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devil duck

a physics puzzle

So last night after Thanksgiving dinner, we went to see "Bolt". Which was a lot of fun, and heart-warming, and all, and gorgeous computer graphics and all, but that's for another post.

It's also in 3-D, which is usually accomplished by showing slightly different pictures to the left and right eyes to create parallax. Now, a few decades ago, this was done with one picture in red and the other in green; everybody wore glasses that were red on one side and green on the other (which puts severe limits on the use of color in the movie!). Obviously, all right lenses in the theater must behave the same, and all left lenses must behave the same, in order for different customers to see roughly the same effect. And, insofar as possible, light that passes through left lenses must not pass through right lenses, and vice versa, in order to achieve cleanly separate pictures.


We brought home two pairs of glasses. I had heard that it was being done now with polarization these days, to allow a full range of colors. I assumed that right lenses would be vertically polarized and left lenses horizontally (or vice versa). This would produce the following effects, if you positioned two lenses in the same line of sight between you and a light source:
R to R, right side up or one upside-down -> fairly clear
L to L, right side up or one upside-down -> fairly clear
R to L, right side up or one upside-down -> dark
R to R, one rotated 90 degrees -> dark
L to L, one rotated 90 degrees -> dark
R to L, one rotated 90 degrees -> fairly clear

So just to confirm that this was what they were doing, I checked. Here's what I actually observed:
R to R, right side up or one upside-down -> fairly clear
L to L, right side up or one upside-down -> fairly clear
R to L, right side up or one upside-down -> somewhat dark, purple
R to R, one rotated 90 degrees -> fairly clear but bluer
L to L, one rotated 90 degrees -> fairly clear but bluer
R to L, one rotated 90 degrees -> dark

WTF?

Two questions occur to me. First, how did they achieve this combination of effects? (My last physics class was in 1981....) Second, why? I would think that to maximize the 3-D effect, you would want any light that got through one lens to be maximally stopped by the other, i.e. "dark", not "somewhat dark". If we assume that they did do that, then one of the lenses must be not simply passing light through but modifying it.

In which case the lenses might behave differently front-to-back than back-to-front. All the above observations were made face-to-face, i.e. with the "outside" of one lens facing the other, so light was going in the back of one lens, out the front, in the front of the other and out the back. So let's try
back-to-back, so the light is going in the front of one lens, out the back, in the back of the other and out the front.
R to R, right side up or one upside-down -> fairly clear
L to L, right side up or one upside-down -> fairly clear
R to L, right side up or one upside-down -> fairly clear
R to R, one rotated 90 degrees -> dark
L to L, one rotated 90 degrees -> dark
R to L, one rotated 90 degrees -> dark

Now let's try both facing the same direction.
R to R, right side up or one upside-down -> fairly clear but yellower
L to L, right side up or one upside-down -> fairly clear but yellower
R to L, right side up or one upside-down -> fairly clear but yellower
R to R, one rotated 90 degrees -> fairly clear but bluer
L to L, one rotated 90 degrees -> fairly clear but bluer
R to L, one rotated 90 degrees -> fairly clear but bluer
(BTW, none of these depend on whether the lenses are both facing the light, or both facing me.)

Let me point out the most surprising observations again:
R to L right-side up, back to back -> fairly clear
R to L right-side up, front to front -> somewhat dark, purple
That is, the light is going through the exact same two lenses, in the same direction, but it makes a difference which one it goes through first.

R to R right-side up, back to back or front to front -> fairly clear
R to R right-side up, front to back -> fairly clear but yellower
This time, the light is going through the exact same two lenses, in the same order, but it makes a difference whether it goes through them in the same direction or opposite directions.

R to R, one rotated 90 degrees, back to back -> dark
R to R, one rotated 90 degrees, front to front -> fairly clear but bluer
R to R, one rotated 90 degrees, front to back -> fairly clear but bluer
The light is going through the exact same two lenses, but if the front of either or both is facing the other, you get a different effect from if the backs of both are facing one another. It's an OR gate.

Then think about the color shifts. I could imagine a certain combination of polarized lenses or diffraction gratings or something selectively stopping low-frequency light while allowing through high-frequency light whose wavelength is smaller than the grating. But what would selectively stop high-frequency light? Or is it a matter not of "stopping" but of destructive interference at particular frequencies and constructive interference at others?

OK, so what can I conclude?

  1. the lenses do not simply "pass or not" a given photon; they change it, so the lenses aren't idempotent (i.e. passing through several of the same lens in a row isn't the same as passing through one).

  2. the change passing through a lens from front to back is considerably different from the change passing through from back to front of the same lens.

  3. 90 degree rotation does make a difference (unlike with the red/green lenses), but...

  4. the change is not equivalent to a 90 degree rotation, and

  5. one lens is not equivalent to a 90 degree rotation of the other.

  6. it's too late at night to figure this out.


Comments

The lenses are polarized. http://en.wikipedia.org/wiki/Polarization

In one lens only up-down lightwaves pass, in the other only right-left waves. If you take two of these glasses and hold the left lens of one over the right of the other (with the glasses oriented the same way) no light should pass.

