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Categories: Physical quantity | Radiometry

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. 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)

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