Lambertian Reflection

• Initially, a third assumption:

  Incoming light is partially absorbed and partially transmitted equally in all directions

  \

• This is approximately the behavior of matte materials.
• We want an expression for , the intensity of light reflected in any direction, given
  • the incoming direction,
  • incoming intensity,
  • and the material properties.
• Given the intensity of light striking the surface from a direction , we want to determine the the intensity of light reflected to a viewer at direction .

  \

• Working differentially:

  

  where relates , , and surface properties.

  If we look closely,

  \

  

  so

  

  for . Since independent of outward direction,

  

  And therefore,