If you take a left- and right-handed circular polarizer and you lay them on top of each other on a light box, you will see that they will extinguish the light.  Do the experiment by using the filters from a pair of glasses from a MasterImage or a Real D show and put the polarizers together so that the retarders are facing each other (those are the sides of the filters that are facing the screen). If you rotate one with respect to the other you will see that the extinction varies.  What’s going on here?  It’s circularly polarized light and you would think that you wouldn’t get a variation in extinction as you do for linear.  But you do get a variation and you will see that the image will go from pretty dark to, depending upon the material you’ve got, a sort of amber color that transmits more light. There is quite a noticeable variation in both density and color with rotation. So the head orientation does matter, except that the falloff isn’t as great as it is for linear polarized light. (You can also hold the filters sandwich up to a light source – like a desk lamp.) If you flip the filters around the other way so the retarders are facing outward you have linear polarizers and you can try rotating them to confirm that they work as described earlier. You will note that even for the circular case you perceive the extinction to be at a maximum when the linear axes components’ are at right angles. 

With circular polarization the extinction at its maximum is never as good as linear polarizers.  In fact, it’s usually an order of magnitude less.  The reason for this is that for the retarders used for 3D selection the phase shift can be maximized only for a specific wavelength.  That means that the retardation for “green” at about 550 nanometers may be chosen but for the rest of the visible spectrum on either side (in others words, towards the red and blue ends) the less effective the retarder.  Thus only the green can be properly analyzed.  Moreover we cannot assume that the values of the retarders for the polarizer and the analyzer match.  This is actually is a rare occurrence because of the slack manufacturing tolerances for this product. 

In order to get the maximum extinction the linear polarizer component of the projector polarizer and of the analyzers have to be orthogonal.  That’s what was demonstrated in the above experiment.  For circular polarization projection the audience must be wearing analyzers that have left and right handed polarizers, and the same kind of metallic polarization-conserving screen used for linear is also used. To recap: The circular polarizers are made up of two pieces of plastic: one that is a linear polarizer, and the other that is the quarter-wave retarder.  The axis of the quarter-wave retarder has to be at 45 degrees or 135 degrees to the linear polarizer’s axis.  This is true for the analyzers and this is true for the polarizers on the projectors.  You may be able to see a color shift if you tip your head during a circular polarization projection. 

It is often said that circularly polarized light for image selection can help with the head-tipping issue related to linear polarizers and the law of Malus. I think that it is not as big an issue as it has been made out to be by its advocates.  After all IMAX and theme parks have been using linear polarizers to good effect for years.  Both Real D and MasterImage must use circularly polarized light because of the physics of the ZScreen (Real D) and the spinning mechanical filter device (MasterImage).  For MasterImage, for example, attempting to use the same kind of a spinning device with linear polarization would produce a reduction in dynamic range because of the rotation of the polarization axis of the sheet polarizer as it spins in front of the projector lens. 

As I mentioned, the dynamic range of circularly polarized light is a lot less than linearly polarized light.  That means that you’re lucky to get something like 20:1 dynamic range from the light that is reflected from the screen and analyzed by the analyzers in the eyewear – which is about an order of magnitude less than you get from linear polarized light.  It’s interesting to see how the universe gives and takes.  On the one hand it gives us a high dynamic range for linear, but with a head-tipping constraint; on the other hand it gives us a low dynamic range for circular, with less of a head-tipping constraint. 

There is extensive literature on how to handle crosstalk that arises from circular image polarization image selection, and it was offered to StereoGraphics (the company I founded in 1980) over the years by different people and that is the concept of the anti-ghost.  When you look at a stereoscopic image through a selection device, whether it’s linear or circular, there is a certain amount of light that leaks through (as noted earlier it’s called leakage) because of the incomplete extinction of polarization.  This leakage results in what is called a “ghost image.”  So there is some crosstalk between the left and right images, and you may see a bit of the left image through the right eye and vice versa. It can look like a double exposure. One way to deal with this is to create an anti-ghost.  The anti-ghost has the opposite density of the ghost, and it can be created by any one of a number of algorithms.  The anti-ghost is added to the print so that it will perceptually cancel out the ghost. 

It is an improvement but it is not a cure-all.  For one thing, ghost images and their perception are a function of several factors including parallax.  If the image has low or zero parallax the ghost corresponds to the image itself and you won’t see it.  In high-contrast images, let’s say for example the moon against a black sky; you are going to see the ghosting more than you’ll see it in other circumstances.  And finally, if the image has a great deal of textural complexity – in other words, lots of leaves in the jungle – the ghost tends to be very hard to see. Since the anti ghost is dark it cannot work with dark backgrounds since it cannot be blacker than black – so just where it might be most useful it has no benefit — like the moon against a black sky.


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