A Very Basic Introduction to Light Scattering
(Or why the sky is blue and how polarizer filter makes the sky darker)
Scattering is a complex physical process where electromagnetic waves like the visible light, microwaves, X-Rays, and some mechanical waves like the sound, suffer some degree of deviation from a straight line due to some particles in the path that the wave would supposedly pass.
This process may be derivative from collisions between a myriad of things and from subatomic particles other than photons, like electrons, neutrons, and molecules to larger particles dust in suspension and water vapor droplets, just to mention the most common ones.
Near perfect reflections, like the incidence and emergence angles are due to the scattering process, but other types of reflections like specular and diffuse are also possible by this process.
Let's concentrate on the very basic aspects of light scattering. Believe me, it's a very complicated process to be deeply analyzed. If you're interested, here is a good starting point. Further deeper analysis is beyond the scope here.
One of the most known visual effects of light scattering is when someone sees a distant lamp on a foggy night. You will perceive that the light makes the fog visible (of course) but some other interesting effects are also visible, like halos (they are a combination of scattering, refraction and some other phenoms).
If you put some drops of milk in a water glass and point a strong collimated or focused light source through the class you will "see the light beam". The same thing will happen if you use a laser. It can be seen because of the Tyndall Effect (Willys-Tyndall scattering). The Tyndall effect occurs when the particle size in suspension or emulsion is near the wavelength of the light.
Milk is a colloid made from water, fat, cells and other substances, but milk is not exactly transparent, that's the reason to dilute just some drops on the water to make a usable colloid.
When I studied chemistry at the university, we used to demonstrate the Tyndall Effect using a beaker with something like 1cm of metallic mercury at the bottom and most of the beaker filled with distilled water. Then we passed two insulated wires with just the tip exposed, one going directly to the beaker bottom, connecting the metallic mercury to one pole of a 12V battery and the other wire, connected to the other pole. Then we started to insert the second wire on the water until it touched the metallic mercury. At the contact moment, a spark was formed and a small quantity of mercury was vaporized but immediately condensed into extremely small droplets (some nanometers to micrometer size). The result was what we call a colloid (water-mercury colloid) and it was very clear, but when we pointed a laser beam to it, the beam turned perfectly visible.
Things become more interesting when you have a powerful laser beam perfectly visible in the atmosphere.
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| The laser used as part of the Adaptive Optics System of the ESO telescopes (C) ESO - Babak Tafreshi - All rights reserved |
But the laser beam itself shouldn't be visible (it isn't in the vacuum). It occurs when the light is scattered by particles in suspension on the atmosphere.
The same scientist John Tyndall made some very interesting experiments in the late XVII century with polarized light and finally demonstrated that the cause of this polarization was mainly (not only) due to the light from the sun being scattered by particles in atmospheric suspension.
If you like to read about classic experiments, I recommend to dig about Tyndall's publications, they are an awesome lecture. Here is his famous article "On the Blue Colour of the Sky, the Polarization of Skylight, and on the Polarization of Light by Cloud Matter Generally", reproduced from Proceedings of the Royal Society of London Volume 17 of 1868-1869. You can freely download it from JSTOR.
He discusses and demonstrates the nature of why vapors made from tiny particles of solids or liquids look bluish (smoke for example). During this experiment he measured the light polarization (using a Nicol prism) of the light when it passed through a vapor filled glass tube, illuminated by an external light source. He did the polarizing angle measurements from all directions around the tube.
He had a brilliant and extremely important insight:
When a plate of tourmaline was held between the eye and the bluish cloud, the quantity of light reaching the eye when the axis of the prism was perpendicular to the axis of the illuminating beam, was greater than when the axes of the crystal and of the beam were parallel to each other.
This was the result all around the experimental tube. Causing the crystal of tourmaline to revolve around the tube, with its axis perpendicular to the illuminating beam, the quantity of light that reached the eye was in all its positions a maximum. When the crystallographic axis was parallel to the axis of the beam, the quantity of light transmitted by the crystal was a minimum.
From the illuminated bluish cloud, therefore, polarized light was discharged, the direction of maximum polarization being at right angles to the illuminating beam; the plane of vibration of the polarized light, moreover, was that to which the bean was perpendicular.
John Tyndall
Keeping it simple, this means that the polarization effect is ALWAYS at its maximum when the light source is perpendicular to the illumination axis and explains why when we use a polarizer filter when photographing the sky the darkening (polarizing) effect will be at its maximum strength when the sun is located at 90 degrees from where the polarizer is aimed. Remember that we are talking about angles on a sphere, not in a plane. This also means that when the light source is located at a zero (or 180) degrees, the effect will be minimal.
He continued this awesome experiment trying to figure the nature of the bluish color of the studied vapor clouds.
