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).
Contents
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.