either for sending light to the viewfinder, or to a metering sensor or autofocus sensor. If polarized light starts going through these optical systems, some will be absorbed, possibly nearly completely absorbed, depending on the exact orientation of the filter's polarization plane axis relative to the various internal reflecting surfaces in the camera. The result will be chaos. The autofocus system may not work, or the light metering system won't get a correct reading. So unless the camera is very simple in design, with no internal reflecting surfaces, a linear polarizing filter cannot be used.

The solution to this problem is a circular polarizer. This little piece of optical magic effectively blocks incoming light with a certain polarization, just like a linear polarizer (in fact, as we'll see later, a circular polarizer contains a linear polarizer). But it does a trick to the light that does pass through the filter that causes the light to behave for all practical purposes just as if it were not polarized anymore. It's like a polarizer followed by an un-polarizer.

The next two sections explain what circularly polarized light is and how to make it. They are pretty complicated. For the bottom line -- the practical reasons why a circular polarizer is needed for most cameras rather than a linear polarizer -- just go to the end section, Why circular polarizers are important.

Circularly polarized light

Just to be clear, let's remind ourselves that linearly polarized light is an electromagnetic wave where the electric field oscillates up and down in a single plane. To be concrete, imagine looking directly at this wave as it is coming toward you (your eye is directly aligned with the axis of propagation). Also imagine that the wave is polarized so that the electric field oscillates in the vertical plane, up and down.

Now imagine that instead of oscillating up and down, the electric field is rotating in a circle as it travels toward you. We'll get into how we can make that happen a little later, but if you can imagine that, then you've got a good grasp of what circularly polarized light is. The electric field rotates around in a circle, so that as the wave moves toward you, it traces out a spiral winding around the axis of propagation.

Circularly polarized light is one of the hardest concepts to grasp in electromagnetic theory, especially without the help of a picture -- multiple pictures, really. But I love to hear myself type, so let's try. Sorry if this isn't clear. There's a summary at the end that just reviews the important points.

So, how do we make circularly polarized light? We first need to understand something about circular motion. Something going around in a circle is really the same as something oscillating both horizontally and vertically, with the two oscillations out of phase. By "out of phase" we mean that when the vertical oscillation is at a peak (say the electric field is pointing straight up), the horizontal oscillation is at a zero; when the vertical oscillation is at zero, the horizontal oscillation is at a peak. We can see that circular motion is a combination of a vertical (up-down) component and a horizontal (left-right) component with the up-down wave out of phase with the right-left wave by thinking about what each component is doing at each of the four quadrants of the circle, as shown in the table below.

Point on circleHorizontal componentVertical component

We can see that the horizontal and vertical components are both oscillating back and forth, but their peaks are shifted. Since there are 360 degrees in a circle, and the peaks are shifted by one quarter of a circle, we say the waves are 90 degrees out of phase. This table demonstrates clockwise rotation; obviously just reversing right-left or up-down will give counterclockwise rotation.

It is important for what comes later (about why circular rather than linear polarizers are important in photography) to understand that circularly polarized light is nothing more than a combination of an up-down polarized wave and a left-right polarized wave that are just 90 degrees out of phase temporally.

So now we understand what circular motion is, but we still don't know how to make an electric field actually do this. This is a little tricky. It turns out that when an electromagnetic wave passes through a material, it slows down. Any material will slow electromagnetic waves to some extent; even air slows them down very very slightly. This slowing down is what causes light to bend when it passes through glass (or water, or whatever) and is the basis for how lenses are designed. (Why the slowing causes the bending is not immediately obvious, and is best left for another page.) The amount of slowing is described by a number called the index of refraction, which is defined to be exactly 1.0 for a total vacuum, and has some value greater than 1.0 for anything else. The more a medium slows down light, the larger its index of refraction.

Anyway, when light enters a material, it slows down. If the medium is isotropic, which means that it has exactly the same properties in all directions from any point within it, then light with any polarization is slowed down by the same amount. (By the way, isotropic is not the same as homogeneous, which means that a material's properties are the same from point to point.) One large group of substances which are usually very nicely isotropic are called amorphous. These are substances which are built up of atoms that are randomly arranged, like air or glass, and they affect all directions of polarization equally. On the other hand, materials which have very regular lattice-like arrangements of atoms are called crystals. Some cystalline materials are also isotropic, as long as the lattice arrangement is the same in all directions, like a cube, for example. But some crystalline materials have a molecular structure which, although regular from point to point, is not the same in all directions. Imagine a crystal made up of long, skinny molecules. They can be arranged in a perfectly regular cubic lattice with their long directions all lined up parallel to each other. Even though the basic structure is cubic and homogeneous, the fact that the molecules are different in one direction than the other (long and skinny) means that the material is not isotropic. It is different in the direction parallel to the molecules than it is in the other directions. Similarly, if the structure of a crystal is not the same in all directions, for example, if the atoms are arranged in a rectangular lattice rather than a cubic lattice, then there is a direction where the material is different. Since a rectangular box has one side longer than the other sides, it is not hard to believe that something might be different about the material in different directions. Such substances are said to be anisotropic.

It turns out that many crystalline materials -- in fact, most of them -- are not isotropic and do indeed have different optical properties depending on how they are oriented. The main thing we need to know for our purposes here is that some crystals will slow down light that is polarized one way more than they slow down light polarized the other way. The direction that is slowed less is called the "fast" axis, and the direction that's slowed more is called the "slow" axis. Such a material will have two different indices of refraction too, since it slows light differently in two different orientations. The term for this is birefringent.

How to make circularly polarized light

Now we are ready to understand how to make circularly polarized light.

We start with a linear polarizer. Let's say it is oriented vertically, so light coming out of it is polarized up-down. Now we will add a piece of birefringent material, and place its fast axis at a 45-degree angle to the linear polarizer's axis. This means that half of the linearly polarized light will be aligned with the fast axis, and half will be aligned with the slow axis. (Just like any vector can be projected onto any two coordinate axes.) If we choose the thickness of this piece of birefringent material carefully, we can get the slow wave to slow exactly one-quarter of a wave phase relative to the fast wave. This is called a "quarter wave plate" since it shifts the fast and slow axis waves by one-quarter of a wave phase.

The result, when the light exits the birefringent material, will be a component polarized parallel to the fast axis and a component polarized parallel to the slow axis (which, remember is perpendicular to the fast axis), with a 90-degree phase shift in time. This is exactly how we described circularly polarized light in the previous section.

So a circular polarizer is just a linear polarizer followed by a quarter wave plate that is oriented with its fast and slow axes at 45 degrees to the linear polarizer's axis.

 Why circular polarizers are important

After all that, you may still be wondering why this circularly polarized light is useful, and why a circular polarizing filter solves the problems that a linear polarizer creates in modern cameras. In the previous two sections, we saw that circularly polarized light consists of both horizontally and vertically polarized light with a 90-degree phase shift. Even if you didn't follow all the details, the important end result is that the light coming from a circular polarizer contains both horizontal and vertical components again, even after the linear polarizer removes all the light not parallel to its own axis. Although the horizontal and vertical components have a special temporal phase relationship with each other that is not present in natural, unpolarized light, none of the optical components in a camera can detect this, and the circularly polarized light behaves exactly like unpolarized light.

So, since a circular polarizer has a linear polarizer as its first element, it will reduce unwanted light not aligned with the polarizer's axis. But the quarter wave plate after the linear polarizer breaks the light down into two new components and changes their phase so that outgoing light no longer has any preferential direction in space and will interact with mirrors and prisms just like unpolarized light would.