Radiance
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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
- <math>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 \ \ <math>
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) |
| <math>\vec{\omega}<math> | is the | solid angle (sr) |
whereas
- <math>\Phi = \frac{dQ}{dt} <math>
- <math>Q = \int_0^{\infty} Q_{\lambda} d\lambda <math>
- <math>Q_{\lambda} = n_{\lambda}e_{\lambda} \,<math>
- <math>e_{\lambda} = \frac{hc}{\lambda} <math>
where
| Q | is the | energy of light (J) |
| t | is the | time [s] |
| <math>Q_{\lambda}<math> | is the | energy of light at wavelength λ (J) |
| λ | is the | wavelength (m) |
| <math>n_{\lambda}<math> | is the | number of photons at wavelength λ |
| <math>e_{\lambda}<math> | 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) |