Radiometry

  • Definition of foreshortening and its mathematical expression.
  • Definition of solid angle and its units.
  • Relationship between angle and the foreshortening of a 2D line with respect to a circle
  • Relationship between solid angle and the foreshortening of a 3D surface patch with respect to the sphere
  • Definition of Radiance
  • Definition of Irradiance
  • Radiance is constant along straight lines
  • Local interaction model (local shading model)  : no surface interreflections.
  • Emissivity : we do not consider "glowing surfaces", i.e., surfaces which emit their own illumination.
  • Definition the Bidirectional Reflectance Distribution Function (BRDF) : the ratio of the outgoing radiance to the incoming radiance.
  • Constraints on the BRDF : conservation of energy.

Putting it all together : The Radiometry of Thin Lenses 

  • energy emitted onto a pixel  (irradiance) is proportional to the size (area) of the lens.
  • energy emitted onto a pixel  (irradiance) is inversely proportional to the distance between the lens center and the image plane.
  • energy emitted onto a pixel  (irradiance) is proportional pixel brightness. 
  • energy emitted onto a pixel  (irradiance) is inversely proportional to the f number  or directly proportional to the relative aperature (the ration of the lens width to the focal length).
  • energy emitted onto a pixel  (irradiance) decays as cos^4(alpha) where alpha is the angle of the ray with respect to the optical axis. This means that the image periphery has less irradiance than the image center.

Definition of Radiositty

Properties of a Lambertian or diffuse surface, i.e., surfaces with constant radiance (where radance is independent of angle).

Definition of albedo.

Properties of Specular surfaces, models for specular surfaces and specifically the Phong model.

Combining the diffuse and specular model to generate models of generic (non-emissive) surfaces.