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

## I [W/sr] |

The **power P [W]** from a source that is directed into a particular direction along the center of a cone encompassing a **solid angle Ω [steradians] or [sr]** is called the **Radiant Intensity, I [W/sr]**.

The **solid angle ** Ω describes the size of the cone of intensity radiated by the source. Consider a sphere with radius R and a cone which intersects the sphere surface to form a circle with a radius r. For the case of a narrow cone and small cone area on the sphere surface, the following approximation holds. The area of the spot is A_{circle} and the surface area of the sphere is A_{sphere}, as shown in the figure below. There are 4π steradians over the entire surface of a sphere. So the ratio A_{circle}/A_{sphere} is the fraction of the total 4π [sr] of the sphere which is encompassed by the cone.

The expressions in the above figure are correct in the limit of a small solid angle. Note that r/R equals θ in the limit of small θ. The general expression for solid angle regardless of its size is:

For an isotropic source of radiant power P [W] which radiates light equally in all directions, the radiant intensity is equal to P/(4π) [W/sr].

EXAMPLE: Radiant intensity of a flashlight

More generally, intensity refers to the limiting case of the ratio P/Ω for a vanishingly small cone as Ω approaches zero:

Therefore, the local radiant intensity within an irregularly shaped non-uniform-intensity region can be mapped by interrogating each portion of the region with a small cone. One is not restricted to discussing only cones.