symbol: $L_{\lambda}^{\rm{a}} (\boldsymbol{x},t)$; units: $\pu{W m-4}$, $\pu{W cm-3 nm-1}$
synonym: local volumetric rate of energy absorption
https://doi.org/10.1351/goldbook.13987
Local value of the spectral radiance, or energy density absorption rate, defined for a three-dimensional space, often in terms of napierian properties.
Notes:
- Mathematical expression for one spatial dimension is \[L_{\lambda}^{\rm{a}} (x,t) = \alpha_{\lambda} (\boldsymbol{x},t) L_{\lambda} (x,t)\] where \(L_{\lambda}(x,t)\) is the time-dependent spectral radiance incident from one direction at a point \(x\) defined in the space coordinates, \(\alpha_{\lambda}(\boldsymbol{x},t)\) is the space- and time-dependent linear napierian absorption coefficient. SI unit is \(\pu{W m-4}\). Common unit is \(\pu{W cm-3 nm-1}\).
The equation above is valid for a collimated beam of radiation, for which \(E_{\lambda,{\rm{o}}}(\boldsymbol{x},t) = L_{\lambda}(\boldsymbol{x},t)\). - For a divergent beam, the mathematical definition is: \[L_{\lambda}^{\rm{a}} (\boldsymbol{x},t) = \alpha_{\lambda} (\boldsymbol{x},t) E_{\lambda,o} (\boldsymbol{x},t)\]. In this case, \(\boldsymbol{x}\) is a position vector in a three-dimensional space. Units are the same as above.
- Rigorously speaking, the general definition should be written in terms of \(E_{\lambda,o}\). However, for a collimated beam of radiation, it is clearer to write it directly in terms of \(L_{\lambda}\).
- Also called local volumetric rate of energy absorption, LVREA, [either \(e_{\lambda}^{\rm{a}}(x,t)\) for one spatial dimension or \(e_{\lambda}^{\rm{a}}(\boldsymbol{x},t)\) for three dimensions].
- In practice, for polychromatic irradiation, the quantity is integrated in the wavelength range used.