Radiant exposure

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 (J/m2), while that of spectral exposure in frequency is the joule per square metre per hertz (J⋅m−2⋅Hz−1) and that of spectral exposure in wavelength is the joule per square metre per metre (J/m3)—commonly the joule per square metre per nanometre (J⋅m−2⋅nm−1).

Mathematical definitions

Radiant exposure

Radiant exposure of a surface, denoted He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as

H

e

=

∂

Q

e

∂

A

=

∫

0

T

E

e

(

t

)

d

t

,

{\displaystyle H_{\mathrm {e} }={\frac {\partial Q_{\mathrm {e} }}{\partial A}}=\int _{0}^{T}E_{\mathrm {e} }(t)\,\mathrm {d} t,}

where

∂ is the partial derivative symbol;

Qe is the radiant energy;

A is the area;

T is the duration of irradiation;

Ee is the irradiance.

Spectral exposure

Spectral exposure in frequency of a surface, denoted He,ν, is defined as

H

e

,

ν

=

∂

H

e

∂

ν

,

{\displaystyle H_{\mathrm {e} ,\nu }={\frac {\partial H_{\mathrm {e} }}{\partial \nu }},}

where ν is the frequency.

Spectral exposure in wavelength of a surface, denoted He,λ, is defined as

H

e

,

λ

=

∂

H

e

∂

λ

,

{\displaystyle H_{\mathrm {e} ,\lambda }={\frac {\partial H_{\mathrm {e} }}{\partial \lambda }},}

where λ is the wavelength.