I went and saw Avatar in 3D last night.  Everybody told me it was visually amazing but the story was lame.  The first part is definitely true, but (probably in part because my expectations had been lowered so much) I was actually pleased by the story.  It’s totally formulaic, but I’m not sure that’s such a bad thing.  There are lots of things worse than a well-executed formula.

But that’s not what I want to talk about.  Naturally, after the movie was over, I had to try to reverse-engineer how the 3D glasses work.

To get 3D, you have to present slightly different images to the two eyes.  In the old days, the glasses had color filters on them, and the two images were presented on the screen in different colors. That has the significant disadvantage that you can’t use color to convey other information (i.e., color!).  So in modern 3D, the different images for your two eyes are projected onto the screen using two different polarizations.

The simplest way to do this would be to use horizontal and vertical linear polarizations.

[(Information for people who don’t know / don’t remember optics.  If you do know, then skip everything in brackets.) Light is a wave of electric  and magnetic fields.  The fields have to be perpendicular to the direction the light is traveling, but subject to that constraint they can be oriented in different ways.  Linearly polarized light just means light where the electric field is wiggling back and forth in a particular plane.]

The simple procedure would be to stick a filter in front of your left eye that only lets through horizontal polarization, and one in front of your right eye that only lets through vertical polarization.  Then project the two images onto the screen with the appropriately matched polarizations, and you’ve got it.

That’s not how it’s done, though.  One reason is that if you tilted your head, the polarizers wouldn’t be aligned right.  In fact, if you tilted your head 90 degrees, the image intended for each eye would reach the other one, which would have the disconcerting effect of flipping the image, so that stuff that was supposed to look close to you looked far away, and vice versa.  Even if you tilt your head less than 90 degrees, you’d get an unacceptable distortion.  This doesn’t happen — I tried it.

The solution to the head-tilting problem  is to use circular polarization rather than linear polarization.

[With circularly polarized light, the electric field rotates as the light propagates, so that the tip of the electric field vector traces out a spiral pattern.  In other words, it rapidly switches between horizontal and vertical as the light moves along.  There are two kinds of circular polarization, left and right, corresponding to clockwise and counterclockwise spirals.]

The images for your two eyes are actually projected on the screen in left and right circular polarizations.  Since a clockwise spiral is still clockwise no matter how you tilt your head, this solves the head-tilting problem.

So you might imagine that the 3D glasses just consist of a filter for each eye, one that lets through left circularly polarized light and one that lets through right circularly polarized light.  I think that is the general idea, but the details are a bit more complicated.  One way to see this is to take two sets of glasses and hold them up so that light passes through the left lens of one pair, followed by the right lens of the other.  (They’re not really lenses, of course; I’m just using “lens” to mean one of the two things in a pair of glasses.) In the simple picture I just described, you might expect to see no light at all get through: the first lens would block all of one polarization, and the second would block the other.

[If you’re just looking at a natural light source, it’s probably unpolarized, meaning that the electric field points every which way.  But even unpolarized light can be thought of as a combination of left and right circular polarizations, so the first lens would knock out half the light, and the second would knock out the other half.]

But that’s not what happens. Quite a bit of light gets through in this experiment.  Moreover, if you rotate one lens with respect to the other, the light that gets through changes from gray to yellow.  What’s up with that?

A couple of clues: First, the fact that the image changes as you rotate the lenses suggests that linear polarization is involved after all.  Second, there’s a fact you can dredge up if you’ve studied optics: it’s not easy to make a filter that passes one circular polarization and not the other.  What you can make is something called a quarter wave plate, which magically converts circular polarization into linear polarization and vice versa.  For instance, you can make a quarter wave plate that turns left circular polarization into horizontal linear polarization and right circular polarization into vertical linear polarization.

So now we can make a guess: each lens consists of two parts: a quarter wave plate to turn circular into linear, followed by a polarizing filter that just lets through one linear polarization.  The two lenses either have different linear polarizers at the back end (one horizontal and one vertical), or different quarter wave plates at the front (one that turns L/R into H/V, and one that turns L/R into V/H).  Either way should work.

Here’s one test of this theory.  Take two sets of glasses, and hold them up to a white light source, so that the light passes through one lens in the usual way, and then through another lens in the reverse direction.  According to the hypothesis, the light coming out of the first lens should be linearly polarized, and when it hits the second lens it should hit a second linear polarizer.  That polarizer will let light through if it’s lined up the same way as the first one, but block it if the two are perpendicular.  Sure enough, that’s what happens. When you rotate one lens with respect to the other, the amount of light that gets through changes, dropping to essentially zero when the rotation is 90 degrees.  This is true whether you’re using the left or right lens in each case.

So the answer’s got to be version 2 of the hypothesis: both lenses have the same kind of linear polarizer at the back end (let’s say vertical), but they have two different quarter wave plates at the front end: one converts left circular polarization to vertical and one converts right circular polarization to vertical.

