What is the effect of an achromatic retarder with cross-polarized crystals?

[Leonardo]

An example: https://www.reddit.com/r/Optics/comment ... _circolar/

Maybe I missed something, several people point out the dependence of phase shift on wavelength but why the dramatic violet/magenta color? I haven't seen anything like that with the circular polarizing camera filters I have or plastic sheets with optical path difference less than 1/2 green wavelength or so.

You need to flip both circular polarizer in the "right way" to reproduce the purple light. This is the explanation (from the reddit thread):

The circular polarisers have poor extinction ratios in the violet. circular polarisers have a quarter wave plate which is designed to give a 90 degree phase difference between the two linear polarisation states. The amount of phase difference depends on the length of the material in wavelengths, which means that for when you have the correct length at one wavelength you are too short or too long at another wavelength. The more off the thickness, the less circularly polarised it will be. This then causes the extinction ratio to be worse at wavelengths far from the design wavelength (probably green or yellow)

[rjlittlefield]

You need to flip both circular polarizer in the "right way" to reproduce the purple light.

I think it's even more demanding than that. To get extinction, we need to either have one left-circular and one right-circular, or we need to bounce the light off a mirror to change the handedness. There's no mirror in the setup as shown, so apparently one of the CP's is left-circular and the other is right-circular.

This can get confusing in a hurry, because even two CP's bought from the same manufacturer at the same time may be the same handedness or different. (I have in hand an example of a mixed pair.)

So, to make things more clear, I have reproduced the experiment using RealD 3D glasses, which of course have to be consistent in order to work correctly.

Here's the setup. Note that with these glasses, it's the screen side that is circular so those are the sides that have to be facing.



Here are the results of overlapping the lenses in various ways.

• Upper left is with the two right-eye lenses aligned, so the handedness is the same. In this configuration there is no extinction.
• Upper right is with one glasses flipped, so now we have left-circular facing right-circular on both sides. This should give extinction, but the result is only partial extinction with a lot of leakage due to imperfect retarders.
• Lower left shows no-extinction versus partial extinction using just one lens of the foreground glasses.
• Lower right shows no-extinction versus greatly improved extinction from rotating the foreground lens by 90 degrees.

To understand these results, it helps to know that the linear polarizers for both lenses are oriented the same way. (That way is the opposite of sunglasses; they have to be turned 90 degrees to block reflections from a water surface.) The waveplates will be at 45 degrees, one tipped left and the other tipped right.

So, when we turn the glasses around so that a left-eye lens is facing a right-eye lens, as in the upper right panel, we have a sandwich consisting of a linear polarizer, two nominally 1/4-lambda waveplates with the long axes facing the same direction, and another linear polarizer that is parallel with the first. For wavelengths where the waveplates really are 1/4-lambda this results in extinction, which I can think of as either "left-circular blocks right-circular" or as "1/2-lambda at 45 degrees rotates polarization by 90 degrees so the light is then blocked by the second polarizer". But for wavelengths where the waveplates are not really 1/4-lambda, the blockage is incomplete and we get leakage. On the other hand, if we rotate one lens by 90 degrees, as shown in the lower right panel, then the two waveplates are at 90 degrees to each other, so their effects cancel, and then we essentially just have crossed polarizers which have good extinction.

Based on only the results shown here, we might expect that the projection linear polarizers would be aligned perpendicular to the glasses because that would minimize crosstalk with only a small hit to transmission. But as I understand published descriptions, for example the patents referenced by https://en.wikipedia.org/wiki/RealD_3D , the projectors use an electronically switched circular polarizing element whose characteristics I don't know anything about. So for the moment my conclusion is that I have no idea how the RealD 3D projection system is set up. Clearly I need to pay closer attention the next time I go to a 3D movie!

An example: https://www.reddit.com/r/Optics/comment ... _circolar/

Maybe I missed something, several people point out the dependence of phase shift on wavelength but why the dramatic violet/magenta color? I haven't seen anything like that with the circular polarizing camera filters I have or plastic sheets with optical path difference less than 1/2 green wavelength or so.

I can think of a couple of reasons why you haven't seen anything like that.

First is that you might have overlooked that the example was using two circular polarizers in a configuration that logically should have produced extinction. That's not a common configuration, so it might have escaped your attention.

Second is that your polarizers might be different from what's shown in the Reddit post. When I go to Edmund Optics to look for retarders, I see that I can buy essentially three different classes. First, there's polymer film in nominal 1/2-lambda and 1-lambda, which has wavelength dependence almost like what we'd expect from quartz. Second, there's polymer film in nominal 1/4-lambda, which is called "achromatic" because it has a lot less wavelength dependence, though still significant. And finally there are the very expensive "precision achromatic" waveplates.

Here are Edmund's retardance graphs for the three classes.

Film but like quartz:


"Achromatic" film:


"Precision achromatic":


If your experiences are with what Edmund Optics calls "achromatic film", but the Reddit polarizers were made with non-achromatic films, that would also go a long way toward explaining differences.

