Radiant exposure

Template:Redirect In radiometry, radiant exposure or fluence is the radiant energy received by a surface per unit area, or equivalently the irradiance of a surface, integrated over time of irradiation, and spectral exposure is the radiant exposure per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant exposure is the joule per square metre (Template:Nobreak), while that of spectral exposure in frequency is the joule per square metre per hertz (Template:Nobreak) and that of spectral exposure in wavelength is the joule per square metre per metre (Template:Nobreak)—commonly the joule per square metre per nanometre (Template:Nobreak).

Mathematical definitions

Radiant exposure

Radiant exposure of a surface, denoted H_e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as $$H_{\mathrm{e}}=\frac{\partial Q_{\mathrm{e}}}{\partial A}=\underset{0}{\overset{T}{\int }}{E}_{\mathrm{e}}(t)\mathrm{d}t,$$ where

• ∂ is the partial derivative symbol;
• Q_e is the radiant energy;
• A is the area;
• T is the duration of irradiation;
• E_e is the irradiance.

Spectral exposure

Spectral exposure in frequency of a surface, denoted H_e,ν, is defined as $$H_{\mathrm{e},\nu }=\frac{\partial H_{\mathrm{e}}}{\partial \nu },$$ where ν is the frequency.

Spectral exposure in wavelength of a surface, denoted H_e,λ, is defined as $$H_{\mathrm{e},\lambda }=\frac{\partial H_{\mathrm{e}}}{\partial \lambda },$$ where λ is the wavelength.

See also

• Exposure (photography)
• Irradiance
• Radiant energy