# On optical irradiance versus fluence rate

Sept. 7, 2005, Steven L. Jacques

This week, Magnus Lilledahl, Scott Prahl and I are having a discussion of the definition of irradiance and its distinction from fluence rate . Below is my attempt to illustrate the definitions.

Consider a uniform beam of circular cross-sectional area A [cm2] and power P [W]. The cross-sectional flux density of the beam is

Jbeam = P/A [W/cm2]

The beam strikes the surface at a variable angle B. (Let the media on either side of the boundary be non-scattering and non-absorbing. Let the refractive index across the surface boundary be matched, for simplicity.) The flux density crossing the surface is

Jsurface = P/A/cos(B) [W/cm2]

Finally, consider a small absorbing sphere within the lower medium. This absorber negligibly perturbs the light field distribution. Despite the angle of incidence, the small absorber will see the same flux density and will be heated the same amount.

This example illustrates the difference between the flux density of the beam, Jbeam, and the flux density crossing the surface, Jsurface. The absorber is heated by the Jbeam and is insensitive to the variations in the value of Jsurface. Also note that the concentration of photons within the absorber, C [J/cm3], at any given moment equals Jbeam/c where c is the speed of light in the medium, and C is independent of the angle of incidence.

• The Irradiance E [W/cm2] is equal to the flux density crossing the surface, Jsurface.
• The Fluence rate F [W/cm2] is equal to the flux density seen by the absorber, which is Jbeam in this case of a non-scattering non-absorbing medium.
• The Irradiance and Fluence rate are only equal when the beam is orthogonal to the surface