Scattering on the View Ray

Why do we see things that do not emit light at all?

Because they reflect light from a light source that then passes into our eye. If an object reflects each photon the same way according to the law of reflection, it is a mirror. If it reflects more or less all photons, but into random directions, the object is white. If it absorbs all photons that ever hit it, it is black. And if it absorbs only a certain wavelength and reflects the rest, it is colored.

So just like from the Sun, there is light traveling from an illuminated object to the eye. We have referred to that as the View ray, but we haven't talked much about it yet. What about that light - does it not scatter in the atmosphere?

Well, in fact it does. It undergoes the same Rayleigh, Mie and diffuse scattering that happen on the observation ray. The reason we don't see the effects so prominently is rather that the direct sunlight is so much stronger than the light that is reflected on distant illuminated objects, so much of what we see in the atmosphere is what happens to direct sunlight.

In- and out-scattering

To see the effect of scattering on the view ray, it is easier to at first study a situation during the day where the illumination ray is not much modified. We can then have the following situation:

The Sun illuminates the air between observer an object. That causes Rayleigh scattering on air molecules and dry haze, and by chance part of that bluish light is exactly along the view ray, so we see the original light plus a blue component that has been added on the way. Generally anything that distorts or obscures our view we perceive as haze, so this in-scattering gives a blue Rayleigh haze that grows with distance as the amount of air between eye and object increases.

Blue Rayleigh haze in the distance.

At the same time of course, the light reflected from the distant object also undergoes scattering - Rayleigh scattering on that light removes part of the blue and leaves it more red.

So what we see is the original light, minus some of its blue, but with additional blue from the atmosphere added. Which wins out?

Normally the in-scattering is stronger, because the direct sunlight is so much stronger than reflected light. But if the reflected light is sufficiently bright... Look carefully at the clouds in the distance in the photo above - they have an ever-so-slight red tint. That is Rayleigh out-scattering.

Now, of course in can happen that we see through unlit air - because a cloud above casts a shadow. In this case only out-scattering is left - and we see the red-shift of the light much more clearly, as in the following shot:

A shadow wedge removes Rayleigh in-scattering.

Generally Rayleigh out-scattering gives distant objects a dirty yellow-red appearance - pretty much as if the object would be in smog.

What about Mie in- and out-scattering?

The out-scattering certainly happens, but we usually can't see much of it, it just reduces the light intensity a bit but does not shoft color, and one needs an exceptional bright reflection to really see a halo around it.

Mie in-scattering is absent during the day, because that we would only see when the light source and the viewed object are close together - but during the day the sun is high in the sky and the distant objects are at the horizon. So Mie in-scattering can only happen in low sun and we'll see an example of it below.

Rayleigh out-scattering in low sun

When the Sun is low, Rayleigh in-scattering on the view ray is much reduced, especially when looking into the setting Sun. For starters, there is not much blue light illuminating the object, because the illuminating ray has already traveled a long path through the air. And then of course any blue light scattered into the direction of the view ray directly competes with the bright, red-orange colored Mie halo around the Sun - which is in the same direction. And then of course most of the objects we tend to view are clouds - and they cast shadows on the view ray, so often the air isn't much illuminated.

So we mainly see Rayleigh out-scattering on the view ray - which in turn is difficult to spot, because the color shift is of course the same as for the illumination ray - the scene gets more yellowish-red. So which is which?

Here is a good candidate I'd say.

Rayleigh out-scattering in low light.

The whole horizon seems wrapped in some dirty-yellowish haze that has the color expected from Rayleigh out-scattering. Moreover, we know that the distant cloud layer should brighten towards the horizon as that is a more sunward position - but something makes it darker.

The next shot shows the same phenomenon - the cloud closest to the horizon actually appears more red than the closer ones - yet the colors should not work out that way.

Another possible example for Rayleigh out-scattering.

Neither example is actually particularly stunning or makes the effect stick out - as said above, generally it's hard to see because the color shift competes with a rather similar color shift for the illumination ray.

Mie in-scattering

A typical situation when Mie in-scattering happens is when there is fog on the ground during sunset. The fog is then illuminated by the light. The resulting illumination is not pure Mie-scattering - there is no well-defined Halo around the light source. It is also not pure diffuse scattering - turning around makes a difference, the illumination is markedly stronger when facing the sun.

Low haze glowing in Mie scattering.

So this actually is a complicated region in which the medium is neither optically thin (most of the photons scatter at least once) but not yet optically thick (a significant proportion still makes it through without scattering, so one can still see clear contours). This can bring some light into regions which should be shaded, for instance look at the trees at the horizon, there is glowing haze between them and the light.

The ground fog has to be 'just right' - if it is too strong, diffuse scattering takes place and only grey light filters through and the sky can no longer be seen, if it is too weak it doesn't alter the visuals much.

Continue with The Question of Green.


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