To make it short and less boring to photographers to read, he demonstrated that the sky is blue because of the light being scattered by very small particles, with the size near to the blue light wavelength and the scattering caused by water droplets and ice crystals from the sky clouds are white because their "component particles" are much larger than, scattering more wavelengths (colors).
A shorter and more "modern" explanation of the sky's blue color can be found on the Physical Notes of the Boston University:
"The way light scatters off molecules in the atmosphere explains why the sky is blue and why the sun looks red at sunrise and sunset. In a nutshell, it's because the molecules scatter light at the blue end of the visible spectrum much more than light at the red end of the visible spectrum.
This is because the scattering of light (i.e., the probability that light will interact with molecules when it passes through the atmosphere) is inversely proportional to the wavelength to the fourth power.
Violet light, with a wavelength of about 400 nm, is almost 10 times as likely to be scattered than red light, which has a wavelength of about 700 nm. At noon, when the Sun is high in the sky, light from the Sun passes through a relatively thin layer of the atmosphere so only a small fraction of the light will be scattered.
The Sun looks yellow-white because all the colors are represented almost equally. At sunrise or sunset, on the other hand, light from the Sun has to pass through much more atmosphere to reach our eyes. Along the way, most of the light towards the blue end of the spectrum is scattered in other directions, but much less of the light towards the red end of the spectrum is scattered, making the Sun appear to be orange or red.
So why is the sky blue? Again, let's look at it when the Sun is high in the sky. Some of the light from the Sun traveling towards other parts of the Earth is scattered towards us by the molecules in the atmosphere. Most of this scattered light is light from the blue end of the spectrum, so the sky appears blue.
Why can't this same argument be applied to clouds? Why do they look white, and not blue? It's because of the size of the water droplets in clouds. The droplets are much larger than the molecules in the atmosphere, and they scatter light of all colors equally. This makes them look white."
The last paragraph is 100% according to Tyndall's observations and conclusion.
If you like Wikipedia, they also have an excellent explanation about the Rayleigh sky model, but it's a complex matter reduced to bare bones, so if you're not familiar with physics and optics at the university level, it may be difficult to digest.
From Wikipedia's article, I bring here an important diagram that is completely according to Tyndall's observations.
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| Rayleigh sky geometry source: Wikipedia |
Explanation:
"The geometry for the sky polarization can be represented by a celestial triangle based on the sun, zenith, and observed pointing (or the point of scattering). In the model, γ is the angular distance between the observed pointing and the sun, Θs is the solar zenith distance (90° – solar altitude), Θ is the angular distance between the observed pointing and the zenith (90° – observed altitude), Φ is the angle between the zenith direction and the solar direction at the observed pointing, and ψ is the angle between the solar direction and the observed pointing at the zenith.
Thus, the spherical triangle is defined not only by the three points located at the sun, zenith, and observed point but by both the three interior angles as well as the three angular distances. In an altitude-azimuth grid the angular distance between the observed pointing and the sun and the angular distance between the observed pointing and the zenith change while the angular distance between the sun and the zenith remains constant at one point in time.
From Wikipedia"
Going back to the maximum and minimum polarization they are brilliantly explained by the Q and U Stokes parameters. Yes, that Stokes, Sir George Gabriel Stokes. This guy was a true mathematical and physics badass. If you have the guts, here are some sources for your fun:
But honestly, I would not advise you to dig a lot about this subject. It's extremely complex and needs a deep and solid physics and calculus base to start to understand it.
Ok, back again to the resumed Wikipedia article on the Rayleigh sky. Here are the most important notes, quoted from there (you can check by yourself later if you think you need)
- When the sun is located at the zenith, the band of maximal polarization wraps around the horizon. Light from the sky is polarized horizontally along the horizon. (note: the horizon is at 90 degrees related to the zenit)
- When the sun is near the horizon, the maximum polarization is, again at 90 degrees from the horizon, or in the Zenit.
- Note that because the polarization pattern is dependent on the sun, it changes not only throughout the day but throughout the year. (note: the apparent position of the sun changes during the day)
- Many animals use the polarization patterns of the sky at twilight and throughout the day as a navigation tool. Because it is determined purely by the position of the sun, it is easily used as a compass for animal orientation. By orienting themselves with respect to the polarization patterns, animals can locate the sun and thus determine the cardinal directions. (Bees and birds would have a huge problem on contrary)
- As the sun sets due West, the maximum degree of polarization can be seen in the North-Zenith-South plane. Along the horizon, at an altitude of 0°, it is highest in the North and South, and lowest in the East and West. Then as altitude increases approaching the zenith (or the plane of maximum polarization) the polarization remains high in the North and South and increases until it is again maximum at 90° in the East and West, where it is then at the zenith and within the plane of polarization.
Don't blame me for quoting Wikipedia. This explanation is PERFECT and I dare anyone to prove the contrary if you disagree.
