Radiance

Radiance is a physical quantity used in the sphere of radiometry to measure the intensity of a light beam, defined as power per unit solid angle per unit projected area of the source. The SI unit of radiance is the watt per steradian per square metre (w·m^-2·sr^-1)

Definition

$L = \frac{1}{\cos \theta} \cdot \frac{d^2 \Phi}{dA d\vec{\omega}} = \frac{hc}{\cos \theta}\int_0^{\infty} \left\{ \frac{d^3n_{\lambda}}{d\vec{\omega}dAdt}\right\} \frac{1}{\lambda}d\lambda \ \$

where

L	is the	radiance (watt · m^-2 · sr^-1)
Φ	is the	radiant flux (watts)
θ	is the	angle formed by surface normal and direction of radiance L (rad)
A	is the	area (square metres)
$\vec{\omega}$	is the	solid angle (sr)

whereas

$\Phi = \frac{dQ}{dt}$

$Q = \int_0^{\infty} Q_{\lambda} d\lambda$

$Q_{\lambda} = n_{\lambda}e_{\lambda} \,$

$e_{\lambda} = \frac{hc}{\lambda}$

where

Q	is the	energy of light (J)
t	is the	time [s]
$Q λ$	is the	energy of light at wavelength λ (J)
λ	is the	wavelength (m)
$n λ$	is the	number of photons at wavelength λ
$e λ$	is the	energy of a photon at wavelength λ (J)
h	is the	Planck's constant (J·s)
c	is the	speed of light (m/s)

SI radiometry units

SI radiometry units edit
Quantity	SI unit	Symbol	Notes
radiant energy	joule	J	energy
radiant flux	watt	W	radiant energy per unit time, also called Radiant power
radiant intensity	watts per steradian	W·sr^-1	power per unit solid angle
radiance	watts per steradian per square metre	W·sr^-1·m^-2	power per unit solid angle per unit projected source area
energy flux density	watts per square metre	W·m^-2	power per unit area of the receiver (irradiance) or the emitter (radiant emittance or radiant exitance)
spectral radiance	watt per steradian per cubic metre	W·sr^-1·m^-3	commonly measured in W·sr^-1·m^-2·nm^-1
spectral irradiance	watt per cubic metre	W·m^-3	commonly measured in W·m^-2·nm^-1

Radiance

Definition

SI radiometry units

See also

See also: Radiance, Angle, Area, Cubic metre, Energy, Intensity, Irradiance, Joule