You can try a bunch of other similar tests, flipping the orientations of the two lenses various ways.  I think they’re all consistent with this theory, with the exception of one thing: sometimes, as noted above, the way the light gets through depends on color.  The most dramatic example is if you send white light through, say, the left-eye lens backwards, and then through the right-eye lens forward.  The result is a nice, rich purple.  What’s up with that?

According to the theory I sketched, the experiment I’m describing consists of sending the light through four elements: a linear polarizer and quarter-wave plate for the first lens, and then a quarter-wave plate and a linear polarizer for the second lens:

LP1  QWP1  QWP2  LP2

The two quarter wave plates next to each other form something called (not surprisingly) a half wave plate.  A half wave plate rotates linear polarizations by 90 degrees — that is, turns horizontal into vertical and vice versa.  In that case, we’d expect this sequence to let through no light at all: the first linear polarizer lets through only (say) vertical, then the HWP turns it to horizontal, and the second linear polarizer blocks horizontal.  So we should see black, not purple.

I think the explanation is that a quarter wave plate (or a half wave plate) can only be designed to work perfectly at one wavelength [i.e., one color].  The glasses are probably designed to behave correctly in the middle part of the visible spectrum, which means they’ll be imperfect at the two ends.  So this particular combination of lenses would do a good job at blocking out light in the middle of the spectrum (yellow, green) but not so good at  blocking out light at the edges (red and violet).  That seems consistent with what I observe.

I guess this must mean that the 3D effect is only perfect for light in the middle of the spectrum, and for other colors some of the image meant for one eye actually reaches the other.  Presumably this imperfection isn’t very noticeable “in the wild.”

One experiment I wish I’d tried during te movie: put the glasses on upside down, so that the image meant for the left eye goes to the right eye and vice versa.  This should have two effects:

  1. Make you look even goofier than the other people in the room wearing 3D glasses.
  2. Show you the picture inverted in depth (close stuff looks far and far stuff looks close).

If you try this during a 3D movie, let me know if it works (particularly #2 — I’m pretty confident about #1).

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Ted Bunn

I am chair of the physics department at the University of Richmond. In addition to teaching a variety of undergraduate physics courses, I work on a variety of research projects in cosmology, the study of the origin, structure, and evolution of the Universe. University of Richmond undergraduates are involved in all aspects of this research. If you want to know more about my research, ask me!

16 thoughts on “3D”

  1. “I guess this must mean that the 3D effect is only perfect for light in the middle of the spectrum, and for other colors some of the image meant for one eye actually reaches the other. Presumably this imperfection isn't very noticeable "in the wild."

    I’m pretty sure a) that this is the case and b) that practically no-one notices it. Even 2-D film and (even more so) television use quite a few tricks to make it look much more close to reality than it is, relying on the brain to piece things together to give a full impression. (This happens even in the real world; you can see sharply only immediately ahead, but you have the impression that your usable field of view is much larger because the brain “fills in the blanks”.

    With regard to the story (I haven’t seen the film yet; I’m looking for a cinema which is showing it a) in 3-D and b) in English (one of my biggest gripes about living in Germany is that, as a rule, films and television programmes are dubbed rather than using subtitles)): I think the criticism, at least the valid criticism, is less that it is formula—Titanic, by the same director, was formula yet didn’t get that much criticism for being so—but rather that the story makes too much use of stereotypes (whether or not they are true); I’m sure you’ve seen the discussion over at Cosmic Variance: http://blogs.discovermagazine.com/cosmicvariance/2010/01/05/black-and-white-and-blue-all-over/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+CosmicVariance+%28Cosmic+Variance%29

  2. I think I pretty much agree with what Sean says over at Cosmic Variance. David Brooks makes similar points in his column in today’s NY Times. I guess I’m just not that bothered by it. Not sure why.

    I have to admit that I’d have a much stronger negative reaction if the story were about actual indigenous people on Earth rather than about an alien species, even though the fact that one is a stand-in for the other is glaringly obvious. I can’t really say why I react that way, but I do.

    Some people I talked to were bothered by the simplistic dualism (Humans: destructive, violent, out of touch with nature. Aliens just the opposite.), but I think that’s silly. We’re in a mythic storytelling genre here. Being bothered by that would be like being bothered that Aragorn is noble and Orcs are evil. But I understand that Sean and Brooks and others are making a different and much more sensible point.

