Irradiance ( $E = d Φ_{incident} / d A$ )

Irradiance measures incident radiant flux per actual receiving area. Its units

W m^{- 2}

match radiant exitance, but it counts the incoming side of the radiation exchange. Measure incoming angles from the unit normal pointing toward the incident hemisphere. Then

E = \int_{Ω_{incident}} L_{incoming} (θ, φ) cos θ d Ω.

For

2 W

distributed uniformly over

0.010 m^{2}

E = 200 W m^{- 2}

. If the receiving plane is tilted

6 0^{\circ}

in the same broad uniform parallel beam, the incident power per actual area is halved to

100 W m^{- 2}

. This receiving-surface cosine factor is geometric and does not assume Lambertian reflectance. Together, irradiance and radiant exitance describe how radiation supplies and removes energy at a surface, while radiance preserves the directional information.

Spectral irradiance ( $E_{λ}, E_{ν}$ )

Incident radiant flux per unit area and unit wavelength or frequency. Integrating

E_{λ}

over a wavelength interval gives the contribution to irradiance in that interval. Conversion between

E_{λ}

and

E_{ν}

requires the absolute Jacobian determinant associated with

ν = c / λ

A parallel beam incident at elevation

α

has horizontal irradiance

F_{h} = F_{⊥} sin α

τ_{v} / sin α

. Confusing these projections changes both attenuation and intercepted power.

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Irradiance is a measure of the power of solar radiation or other forms of electromagnetic radiation received by a surface per unit area. It is typically expressed in watts per square meter (W/m²). Irradiance quantifies how much solar energy is available at a given location and time, making it an important parameter in fields such as solar energy, meteorology, and climatology.