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Haidinger's Brush

How to see polarization with the naked eye !!!

"I can see it particularly clearly in the twilight when I stare at the zenith; the whole sky seems to be covered by a network, as it were, and everywhere I look I see this characteristic pattern. It is very pleasing to be able to determine the direction of polarization without an instrument in this way, an even obtain an estimate of its degree"  Minnaert, Light and Color in the Outdoors

Haidinger brush - horizontal Haidinger brush - Left circular Haidinger brush - right circular

The eyes of men (AND women) are not designed to distinguish between different types of polarization, contrary to insects, cephalopods, many amphibians, fish, and other animals, for which nature possesses a different class of "colors" (but even common colors do not mean the same to everyone). However, a small quirk in the structure of the human eye gives us (by accident) the ability to tell apart different states of polarization. Thanks to this small aberration or "defect" of the eye we are not completely polarization-blind.  

Yes !!! With some effort you can learn to see what remains invisible to most people! Without the help of any instrument you will be able to tell not only if the light you look at is strongly polarized or not, but also if it is linearly polarized or circularly polarized and, moreover, in which direction it vibrates or rotates. Any time that you raise your eyes to the blue sky you will be rewarded by the same clues that guide bees in their flight.  Acquire P-Ray Vision !

Discovery

Wilhelm K. von Haidinger's (1795-1871), an Austrian mineralogist and geologist, long time director of the Imperial Institute of Vienna, made several important contributions to the science of optics, including an interferometer that produces fringes in thick plates and the first report of dichroism for circular polarization (in amethysts). In 1846 Haidinger was studying minerals under polarized light, carefully trying to discern any special pattern in the refracted light. He then perceived a faint yellowish stain or brush that remained when he looked directly at the light without interposing the crystal. The brush rotated together with the polarizer proving that he was "seeing" the polarization state. That stain is now known as the Haidinger's brush, and he can be credited with the unique discovery of an extra "sense". However, more that a century and a half later, this phenomenon remains little known (even by scientists working in optics!).

In 1954, William Shurcliff (then employed by Polaroid) pointed out that the Haidinger's brush can also detect circular polarized light and distinguish the sense of rotation.

The Brush

Observers generally describe the Haidinger's brush as a diffuse elongated yellowish pattern, pinched at the center. Bluish leaves, generally shorter, cross it at 90 degrees. This pattern is created by the eye and therefore cannot be photographed and it actually changes somewhat between observers. Some people see the yellow continuous until color fatigue makes the blue continuous, while others claim that the continuous color is whichever is perpendicular to the line joining the eyes. Some only see the yellow part (but I generally notice the blue first). The pattern is considerably more diffuse and fainter than shown in the drawings and requires some practice to recognize it. Some people see it more clearly, others with more difficulty, and some may not be able to see it at all.

The yellow branches point in a direction perpendicular to the vibration plane for linearly polarized light. Thus, horizontal polarization causes a vertical (with respect to the ground) yellow brush irrespective of the inclination of the head. On the other hand, circularly polarized light generates a yellow brush slanted with respect to the line bisecting the face, even if the head leans sideways. For right-handed circularly polarized light it will go up to the right and down to the left, while the contrary will happen for left-handed light. This is true for both the right and left eye: no bilateral symmetry here (although there is some change between the eyes in the exact angle the brushes make, which depends on the individual). The way of distinguishing between circular polarized light and slanted linearly polarized light is, of course, to lean the head sidewise and note if the brush is fixed with respect to the source of light or to the eyes.

The Haidinger's brush is relatively small, occupying 3 to 5 degrees (about the size of the above drawings at arm length on a standard monitor). Interestingly, it should be affected by the same illusion as the moon and the sun close to the horizon, where it will be perceived as being about two times as big (the size perception changes with the distance of the background where it is unconsciously projected).

The effect is weak and to perceive it the light should have a good degree of polarization (at least of 60%). Because it is faint the background should be uniform with no distracting patterns. In addition, the effect only happens towards the blue side of the spectrum and is missing altogether in the red (interestingly, bees only detect polarization in the ultraviolet, although they can also see the green and blue colors). It just happens that the skylight at 90 degrees from the sun is highly polarized, uniform, and blue, making it an ideal place to see the Haidinger's brush in Nature.