  3. There is, of course, a tradition of messages (be they libertarian like with
    Heinlein in his prime or socialist like with Asimov) in science fiction and one
    can argue that they should be rather obvious since if they are subtle the
    intended audience won’t get them. 🙁

    It’s interesting to look back at the original Star Trek. Today, it seems
    rather dated in places (recalling the title of Fred Pohl’s autobiography: The
    Way the Future Was), but at the time it was radical: a BLACK WOMAN on
    the bridge, a Russian officer at the height of the cold war, an
    extraterrestrial portrayed as being superior to humans etc. (Some
    episodes were even banned in some countries due to interracial kisses and
    things like that.) Roddenberry wanted to go even further, but couldn’t get
    it passed the network executives. With hindsight, we say that it is rather
    wrong that only 1/3 of the crew is female, but that was much better than
    all-male crews, as in early science fiction (there is probably even an
    all-male multigenerational starship somewhere)—and Roddenberry wanted
    to have it 50-50, but the network executives vetoed that with “the viewers
    will think about all of the fooling around [their term] going on up there”.
    What one should conclude from, to paraphrase the Beach Boys, “two boys
    for every girl” is left as an exercise for the reader.

    Anyway, in one episode there is a character with his face half black and
    half white. The crew are surprised at his hatred of another character,
    also with a face half white and half black, until he explains that in the
    other guy’s face it is the OTHER half which is black. The allegory is not
    subtle, especially considering that this was broadcast during the height of
    the civil-rights movement. But I’m willing to be that this allegory got some
    people to think about racism in a light they hadn’t had before, whereas
    real-life documentaries, contemporary dramas (say, Guess Who’s Coming
    to Dinner) etc wouldn’t have.



    For the record, I consider myself to be a fan (though not an avid one,
    and have never been in uniform) of the original series. I have seen all
    of those episodes many times (about 30 years ago) but only a few
    episodes from the later series. Many of the episodes are more like
    stage plays—not because of the cheap special effects (love those same
    styrofoam boulders whatever the planet is this week), but because many
    of the episodes are obviously intended as allegories. As such, they are
    probably better compared to The Wizard of Oz than to, say, more realistic s.f. films. I remember reading an interview with Patrick Stewart, who
    remarked that when he was offered the role he had to ask his children
    what Star Trek was, since he had never seen any episode. He then went
    on to say that it wasn’t such a big challenge for him since the general
    style is quite similar to Shakespeare in some respects. (No-one expects
    a realistic depiction of ancient Rome, or Denmark, when watching
    Shakespeare; many monologues are intended for the audience and not
    for other characters; there are stock characters, both recurring and
    one-time; there is a similar structure whatever the story; and so on.)

  4. That’s an interesting interpretation. Personally I doubt Cameron had anything as sophisticated as this in mind, but maybe I’m not giving him enough credit.

    Here’s another argument against thinking of the Na’vi as simply stand-ins for indigenous peoples:


    But I don’t find this way out of the noble-savage / white-Messiah criticisms all that convincing: It’s awfully hard to watch the movie without feeling like the filmmakers intended you to see parallels with “primitive” peoples on Earth. If Cameron didn’t intend to call up those parallels, he made some very strange choices.

  5. I was actually looking for the depth “fuzziness” in the reds and purples when I saw Avatar (and perhaps as a consequence didn’t like it much). They weren’t noticeable, but I think that had a lot to do with nothing really staying in place much. I think a good place to test this would be the World Cup (which ESPN is doing in 3D). It should be much easier to identify the difference between the red kit of Spain against the yellow of Brazil–especially with a set piece or other still motion. I still don’t think I’ll see anything, since I suspect that the designers were more interested in getting red right than purple, and would center appropriately–purple is generally a background color, while the thing jumping at you is more likely to be red. Too bad there is no purple in the World Cup…

  6. In the latest Physik Journal (magazine of the German Physical Society), there was a two-page article on 3-D techniques. You mentioned three: colour, linear polarisation and the quarter-wave-plate model (your hypothesis was correct; that’s how it works). The last is definitely the best of these three, but shares this problem with linear polarisation: the reflected image has to be polarised, so the screen has to be mirror-like, not just a white screen.

    There are two other techniques. One projects frames at twice the normal rate, altenately for each eye, and the glasses contain infrared-controlled LCD shutters which alternate at the appropriate rate. Probably the best system, but the glasses are more expensive.

    Another one is quite interesting: for one eye, use three primary colours, and for the other eye, use three OTHER primary colours. The filter for each eye only lets through the primary colours intended for that eye. (For a given perceived colour, there are many ways of mixing it out of narrow-band “primary” colours”.

  7. Thanks, Phillip! I’m glad to know what’s really going on. I’m going to quote this in a new post, so that possibly more people will see it.

  8. Ted,
    I agree with your assessment of being pleased with the story. Since my background is in social media and social marketing, I asked my “tribe” if it was worth seeing. I got varying opinions, most of which were very positive. I think most were due to the fact we all had our expectations set fairly low (as I think you did as well.) It really was all uphill from there…
    What I did have a problem with was feeling somewhat nausious from tilting my head up and down since i have bifocals.

  9. The colored 3d glasses are very old, from 1960 or something like that.. but you are wrong! They are still used in our days, probably you’ve heard of Journey to the center of the earth or my Blody Valentine, and there are others 😉

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