Energy of Illumination

Radiance:

Electromagnetic energy flux, the amount of energy traveling

• at some point x
• in a specified direction ,
• per unit time
• per unit area perpendicular to the direction
• per unit solid angle
• for a specified wavelength
• denoted by

Spectral Properties:

Total energy flux comes from flux at each wavelength

• 

Picture:

For the indicated situation is

• energy radiated through differential solid angle
• through/from differential area dx
• not perpendicular to direction (projected area is )
• during differential unit time dt

Power:

Energy per unit time (as in the picture)

• 

Radiosity:

Total power leaving a surface point per unit area

(integral is over the hemisphere above the surface point)

Bidirectional Reflectance Distribution Function:

• is a surface property at a point
• relates energy in to energy out
• depends on incoming and outgoing directions
• varies from wavelength to wavelength
• Definition: Ratio
  • of radiance in the outgoing direction
  • to radiant flux density for the incoming direction

Energy Balance Equation:

• is the radiance
  • at wavelength
  • leaving point x
  • in direction ,
• is the radiance emitted by the surface from the point
• is the incident radiance impinging on the point
• is the BRDF at the point
  • describes the surface's interaction with light at the point
• the integration is over the hemisphere above the point