Polarized3Dglasses test

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Right: visualization and comparison of circularly and linearly polarized light. The helical wave can be interpreted as a superposition of two waves polarized in orthogonal planes and a relative shift of a quarter of the wavelength. Without this shift the superposition is again linearly polarized as shown in the lower part of the figure. The arrows represent the electrical field strength.

The quarter wave plate is exactly "quarter wave" only for a single wavelength. The best choice for that is at the maximum sensibility of the eye, about 555 nm. As a consequence, the left glass which should block right circular light, lets through a little bit of long-wave (red) and short-wave (blue) light; instead of black in Figure 1, we see dark violet which is a mixture of red and blue. Correspondingly, linearly polarized light after passing the λ/4 plate is exactly circular only for the one wavelength; for other wavelengths a small percentage of the opposite handedness remains. Visualizing the electric field on a fixed point by an arrow, the arrowhead moves along an ellipse (elliptical polarization).

The light reflected by the glass plate is horizontally linearly polarized, as the reflection angle is very close to the Brewster angle.

The polarization is changed by the quarter wave plate (of the filter in front of the camera's objective) to circular for λ = 555 nm. For longer waves the optical path difference is less than λ/4, elliptical polarization results, with the long axis of the ellipse horizontal. (If the retardation is zero, the light remains horizontally polarized.) For short waves the shift is larger than λ/4, now the shorter axis if the ellipse is horizontal. Therefore, seeing horizontally polarized light through the 3D-glasses, more than 50% of the long waves are transmitted and less than 50% of the short ones which shifts the grey colour to reddish-yellowish. Rotating the filter by 90° (Figure 9) (or tilting one's head with the 3D-glasses by the same amount) the light reflected by the horizontal glass plate is seen bluish.

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Polarisation 3dcamera

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Figure 4 shows the glasses lying on glossy aluminium foil. There is nothing peculiar to be seen, the mirror image is somewhat blurred but otherwise looks as expected. This is no longer the case in figure 5 where the object is reflected by a black glass plate. The mirror image has darker lenses than the original. Turning the glasses around (figure 6), this is reversed.

For RealD® 3-D movies the viewers have to use special glasses which look like sunglasses. The lenses are filters which either block circularly polarized light or convert it to linearly polarized light which then is seen. The image for the right eye is polarized right circularly and is blocked by the left lens (and vice versa). If lit from behind, the right glass creates right circular polarization, the left one performs correspondingly.

How polarized3Dglasses work

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If the optical path difference is increased, the red light is blocked more and more while the intensity of the transmitted blue light goes up, yielding dark blue colour. Contrary to this, decreasing the retardation lets more red and yellow light pass while the blue is blocked more strongly, yielding brown (which is dark orange-yellow).

Polarized3Dglasses video player

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Let us trace one ray: it first passes a linear polarizer, then the λ/4-layer on top of it, after a short distance through air the λ/4-layer and then the linear polarizer of the opposite second spectacle lens.

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For the next three pictures, the right lens of RealD 3D glasses has been used as a filter in front of the camera's objective lens. Figure 7 shows that the handedness of the circular rays is flipped when reflected by a metal surface. The blue colour (instead of violet) again is due to the inclined viewing angle.

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If now the incident light is linearly polarized at an angle of 45� to the optical axis of the quarter-wave plate, the outgoing light is circularly polarized. Conversely, circular polarization is converted to linear by a λ/4 plate.

The spectacle lenses are horizontal linear polarizers next to the eye to which a retardation foil is laminated. For the right glass, its fast axis goes from top left to bottom right, for the left glass it goes from bottom left to top right.

Note that in the left image, the dark areas are not black, but dark purple. In the middle image, where the first glasses are rotated, the dark area is black. Looking aslant through the opposed glasses, blue and brown colour is seen.

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Polarisation 3dglasses

What you see is due to the fact that the handedness of circularly polarized light is flipped when reflected by a metallic surface, and that the light reflected by the glass plate is linearly polarized at the chosen observation angle.

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Polarized3Dglasses video

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Linear polarization can be converted to circular by means of a birefringent layer, a so-called quarter wave plate or retardation sheet. If the retardation sheet consists of stretched plastic, the molecules of the polymer are aligned in the stretch direction which is called the optical axis or "slow axis", as the speed of a wave oscillating in this direction ("extraordinary ray") is smaller than that of a wave oscillating perpendicular to it in the direction of the "fast axis" ("ordinary ray"). If the retardation is 90� corresponding to a quarter wavelength, this optical device is called a quarter-wave plate.

Polarized3Dimages

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A right circular wave, to the left represented as the sum of two linear waves, to the right visualized by an animation which ist switched on by a double and off by a single click.

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In movie projection, this undesired admixture of colour can completely be avoided. It is only necessary that the polarizing filter at the projector is rotated 90° with respect to the analyzing filters in the eyeglasses. The second figure demonstrates this. The second quarter wave plate undoes the effect of the first one and the extinction is as good as that of two crossed linear polarizers.

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The glasses in the left half of figure 3 are tilted about the slow axis, those in the right half about the fast axis of the retardation layers. By the tilting, the path length within the plates is increased which increases the optical retardation. Tilting about the slow axis, this is the only effect, the retardation becomes larger. When the tilting is about the fast axis, the refractive index of the extraordinary ray decreases as the electric field is no longer parallel to the optical axis. This more than outweighs the increased path length, leading to a net reduction of the retardation.

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The two quarter wave sheets are equivalent to a half wave plate which converts horizontal to vertical linear polarization, but again exactly just for one wavelength (555 nm) which means that some red light and some blue light is able to pass the sandwich, as seen in Figure 1.

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Our eyes are not equipped to detect polarization. Moreover, circularly polarized light is rare in natural environments. Therefore, the following photographs, except the first one, seem to be weird.

If the light goes through the retardation plate at an oblique angle, the wavelength changes for which the "λ/4 condition" holds. The effect of this can be seen in figure 3. The explanation is a little bit involved.