ECE532 Biomedical Optics © 1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute |

## L [W/(cm |

We now combine the concepts of **Radiant Intensity** and **Irradiance** in the parameter called the **Radiance**.

The **Radiance L [W/(cm ^{2} sr)]** of a source equals the

The radiance can also refer to a target area, describing the power per incremental solid angle irradiating an incremental cross-sectional area of target. The above definition strictly holds in the **limit** of very narrow solid angle (Ω -> 0) and very small surface area (A -> 0) to describe the radiance from a local region into a specific direction.

The following figures illustrate schematically the radiance of a **source (left)** and a **target (right)** for the case of θ = 0, i.e., the surface is perpendicular to the central direction of the cones of radiation. The figures attempt to schematically depict a continuous and uniform distribution of radiating cones, although graphically only some representative cones are shown.

## a source | ## a target |

The following example emphasizes the radiance from a surface that is oriented oblique to the central direction of radiation. The surface is oriented at an angle θ relative to the central direction of radiation. The radiance L refers to the power passing through the area A but weighted by cosθ which equals the area shown in red, area Acosθ:

In the above schematic figure, you might get confused. How does all the power P go through the red circle? Graphically, it is not obvious. The answer is found in emphasizing that the definition of radiance is in the **limit** of a very narrow solid angle (Ω -> 0) and a very small surface area (A -> 0). The following figures schematically illustrate these two limiting cases:

In limit of Ω -> 0 | In limit of A -> 0 |

Hopefully you can see that **in the limit** of narrow solid angle and small area, the power does go through the red area Acosθ. It is common to express radiance by the differential expression:

## Example: | Radiance of a flashlight |

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