What is a polarization compass?
The sky appears blue because air molecules scatter some of the light from the sun towards ours eyes. Scattering also polarizes this light. Over most of the sky, light is linearly polarized to some degree, with the vibration perpendicular to a plane that includes the sun, the scattering molecules and the observer. If you look at a patch of blue sky with a polarizing filter and you rotate it for maximum darkness, the transmission axis will point along a great circle through the sun.
The sky is only partially polarized as a part of the light remains unpolarized. Thus, a polarizer can only darken the sky somewhat but not block it. The human eye is not very good at estimating absolute light intensities making a simple filter a rather poor sky polariscope. A better polariscope is obtained by using two filters side-by-side with the transmission axes perpendicular to each other. It is aligned by finding the maximum intensity contrast between the two. This kind of differential polariscope and its variations (e.g., Minnaert polariscope) are easier to align because the brain is good at distinguishing differences in intensity. The brain is even better in distinguishing small variations in color and the Skylight Compass takes advantage of this capacity.
What is the Skylight Compass?
The Skylight Compass (TM) is a differential polariscope where a pair of dichroic filter windows form two points of a compass. The dichroic filters are made of parallel polarizing filters backed by birefringent films of different retardation. The axes of these films form an angle of 45 degrees with the polarizers.
When looking through the card at an unpolarized background, e.g. a cloud, both points are uniformly gray. Likewise, if the background is linearly polarized in a direction forming 45 degrees with both compass points, they remain gray. But if the compass is rotated (with the same polarized background) the compass points will acquire different colors. Maximum color contrast is obtained when one compass point is aligned with the electrical vibration of the light and the other is perpendicular.
How to use it
Select a patch of BLUE sky that is NOT close to the sun, NOR is it directly opposite to it, as those regions have little or no polarization. Clouds are not polarized and any haze in the sky will also decrease the effect. Look at the FRONT (yellow side) of the card at arm length, so that the card is perpendicular to your line of vision. Notice the color of the sky that you see through the compass windows. Rotate the card until the contrast of colors is maximum. One point will be a yellowish green and the other a bluish purple. Then the green point will point to or from the sun (or, more precisely, along a great circle through the sun). Conversely, the purple point will be aligned in the same direction as the polarization of the sky (i.e., its electric vibration vector).
What is the best region of the sky to look? Best time of the day?
Polarization is maximum at 90 degrees from the sun. For example, with the sun south, halfway between the horizon and the zenith, maximum polarization will happen west and east at the horizon or halfway toward the zenith looking north. During twilight (sun slightly below the horizon) the polarization at 90 degrees can reach 75% (strongly polarized). On the other hand, at 45 degrees from the sun the degree of polarization decreases to 30% or less. Looking at the zenith at dusk, with a clear sky, is your best bet (it helps that towards the zenith the atmosphere is the thinnest and depolarization by multiple scattering is minimized). Remember that the contrast of colors is proportional to the degree of polarization. Atmospheric haze decreases it, so don’t expect good color contrast with whitish skies.
What else can I do with it?
The card is essentially a polariscope that detects linearly polarized light. Reflected light tends to be polarized. You can look at those reflections with the card and find the direction of polarization and estimate the amount. Rotating the compass until the image acquires a maximum bluish tint will align the respective point with the polarization. Examples of reflections to look at, include puddles, windows panels, varnished tables, and shinny leaves. Or look for other ideas elsewhere in this site.