Definition: The radiant flux (power) incident on a surface per unit area, denoted by the symbol $E$.
Unit: $W / m^{2}$
Mathematical Expression: $$E = \frac{d\Phi}{dA}$$

Relationship Between Irradiance and Radiant Intensity for a Point Source on a Differential Surface Element
For an isotropic point source with a radiant intensity of $I$ (unit: $W/sr$) in a given direction, there is a differential surface element $dA$ perpendicular to the direction of incidence at a distance $r$ from the point source.

• The solid angle subtended by the surface element $dA$ at the point source is: $d\Omega = \frac{dA}{r^2}$
• The radiant flux emitted by the point source into this solid angle is: $d\Phi = I \cdot d\Omega = I \cdot \frac{dA}{r^2}$
• Substituting the above equation into the definition of irradiance $E = \dfrac{d\Phi}{dA}$, we obtain:

$$E = \frac{d\Phi}{dA} = \frac{I \cdot \dfrac{dA}{r^2}}{dA} = \frac{I}{r^2}$$

Summary of Relationship: Under conditions of normal incidence, the irradiance on a differential surface element from a point source is directly proportional to the radiant intensity of the source and inversely proportional to the square of the distance from the source to the element, thus following the inverse-square law of irradiance.

See Also
Illuminance, Radiant Flux, Radiant Intensity