- Source: Radiant flux
In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux 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 flux is the watt (W), one joule per second (J/s), while that of spectral flux in frequency is the watt per hertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly the watt per nanometre (W/nm).
Mathematical definitions
= Radiant flux
=Radiant flux, denoted Φe ('e' for "energetic", to avoid confusion with photometric quantities), is defined as
Φ
e
=
d
Q
e
d
t
Q
e
=
∫
T
∫
Σ
S
⋅
n
^
d
A
d
t
{\displaystyle {\begin{aligned}\Phi _{\mathrm {e} }&={\frac {dQ_{\mathrm {e} }}{dt}}\\[2pt]Q_{\mathrm {e} }&=\int _{T}\int _{\Sigma }\mathbf {S} \cdot {\hat {\mathbf {n} }}\,dAdt\end{aligned}}}
where
t is the time;
Qe is the radiant energy passing out of a closed surface Σ;
S is the Poynting vector, representing the current density of radiant energy;
n is the normal vector of a point on Σ;
A represents the area of Σ;
T represents the time period.
The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, giving
Φ
e
≈
∫
Σ
⟨
|
S
|
⟩
cos
α
d
A
,
{\displaystyle \Phi _{\mathrm {e} }\approx \int _{\Sigma }\langle |\mathbf {S} |\rangle \cos \alpha \ dA,}
where ⟨-⟩ is the time average, and α is the angle between n and
⟨
|
S
|
⟩
.
{\displaystyle \langle |\mathbf {S} |\rangle .}
= Spectral flux
=Spectral flux in frequency, denoted Φe,ν, is defined as
Φ
e
,
ν
=
∂
Φ
e
∂
ν
,
{\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \nu }},}
where ν is the frequency.
Spectral flux in wavelength, denoted Φe,λ, is defined as
Φ
e
,
λ
=
∂
Φ
e
∂
λ
,
{\displaystyle \Phi _{\mathrm {e} ,\lambda }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \lambda }},}
where λ is the wavelength.
SI radiometry units
See also
Luminous flux
Heat flux
Power (physics)
Radiosity (heat transfer)
References
Further reading
Boyd, Robert (1983). Radiometry and the Detection of Optical Radiation (Pure & Applied Optics Series). Wiley-Interscience. ISBN 978-0-471-86188-1.
Kata Kunci Pencarian:
- Besaran cahaya
- Radiant flux
- Irradiance
- Flux
- Radiant energy
- Radiant intensity
- Luminous flux
- Radiant exitance
- Lumen (unit)
- Radiance
- Radiometry