I had also been avoiding mentioning rotation. Some specific states in the sequence are rotations of others but the sequence viewed continuously doesn't look much like rotation. And talking about rotation seems to lead easily to confusion with circular birefringence/optical activity as in the earlier thread you linked and others.
...
Not sure reversing/retracing is the best way to describe it since as you mention the handedness switches when passing 180 degree phase difference and I believe that makes every state from 0 to 360 degree phase difference unique? In other words, while the ellipses traced out by the field vectors do repeat in reverse order after passing 180 degrees of phase shift, I think the actual polarization states do not?

All are excellent points, more thinking required. Thanks for pointing out these problems!

--Rik

[Leonardo]

Here another exercise to better understand the effect of a retarder:

Take a small Liquid Cristal display and put it in front of an LCD monitor, rotate it to block the light and you get something like this

lcd blocking light

Now what happen if you put some protective film (cellophane) in between?

protective film

The protective film is acting as retarder and retards different wavelengths by different amounts, resulting in a wavelength-dependent transmission through the polarizer-retarder-polarizer. The different colored bands in the "rainbow" are because the retarder is bending.

If you try turning the retarder at a slight angle to the polarizers, you will observe the colors change. What is happening is that the light travels a longer distance to the film when the film is not perpendicular.

[hans2]

Ok I think I see now, I was confused about how to get such vivid color with half wave or less path difference since transmission varies slowly relative to RGB sensitivity functions. But for a null it doesn't really matter how broad the null is as long as green extinction is good enough relative to red/blue extinction. There is just very low total transmission. Plotted with constant path difference and polarizer/analyzer parallel it looks like this:

(Following previous discussion I added a sort of crude fading effect to the state ellipses to try to give a visual indication of which way the field vector is moving.)

Thanks to Rik's mirror suggestion I was able to reproduce the Reddit photo pretty well:

One problem I ran into with the mirror setup is that surface reflection from the filter almost completely washes out the extinction color reflected via the mirror if the filter is parallel with the mirror. In the photo the filter is tilted just enough away from parallel to separate the darker purple extinction color from the brighter pale blue surface reflection on the wall.

The variety of cases with Real3D glasses is interesting. Still trying to reason through it all, but to make sure I'm following your explanation, the alignment of the waveplates in all the cases shown should be:

• upper left: subtractive, subtractive
• upper right: additive, additive
• lower left: subtractive, additive
• lower right: additive, subtractive

Is that correct?

[rjlittlefield]

Following previous discussion I added a sort of crude fading effect to the state ellipses to try to give a visual indication of which way the field vector is moving.

Nice!

Thanks to Rik's mirror suggestion I was able to reproduce the Reddit photo pretty well:

That demo works well.

The variety of cases with Real3D glasses is interesting. Still trying to reason through it all, but to make sure I'm following your explanation, the alignment of the waveplates in all the cases shown should be:

• upper left: subtractive, subtractive
• upper right: additive, additive
• lower left: subtractive, additive
• lower right: additive, subtractive

Is that correct?

Yes, that's the way I get it.

As a cross-check, we can imagine that the fast axis of each retarder is marked by a line that runs from the center of each lens towards the hinge on the same side.

With those lines imagined, I can "see" upper left as X X, upper right as // \ \, lower left as X \ \, and lower right as // X. Then X's subtract, // and \ \ add.

--Rik

[hans2]

With those lines imagined, I can "see" upper left as X X, upper right as // \ \, lower left as X \ \, and lower right as // X. Then X's subtract, // and \ \ add.

I'm impressed you managed to keep track of all that without actually drawing the lines.

I tried stacking three pieces of some ordinary plastic sheet that is close to 1/6 wave and it shows the dark purple color and appears to get deeper extinction than the Real3D glasses. I wonder whether Real3D is actually trying to make a "good" circular polarizer and that is just the cheapest acceptable performance, or whether there is something more subtle to the design?

[rjlittlefield]

I wonder whether Real3D is actually trying to make a "good" circular polarizer and that is just the cheapest acceptable performance, or whether there is something more subtle to the design?

Good question! The engineer in me wants to think that they optimized for overall cost effectiveness, which I assume would factor in whatever non-ideal behavior their projectors have. But I have no information other than general principles and what few details I have noticed in the patents. If anybody can find some more solid information, I would like to know it also.

In the meantime, all this discussion has prompted me to assemble a simple demonstration of why waveplates are so useful to crystallographers.

It happens that I have handy a clear plastic ruler that is birefringent, but only weakly so.

With the glasses flipped one way to be effectively just crossed polarizers, testing the ruler at various angles clearly shows that it is birefringent, but that's about all. It gives little indication how much birefringence there is, and no clue about which axis is fast versus slow.



However, with the glasses flipped a different way so as to operate like crossed polars plus a first order red waveplate, the very same ruler now clearly shows directionality, and the resulting colors can also give a good estimate of retardance.




As I explained to a friend who has some similar interests:

The reason this works -- to make a very long story short -- is that when properly used, this type of plate moves the overall system from an operating point where small changes in crystal structure only change the appearance between black to gray, to a different operating point where the same small changes in crystal structure change the appearance between several vivid colors.

Below I have copied a bit of figure 5.50 from https://opengeology.org/Mineralogy/5-op ... ineralogy/ and added a couple of indicator bars. The red bar shows how a crystal structure of +-150 nm retardation without the plate will only show as shades of gray (variable transmission), while the green bar shows how the same +-150 nm with a 550 nm plate added will show as a wide range of vivid colors.

--Rik