How to Practice

The easiest way to see the Haidinger's brush is to practice with fully polarized light. For example, look through a sheet polarizer at a piece of white paper illuminated by the sun (but avoid any direct gloss from the paper). Instead of the paper you can also look at a white cloud.  My personal recipe is to look for, say, 20 seconds and then rotate the polarizer 90 degrees. Look again for 20 seconds and then continue rotating back and forth every 5 seconds. If you think you perceive something, rotate faster and check if the pattern switches 90 degrees each time. Rotating the filter has two beneficial effects. First, a changing pattern is easier to distinguish against the static uniform background. Second, color fatigue should help perceive the complementary color when the patterns are swapped. Looking through a green or blue filter will help.

Minnaert gives the following advice: " . . . after you observe for a minute or two, a kind of marble effect will begin to appear. This is followed by the Haidinger's brush . . . It disappears in a few seconds, but if you fix your eyes on a point close to it . . ., you will see it again . . . The task consists in learning to pick out this faint contrast . . . Practice a few times daily for a few minutes at a time. After a day or two, you will be able to distinguish Haidinger's brush fairly easily when you look at the blue sky . . ."

The Haidinger's brush for circularly polarized light is identical to the one for linearly polarized light but most reports I have seen claim that it is considerably more difficult to see. However, in his original report Shurcliff stated: ". . . the brushes appear as prominent by circularly polarized light as by linearly polarized light."  I think the difficulty people find when first trying the experiment with polarizers is that rotating the head or the circular polarizer doesn't change the pattern on the retina, as it does in the former case. You can solve this by using two circular polarizers of opposite handedness and switching between them. Alternatively, if only one polarizer handedness is available, you can replace the second one by a linear polarizer oriented to produce the opposite brush and thus enhance the contrast of the first brush.

Observing the brush in the sky

The sky is the best place to look for the Haidinger's brush in Nature.  Trained observers can see it over a good part of the sky.  The yellow branches point, in most cases, to the sun.  Some observers are able to see the change in sky polarization that occurs close to the sun, where the yellow branches can be tangential  to the sun instead of radial (see Brewster's point), in spite of the lower degree of polarization and background brightness (the sun should be blocked, of course).  Yet, for most people, just detecting the brush at about 90 degrees from the sun should be quite rewarding.  The best time to look is during twilight.

A short explanation

In 1866 H. von Helmoltz related the effect to dichroism of a pigment of the retina and this early explanation has proven well founded, although the exact mechanism is complicated and a full explanation is still lacking.

Although the brush is centered on the center of the visual field, its size is much larger than the fovea (the region of the retina where we see images with higher resolution) and thus must originate in the surrounding macular area of the retina. The fact that it has color means that the cones (and not the rods) are involved. The brush is invisible in the red, a region where the macula pigment is transparent.

The main suspect is the pigment Lutein, which is a long chain molecule that absorbs more for light polarized with the electric vector parallel to the molecular axis than for the perpendicular polarization. That Lutein is dichroic is not enough; the molecules should be aligned for the effect not to average out. A partial alignment of the molecules as concentric circles around the fovea will do, as shown in the following drawing:

macular alignment

If, for example, light is polarized vertically, sector A will have the pigment molecules on average perpendicular to the light vibration, absorbing little light. The reverse is true for sector B. Thus a four leaf pattern similar to the Haidinger brush would be produced. In the example, sector A would be blue and sector B yellow.

The macular pigment is located between the outer and inner limiting membranes of the retina, a region containing radially arranged nerve fibers, which would explain the partial alignment of the molecules. The percentage of molecules aligned is small, explaining the weakness of the effect.

This explanation is not complete as a detailed simulation does not exactly reproduce the Haidenger's brush. The outer layer of the cones is birefringent, which undoubtedly contributes to the effect and more studies are needed. Interestingly, the cornea has also a slight birefringence, with the slow axes generally slanted 20 to 30 degrees down towards the nose. This would create two preferential directions for detection of linear polarization.

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