# Circular polarization of variable-frequency light by 3D cinema glasses

A dominant method to obtain 3D images in the cinemas seems to be circular polarization. Separate pictures are projected with (alternating) circular polarization filters and passive glasses of the viewers block the wrong images for each eye (left-handed is OK for the left eye and right-handed is OK for the right eye, or vice versa). This allows the viewer to rotate his head, something impossible for linear polarizations, and it allows the glasses to be very cheap.

As far as I understand, all methods responsible for creating or filtering circular polarization are based on linear polarization filters with some quarter-wavelength "gaps" in between. But this only seems to work well for a fixed wavelength.

How do the glasses manage to properly filter circular polarized of any color, i.e. variable wavelength? Or are the images projected so that only three particular frequencies – "red, green, blue" – are projected for which it just happens that the glasses work with the right $N+1/4$ multiple of the wavelength?

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I guess they just let the light pass through appropriate polarization filters, the same ones you have in the glasses. I wouldn't look for complicated sciency solution where a simple one can be used :) –  Ondřej Černotík Jan 6 '13 at 9:46
Oh, do you mean just 3 independent filters behind each other so that each of them does its job for one color? One filter just seems unable to filter all right-handed light at all frequencies because the cancellation of the amplitudes doesn't occur. Do you understand my point? –  Luboš Motl Jan 6 '13 at 11:17
Now I see your problem. As far as I know, modern digital cinemas use only three colors for projecting. I suppose you can construct a quarter-wave plate or, more precisely a $(N+1/4)$-wave plate that works for the three wavelengths of interest. –  Ondřej Černotík Jan 6 '13 at 13:02

There are generally two ways that I know of to accomplish this.

• Film stacks
• Optically active film stacks

Normal film stacks are thin stacks of films of different indices of refraction and different thicknesses. With enough stacks and using generalized Snell's refraction and Fresnel coefficients you can usually manufacture fairly exotic polarization elements, even with broad spectral bands.

Optically active materials use an electric - magnetic field feedback loop to generate a circular conversion. You can conceptually think about the bulk material as made up of tiny helices of wire. An electric field will drive current in the wire, creating a magnetic field, which induces another current in the wire, etc. This effect can be used to make circular polarization elements (polarizers, rotators, etc.)

Many polaroid (which is cheap) materials are optically active. I have looked at the circular polarizers in the movie glasses and they look like polaroid to me.

So they are very likely not just three $\frac{1}{4}$ waveplates sandwiched between three sets of linear polarizers, they are probably a set of polaroids, engineered to work at the RGB wavelengths. They are probably made by JDSU, I remember a few years ago seeing a presentation by JDSU about polaroid RGB polarizers for use in 3D applications.

The circular polarizer manufactured from a chiral bulk material like polaroid is very easy to manufacture (and cheap) compared with thin film stacks and with sandwiching polarizers and waveplates...

We will soon (as in 6 months to a year) have a polarimeter in my lab which has a monochromator so that we can measure the full polarization states while scanning over wavelength, when it is finished I'll measure the full polarization properties over wavelength of a pair of these glasses and post them here...

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Very interesting... Seems insightful enough to me to accept it. Hope it's not quite wrong. ;-) –  Luboš Motl Jan 6 '13 at 20:38

It doesn't need to be perfectly half-wave.

The linear polarizer does the important part of separating the left-right eyes. It's important that there is a high level of discrimination or the image will be blurred.

But it's only necessary to partially circularize it in order to allow some head rotation. If you make the quarter wave for green light it will still be 75% correct over the visible spectrum. Especially when you only have to cover the colour gamut of the projector rather than the full visible range.

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So you're saying that for a generic frequency/color, the polarization for the right eye and left eye are some generic elliptic polarizations? Are they orthogonal to each other in the usual QM inner product, i.e. are they mutually excluding? How is this achieved? Some maths, please? I am not getting how "75% correctness" is OK. Doesn't it mean that there will be a right-eye-image pollution of the left-eye image, albeit 4 times (25%) weaker? Is it tolerable for a good experience? –  Luboš Motl Jan 6 '13 at 20:36