A very nice (and not so technical) explanation of the involved processes can be found on this web page. The explanation is so good that I decided to cut my own text to the minimum. Polarization.com also has some very interesting material for further reading.
Another interesting lecture about Polarized Light Patterns in The Sky, specifically item number 2.
So, we have some interesting situations:
- Sun at Zenit: Maximum polarization (MaxPol) on a 360 degrees circle at the horizon.
- Sun at Horizon, let's say to the east. MaxPol is at a semicircle from north to south, passing through the Zenit. MinPol points are at east and west near the horizon.
- For other directions just follow the same rule, but don't forget that the angles and vectors are on a sphere.
Sorry, there is nothing you can do to eliminate this unless at post-processing or using a lens with a narrower field of view.
One more thing that may impact the effect:
There are two types of polarizer filters, linear and circular. Linear polarizers are far more efficient to polarize the light from the sky than the circular one.
This can be a good or a bad thing depending on how do you want to enhance or attenuate the polarization. Linear polarizers tend to make the effect stronger, then sometimes the banding sky will be more visible or less visible depending on the polarizer type used at the moment
Circular polarizers are needed when your camera system has a mirror. This is because the mirror will modify the polarization and some light meter and autofocus systems sensors are placed behind a semi-silvered mirror. This difference in polarization may impact on the readings.
In case you're interested in a more detailed explanation, please check this page at Lindsey Optics website. Bob Atkins also has a very cool explanation on his website.
There are other aspects that can change the sky color, like pollutants and dust. It's a well-known phenomenon that the sun gets redder at the sunrise and sunset. This is due to the combination of two things: scattering, and absorption.
Larger particles in suspension in front of the sun will block the smaller wavelengths (the blue-purple part of the solar spectrum).
This phenomenon is also the cause of why do we perceive the sun color as yellowish, caused by the short wavelengths scattering by the extremely small particles and absorption by the larger ones. The Sun looks white from space.
Scattering and absorption are extremely common processes also in deep space. Looking at nebulas, you will see both processes and also a third one called emission. Actually, a non-scattering system is an exception.
This beautiful image has very interesting examples of what I said. There is a very powerful light source at its center, a star, emitting huge amounts of all sorts of electromagnetic waves, from infrared to x-rays.
The bluish color is caused by the dust behind the star being reflected. The dust particles are so small that longer wavelengths cannot be reflected. The dark areas are caused by light absorption. The shorter wavelengths are being absorbed by the dust between us and the light. This is one of the reasons it looks reddish.
The image at the right was taken using an infrared sensor and it looks completely different. Infrared light wavelength is much longer and the very small dust particles are much less efficient on blocking it. This is why we can see through the dust cloud and see this myriad of stars.
Some of the red/pink light is caused by the ultraviolet light from the star ionizing the hydrogen present in the nebula.
And, to complete the frame, the light is also polarized!
There are two types of polarizer filters, linear and circular. Linear polarizers are far more efficient to polarize the light from the sky than the circular one.
This can be a good or a bad thing depending on how do you want to enhance or attenuate the polarization. Linear polarizers tend to make the effect stronger, then sometimes the banding sky will be more visible or less visible depending on the polarizer type used at the moment
Circular polarizers are needed when your camera system has a mirror. This is because the mirror will modify the polarization and some light meter and autofocus systems sensors are placed behind a semi-silvered mirror. This difference in polarization may impact on the readings.
In case you're interested in a more detailed explanation, please check this page at Lindsey Optics website. Bob Atkins also has a very cool explanation on his website.
There are other aspects that can change the sky color, like pollutants and dust. It's a well-known phenomenon that the sun gets redder at the sunrise and sunset. This is due to the combination of two things: scattering, and absorption.
Larger particles in suspension in front of the sun will block the smaller wavelengths (the blue-purple part of the solar spectrum).
This phenomenon is also the cause of why do we perceive the sun color as yellowish, caused by the short wavelengths scattering by the extremely small particles and absorption by the larger ones. The Sun looks white from space.
Scattering and absorption are extremely common processes also in deep space. Looking at nebulas, you will see both processes and also a third one called emission. Actually, a non-scattering system is an exception.
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| Lagoon Nebula in Visible light (left) and infrared (right) Hubble Space Telescope - (C) NASA |
The bluish color is caused by the dust behind the star being reflected. The dust particles are so small that longer wavelengths cannot be reflected. The dark areas are caused by light absorption. The shorter wavelengths are being absorbed by the dust between us and the light. This is one of the reasons it looks reddish.
The image at the right was taken using an infrared sensor and it looks completely different. Infrared light wavelength is much longer and the very small dust particles are much less efficient on blocking it. This is why we can see through the dust cloud and see this myriad of stars.
Some of the red/pink light is caused by the ultraviolet light from the star ionizing the hydrogen present in the nebula.
And, to complete the frame, the light is also polarized!