The camera has matching polarizing filters left-right, and the projection screen has to be silvered to reflect the light correctly, a white screen won't work.
That's what I thought they were doing, but they're not; read the post again. A right lens rotated 90 degrees does not act like a left lens. Even weirder, it makes a difference whether light goes through a lens from front to back or back to front. And it makes a difference in which order light goes through two lenses.
This may be that they are manufactured cheaply, but you should speak to Brian, the serious stereo hobbyist in the family.
Are they circularly polarized?
That's what I was wondering, but I don't really know what circular polarization is or how it works. Would it produce the results I described?
so Brian sez, yes, they are circular. The lenses are like two nuts - left hand thread and right hand thread. The advantage being you can tilt your head and not lose the picture. Cool.

http://en.wikipedia.org/wiki/Disney_Digital_3-D

Oh, and polarized 3d was available in the '50s. They did the inferior anaglyph in the 70's because it was cheaper. That famous picture of the theatre full of people with red/green glasses on from the 50s was photoshopped to look like that - the original shows plain glasses.
I just looked at the Wikipedia article on Disney Digital 3-D, which mentions the 72-fps projector with alternating polarization screens and refers to the wikipedia article on RealD 3-D, the underlying technology. This article discusses the 72-fps projector with alternating polarization screens and refers to the wikipedia article on circular polarization. This last article provides equations for electromagnetic waves, but doesn't say anything about the practicalities, e.g. what does a circularly-polarized filter DO? In short, nobody has said how the system works.

So let's see what I can figure out, based on the physics I remember from high school. Light in general has electrical and magnetic waves of equal frequencies, perpendicular to one another. In the most straightforward case, they're in phase with one another, so the total amplitude follows a sine wave over time. In circularly polarized light, the electrical and magnetic waves are 90 degrees out of phase so as one is decreasing in amplitude, the other is increasing, and the total amplitude is constant over time. (If they're out of phase by something other than 90 degrees, it becomes "elliptical polarization", and the total amplitude varies over time but never quite drops to zero.) Depending on whether it's +90 or -90 degrees, the energy vector may be rotating clockwise or counterclockwise.

Now, using this for movie projection. Circular polarization has the advantage that, as you point out, you can tilt your head to the side without changing the picture at all. Presumably one lens acts like a right-handed screw and passes only clockwise-polarized light, while the other does the opposite, and the Z-screen alternates 72 times a second between those two roles. It does sound like a great way to achieve a 3-D effect.

So how should such lenses behave?
[see next comment]

How should circularly polarized lenses behave?

A right-handed screw is still a right-handed screw if you rotate it around its axis, or if you look at it from the opposite end, so it shouldn't matter whether you rotate a lens 90 degrees, nor whether light goes in the back and out the front or vice versa.

R to R (rotated 90 degrees or not) (face-to-face, back-to-back, or front-to-back) -> fairly clear
R to L (rotated 90 degrees or not) (face-to-face, back-to-back, or front-to-back) -> dark

That's not at all what I observed.

So maybe it's not really circularly polarized, but rather elliptically polarized: each lens acts like a right-handed or left-handed screw that has been squashed so it's elliptical in cross-section, so it has a preferred rotation (clockwise or counterclockwise) and a preferred transverse axis (e.g. vertical or horizontal). I can't think of any reason they would do that, since the circular solution described above is so much simpler and not subject to head-tilting phenomena. Anyway...

This would explain why 90-degree rotation of a lens makes a difference, although I would expect it to be of the "fairly dark" rather than "dark" variety.

If two different right lenses were both made of the same polarizing material but mounted in their frames at different angles (say, a cheap manufacturing process), they would both work perfectly well for watching the movie, but light passing through two of them would vary from clear to fairly dark depending on the angle between their transverse axes. In fact, I get "fairly clear", but varying in color, depending on the angle of rotation. I guess it's plausible that passing through two "squashed screw" lenses could prefer high frequencies over low frequencies, or vice versa. So this part of the observations might be consistent with the hypothesis.

Light shouldn't care whether it passes through a lens front-to-back or back-to-front, except that those two may have different transverse axes; any lens front-to-back should, with suitable rotation, act just like itself back-to-front. That's not what I observed: the only times I ever got effectively 100% absorption were when light passed through one lens front-to-back and the other back-to-front.

Light passing through one lens front-to-back, and another back-to-front, shouldn't care which one it passes through first, but only whether they're polarized with the same or opposite rotations, and how many degrees apart the transverse axes are. In fact, it does matter which lens the light passes through first. I thought perhaps the first lens the light passes through was imposing not only a polarization limitation but also a phase limitation, but then I would expect the effect to differ with how far apart (in wavelengths) the two lenses were. Since my hand-held lens positioning isn't precise down to visible-light wavelengths, I would expect to see different colors depending on the distance, and probably even different colors from one edge of the lens to the other. I don't see that; I see consistent, replicable effects that are the same over the whole lens.

So I'm still puzzled. But learning things about circular polarization....

(Anonymous)

Circular Polarization

M. Sheahan sent me a link to your blog on 3D. I've been a 3D addict since childhood. The old 3D technique for movies and projected stereo slides used linear polarization at 45 degree orientation (\/). The new stuff is weirder and I'm still trying to figure it out. You may have already found this link
"http://www.nsm.buffalo.edu/~jochena/research/opticalactivity.html". Polarizing filters for cameras use circular polarization - I was told this was done because it doesn't throw off the auto-focus or exposure. The filters act differently in different directions (back/front). I have not been able to understand why a circularly (or elliptically) polarized filter would act on linearly polarized light the way it does (polarized sunglasses cut glare off the road) Specularly reflected light off non-metallic surfaces at approximately a 53 degree angle is quite polarized. The peak of this phenomenon occurs when the transmitted and reflected light are at right angles. (Does this mean you could determine the index of refraction of opaque materials?)

Other interesting subjects: The Pulfrist effect (3D motion video with ordinary equipment) and depth of field as it relates to sensor size in digital cameras. "http://www.wrotniak.net/photo/tech/dof.html#TABLES" . Some of this makes my frontal lobes ache.

- TL