Recently, my wife and I went and saw Avatar in 3D at the local cinema. They used RealD 3D glasses that look just like sunglasses. Rather than dropping ours in the recycling bin after the movie, I took them back to the lab to play with, because they have some interesting optical properties.
Here’s a view through one of the lenses of the big LCD display in the lab:
At first glance, it would seem absurd to have light behave so differently when going forwards or backwards through the glasses. However, there is an interesting explanation for why this occurs.
The way we are used to experiencing light interacting with an object is typically symmetrical. If I can see you in a mirror, then you can see me through that same mirror. However with the RealD glasses, LCD light can pass through relatively freely in one direction but is blocked in the other direction. This effect is only seen when looking at LCD displays, not at other lights, which is a big hint as to what’s going on. Further investigation shows that the brightness when going forwards varies somewhat as you rotate the glasses, and when going backwards it goes from totally black to somewhat visible also when rotating the glasses. So, what’s up?
First, it may be helpful to know a little bit about how our eyes work. The reason that we can experience depth (i.e. 3D) in the real world is because we have more than one optical input device in our head. Each eye gives a slightly different perspective of the image in front of us. Try it out: close your left eye and look out from your right; now close your right and look from your left. The image shifts ever so slightly. When looking through both eyes, adjustments are required in order to focus on a single point. We then associate these adjustments with the relative distance of various objects. Eyes angled inward with tight focus means an object is closer, while eyes looking straight out with a loose focus means the object is further away. Normal 2D movies don’t require these eye adjustments because they were shot with a camera that has only one optical sensor.
3D movies use a special process to simulate depth by requiring these eye adjustments. To do this, we have to receive two different optical signals from a single movie screen. This paricular 3D projection system uses circularly polarized light in order to achieve this. That is quite a big word, so let me break it down. As light is emitted from a source, it moves in a somewhat random fashion. Polarized light, on the other hand, has been lined up in some way. It could be compared to the difference between kids running around chaotically on a playground and kids walking in an orderly straight line. This organization can take different patterns. If polarization is circular, then light takes on a small circular pattern of movement as it travels through space. Similar to a rotating propeller, it spins as it moves forward.
The projector uses this circularly polarized light to send alternating images, one for each eye, and the viewer wears something that allows only the appropriate images to enter the appropriate eye. The left lens allows certain images through and the right lens allows others. So the glasses worn by viewers use “circular polarizers” to block specific parts of the light.
Now back to the LCD screen. LCDs emit linearly polarized light, or light that lines up along a single plane. So why would a circular polarizer affect linearly polarized light differently depending on which side was facing the light source?
It turns out that circular polarizers can be made by stacking a quarter wave plate and a linear polarizer. A wave plate alters the type of polarization of the light that passes through. A quarter wave plate changes the orientation by 90 degrees. Essentially, this set up nudges the linearly polarized light, giving it a rotation, resulting in circular polarization. Consequently, the wave plate can also take circularly polarized light and “straighten” it to linear.
Vector addition allows us to represent linearly polarized light as the sum of two orthogonally polarized waves, one vertical and one horizontal. In other words, linearly polarized light, which behaves in a single plane, can be broken down into its horizontal (x) and vertical (y) components. It’s like instead of asking you to walk 50 paces in some diagonal direction, I could tell you to walk forward 40 paces and then left 30 paces. The same principle is sometimes used to calculate vectors of light.
A linear polarizer allows light linearly polarized in one direction through, and blocks orthogonally-polarized light, or light whose orientation differs by 90 degrees. You could imagine the vertical bars of a jail cell (linear polarizer) would only allow through pizza boxes (linearly polarized light) with the same orientation. Vertical pizza boxes pass while horizontal pizza boxes get blocked. These two facts allow us to explain, for example, what the amount of polarized light is that gets through a linear polarizer as the polarizer is rotated: simply represent the incident polarized light as two vectors, one of which is parallel to the orientation of the polarizer and the other of which is perpendicular (according to vector addition explained above), and eliminate the amount of light in the perpendicular direction. The following two diagrams illustrate this point. The first shows what happens when linearly polarized light aligned in different directions goes through a linear polarizer. In the first case, when it’s aligned in the same direction, the light goes through. In the second case, when it’s perpendicular, the light is blocked.
But since we can represent light as being the sum of any two orthogonal components (as seen in the top half of the next diagram), we see that a linear polarizer will allow some but not all of the light that is rotated less than 90 degrees through the polarizer.
With this information, we can now explain the odd behavior of the 3D glasses and the LCD display. The following table lists the various cases we need to examine. The left-most column lists a kind of light heading into the glasses used with the 3D projection system. The “Forwards” columns show what happens when the light goes through the quarter wave plate (QWP) first, and then the linear polarizer (LP) second. The “Backwards” column shows what happens when the light goes in the opposite direction. “Circ” means circularly polarized, “Lin” means linearly polarized, and “1/2″ means that some fraction of the light makes it through, with the polarization one would expect.
In the theater, they send out circularly polarized light, with a different handedness for each eye. The 3D glasses could have the linear polarizers in each lens oriented in different directions for each eye. So (referencing the bottom two rows in the table above) the right-circular light would go through one lens but not the other, but vice versa for left-circular light.
When we look through the glasses at an LCD, which puts out linearly polarized light, we can see that at least some light will get through both lenses at the same time in one direction (the first two rows in the table above) but in the opposite direction, there is an orientation where no light will get through.
As it turns out, the particular glasses I have appear to be built slightly differently. If the linear polarizers were orthogonal to each other, then the reverse view of an LCD should have one lens letting all the light through while the other lets none through. But in fact they are both identical. This suggests that the quarter wave plates (QWPs) are the elements oriented at 90 degrees to each other instead of the linear polarizers. This would mean that circularly polarized light going through one QWP would come out horizontally polarized, and going through the other would be vertically polarized.
Research grade quarter wave plates are expensive, but apparently there are lower quality ones available in plastic at much lower prices, and their quality would be good enough for watching a movie.
You can read more about the history of 3D films on Wikipedia.