Searching for Sub-Visual Atmospheric Structures in the Daytime Sky

On sunny, warm days the sun heats the Earth’s surface and the air close to it. Periodically a parcel of air will rise from this area due to the warmed air being buoyant. This parcel is thought to rise in an elongated column of fairly large size such that several hundred tons of air are lofted skyward. In doing so many of the particles generated by Earth-bound processes (pollen, smoke, dust, pollution, water vapor, etc.)  are brought with it. These particles are commonly known as aerosols. If the column reaches an altitude where the contained water vapor condenses then a cumulus cloud will form.

It is known that aerosols have a large effect on polarization of light, up to 30% or so. My first experiment in photographing these columns of air was to take 2 sequential photos of the sky with a linear polarization filter set to 90 degrees apart. Then in accordance with the article excerpt shown below and using an image processing program (Image Magik) I calculated the degree of linear polarization (DOLP) of each pixel from the formula given in the article. The resulting pictures are interesting and strange but do not show the expected structures.

I encourage others to make their own attempt at this goal as I am really a novice at image processing. No doubt there are many other ways of looking at this problem and I welcome all comments, thoughts and ideas. Thanks!

Excerpt from the article “Digital All-Sky Polarization Imaging of Partly Cloudy Skies” from Nathan J. Pust and Joseph A. Shaw

“It is our feeling that unseen aerosols and possibly thin clouds in what has recently been called the “twilight zone” between a cloud and the clear sky are reducing the DOLP in what appears to be clear sky. We believe that this effect on the sky polarization is directly related to the recently described observations of enhanced optical depth near clouds. In partially cloudy skies, we see DOLP reductions in clear sky areas between clouds that appear to be caused by subvisual aerosols and/or clouds. (Even though clouds appear to have hard edges, they are in fact surrounded by thin clouds.) Furthermore, these DOLP reductions show up in the clear sky long before we can physically see clouds in the sky.”

To determine Degree of Linear Polarization (DOLP) in each pixel he uses this formula:
(Image1pixel value – Image2pixelvalue) / (Image1pixel value + Image2pixelvalue)

Then he normalizes and stretches the result so it fills the whole 8 bit range of 0 to 255 pixel brightness values.

Some of my resulting pictures:

Author: Deane Williams, Connecticut, USA

The black drop effect is not an atmospheric phenomenon

The so-called black drop effect is an optical phenomenon which can be seen during transits of Mercury or Venus in front of the sun. It can only be observed through a telescope protected against the bright sunlight. When the planet begins to cover the sun, it seems as if the silhouette of the planet would form a kind of black drop when it detaches from the rim of the solar disk. The same effect appears again when the silhouette touches the rim of the solar disk at the end of the transit. It looks as if the planet merges with the rim of the solar disk like two converging drops of water.

Originally astronomers thought that this phenomenon was caused by different refraction of light in the atmospheres of the planets. But today we know that the phenomenon is caused by the limited resolving capacity of the telescopes used. In this context experts often refer to an experiment which everybody can realize using his own fingers:

Just form a ring with your thumb and your trigger finger, but exactly so that the fingers just do not touch each other. Hold this narrow gap in font of your eyes, so near that  they cannot focus it. A “shadow bridge” appears between the fingers, especially when the fingers are held in a different distance from the eyes and you start closing the gap by changing the perspective. The shadow bridge then moves from the finger which is further away from your eyes to the closer one.

Shadow bridge between thumb and trigger finger. The camera had been focused behind the fingers

The gap between the fingers has been exactly focused a no shadow bridge appears

Important for the successful execution of this experiment is that your eyes are defocused. If you move the fingers away from your eyes so that they can focus them, the shadow bridge completely disappears.

I slightly modified and analyzed this simple experiment. Instead of two fingers, I only used one, but in front of a pattern of blue and white stripes.

Shadow bridge experiment No.2: Heavily defocused photograph of my trigger finger in front of a background of blue and white stripes

With this method I observed two sources of fuzziness , which are the silhouette of the dark brown finger and that of the stripes. In front of the dark stripes, the area of fuzziness of the finger appears more tangent than in font of the white ones. This gives the impression of the finger being as double as wide in front of the blue stripes compared to the white ones. In reality, however, the fuzziness of the finger is always the same as I tried to keep it parallel to the background and perpendicular to the line of sight. The most interesting area is that where the fuzziness of the finger meets the fuzziness of a blue line. There it also causes a deeper tinting of the blue area. As a consequence, a kind of dark “mound” forms in the zone of fuzziness of the blue area which points in direction to the finger tip. Moving the finger so, that its silhouette touches the outer rim of the fuzziness between the blue and the white line makes a shadow bridge appear.

Completed “shadow bridge”

Using this knowledge, you can easily simulate a transiting planet yourself. The experiment is very simple. Just draw a white circle with a black background on your computer and print it. Then die-cut a circle out of a sheet of black paper using a hole puncher. You only need the chad to represent the planet. Put this on a clear CD-cover and put this onto your printed solar disk, so that the planet lies as near to the rim of the solar disk as possible. Here are an animation and two photos illustrating the black drop effect, an exactly focused one with no black drop effect, and another, defocused one, in which the black drop effect appears.

Simulated black drop effect. The picture on the left is exactly focused and shows no “shadow bridge”. The photograph on the right is defocused and shows a “shadow bridge”

Author: Reinhard Nitze, Barsinghausen, Germany