The colour of the sky

The outer layers of the atmosphere contain aerosols that don’t reflect light rays. When light hits aerosols they are refracted in different directions depending on what part of the aerosol they hit. Since there is an innumerable amount of aerosols in the atmosphere and infinite light rays, as they pass through the aerosols they are eventually scattered in all directions. This light scattering is called Rayleigh scattering. The sun’s white light is refracted more or less depending on the light’s wave lengths. That means the light colours are scattered more or less, and are thereby separated.

In inner atmosphere there are also dust particles (like sand etc.) that are too big and opaque to refract, but instead reflect light. This is called Mie scattering. Mie scattering does therefore not alter the light colour, so it is more white. I decided to only implement Rayleigh scattering since this is the most interesting part of atmospheric light scattering. I also did not include clouds in my visualisation.

Only half of a planet is directly illuminated by the sun. Each photon changes direction each time it randomly hits an aerosol. Theoretically it could thereby be refracted along the planet’s curve every time to circle around the whole planet several times. Of course that is not very likely but considering the theoretical infinite number of light rays, it does happen. From around 90 degrees from the centre of the illuminated half some light scatters around to the dark side of the planet – but it fades quickly.

Only light that is scattered back to the viewer is visible as light in the atmosphere. The blue light scatters most, so more blue light is scattered in the direction of the viewer than green, yellow, and red. That means that atmospheric light in the directly illuminated half of the planet has a blue-ish tint. Like-wise, as blue scatters away more aggressively, there is less blue left in the fringes of the illuminated half of the planet – “where the sun rises or sets”. That is why the atmosphere is more yellow and red where the sun does not directly illuminate.

I thought about many ideas for how to implement this in a shader. One idea was to have separate equations for each of the RGB channels. I decided to instead tint the final light with a look-up table of a light colour gradient in the form of a one-dimensional texture. The light colour gradient was made from an actual photo of light spectrum from aerosol-refracted sun light, modified to have around the same brightness value across the gradient.  I sampled the colour left to right in proportion to the angle 0-180 degrees from the planet’s centre of illumination. Since the light intensity is modified by all colours other than multiplication with white, I multiplied with the inverse of the sample colour’s brightness.