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Subsurface scattering is the effect of light bouncing around inside a surface and "tinting" prior to exiting. This is often most obvious in materials like marble but is essential to creating realistic wax or flesh materials. Subsurface scattering also helps simulating liquids such as milk appear more natural. In humans "SSS" is most often witnessed when thin areas on the ears seem to turn red from back light as the light is being tinted by the tissues underneath the skin itself.
The way subsurface scattering works in modo is to measure the distance light travels through and along the material and then tint that light before it leaves the surface. The color and amount of the tint is determined by the Subsurface Color and Scattering Distance. For instance, if the Scattering distance is set to 1 centimeter, the Subsurface Color is set to a light blue (R= .75, G= .75, B= 1) and the light shining on the surface is pure white, any light that travels 1 cm before exiting the material will be tinted to .75, .75, 1 (light blue). If the light travels 2cm before exiting the light will be tinted .56, .56, 1 (darker blue). This is because as the light travels further each channel (RGB) is reduced according to the initial color. Let's consider the Red channel. When the light entered the surface it was pure white so the Red channel started at 1. Once the light traveled 1 centimeter the light was attenuated to .75 on the Red channel. Travelling another centimeter would reduce the Red channel by the same amount (75% of the initial value) which yields .5625 as the value for the Red channel. In this way as the light travels further prior to exiting the material the channel values are reduced and cause the material to appear darker where there are thicker areas. Continuing this formula through a total of 8 centimeters the Red and Green channels would be attenuated to a mere 10% (.75 * .75 * .75 * .75 * .75 * .75 * .75 * .75 = .1).
With this in mind you can imagine that to create materials that seem to be more translucent you would want higher scattering distance values so that more light escapes the surfaces with less tint/darkening.
Related links:
Subsurface Scattering
Subsurface Amount
Subsurface Color
Scattering Distance
Subsurface Samples
Here we can see an example of subsurface scattering through a marble surface.
The following image shows subsurface scattering in wax.
Here we can see the effect of subsurface on liquid.
Subsurface effects can even be used to give "cartoony" renders a little more "punch".
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