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

[itex]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 \ \ [itex]

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) [itex]\vec{\omega}[itex] is the solid angle (sr)

whereas

[itex]\Phi = \frac{dQ}{dt} [itex]
[itex]Q = \int_0^{\infty} Q_{\lambda} d\lambda [itex]
[itex]Q_{\lambda} = n_{\lambda}e_{\lambda} \,[itex]
[itex]e_{\lambda} = \frac{hc}{\lambda} [itex]

where

 Q is the energy of light (J) t is the time [s] [itex]Q_{\lambda}[itex] is the energy of light at wavelength λ (J) λ is the wavelength (m) [itex]n_{\lambda}[itex] is the number of photons at wavelength λ [itex]e_{\lambda}[itex] 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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