Radiance to Irradiance Conversion Training Level: Intermediate Dr. Richard Young Optronic Laboratories, Inc.

Geometry Source Detector Let us start off with a source of radiance, e.g. a sphere source, and a detector

Geometry Source Detector Each point on the detector is illuminated by light within the solid angle (cone) to the source

Geometry Source Detector A large distance between source and detector is required for even illumination.

Geometry Source Detector Area = Distance = d A The solid angle is calculated by A/d² when d²>>A

Geometry Although it is a simple formula, it works well at d>10 x source diameter

Geometry Source Detector If the source is uniform, then the light in the solid angle to the source…

Geometry Source Detector …is equal to the light in the same solid angle from the source.

Geometry Source Detector x sr Irradiance from Radiance: E = L * A/d² L [W/(cm² sr)] E [W/(cm²)] x sr Irradiance from Radiance: E = L * A/d² Radiance from Irradiance: L = E * d²/A