Fluence ($F=\int Idt$)

For a beam at a specified surface, fluence is the time-integrated incident light intensity: $F=\int I(t)dt$, with units of energy per area. It records how much energy arrived during an exposure rather than the instantaneous rate of delivery.

For a constant rectangular pulse, $F=I_0\tau$. Two pulses can therefore have equal fluence and different peak intensities if their durations differ. This matters in nonlinear optics, where the response can depend strongly on instantaneous intensity, and in comparing exposure protocols. Photon fluence instead counts incident photons per area; converting it to energy fluence requires the photon energies.

Energy carried by incident photons per unit area. For monoenergetic photons, $\Psi =E_{\gamma }\Phi$, where $\Phi$ is photon fluence. With charged-particle equilibrium, $D=\Psi {\mu }_{\mathrm{en}}/\rho$ relates it to absorbed dose.

The number of photons incident per unit area in a specified geometry. It is distinct from a rate per unit time. For a monoenergetic beam, photon energy fluence is $\Psi =E_{\gamma }\Phi$.