Opacity

Etymology

Late Middle English opake, from Latin opacus 'darkened'. The current spelling (rare before the 19th century) has been influenced by the French form.

Radiopacity

Main article: Radiodensity

Radiopacity is preferentially used to describe opacity of X-rays. In modern medicine, radiodense substances are those that will not allow X-rays or similar radiation to pass. Radiographic imaging has been revolutionized by radiodense contrast media, which can be passed through the bloodstream, the gastrointestinal tract, or into the cerebral spinal fluid and utilized to highlight CT scan or X-ray images. Radiopacity is one of the key considerations in the design of various devices such as guidewires or stents that are used during radiological intervention. The radiopacity of a given endovascular device is important since it allows the device to be tracked during the interventional procedure.

Quantitative definition

The words "opacity" and "opaque" are often used as colloquial terms for objects or media with the properties described above. However, there is also a specific, quantitative definition of "opacity", used in astronomy, plasma physics, and other fields, given here.

In this use, "opacity" is another term for the mass attenuation coefficient (or, depending on context, mass absorption coefficient, the difference is described here) \kappa_\nu at a particular frequency \nu of electromagnetic radiation.

More specifically, if a beam of light with frequency \nu travels through a medium with opacity \kappa_\nu and mass density \rho, both constant, then the intensity will be reduced with distance x according to the formula I(x) = I_0 e^{-\kappa_\nu \rho x} where

• x is the distance the light has traveled through the medium
• I(x) is the intensity of light remaining at distance x
• I_0 is the initial intensity of light, at x = 0

For a given medium at a given frequency, the opacity has a numerical value that may range between 0 and infinity, with units of length2/mass.

Opacity in air pollution work refers to the percentage of light blocked instead of the attenuation coefficient (aka extinction coefficient) and varies from 0% light blocked to 100% light blocked:

\text{Opacity} = 100% \left(1-\frac{I(x)}{I_0} \right)

Planck and Rosseland opacities

It is customary to define the average opacity, calculated using a certain weighting scheme. Planck opacity (also known as Planck-Mean-Absorption-Coefficient) uses the normalized Planck black-body radiation energy density distribution, B_{\nu}(T), as the weighting function, and averages \kappa_\nu directly: \kappa_{Pl}={\int_0^\infty \kappa_\nu B_\nu(T) d\nu \over \int_0^\infty B_\nu(T) d\nu }=\left( { \pi \over \sigma T^4}\right) \int_0^\infty \kappa_\nu B_\nu(T) d\nu , where \sigma is the Stefan–Boltzmann constant.

Rosseland opacity (after Svein Rosseland), on the other hand, uses a temperature derivative of the Planck distribution, u(\nu, T)=\partial B_\nu(T)/\partial T, as the weighting function, and averages \kappa_\nu^{-1}, \frac{1}{\kappa} = \frac{\int_0^{\infty} \kappa_{\nu}^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}. The photon mean free path is \lambda_\nu = (\kappa_\nu \rho)^{-1}. The Rosseland opacity is derived in the diffusion approximation to the radiative transport equation. It is valid whenever the radiation field is isotropic over distances comparable to or less than a radiation mean free path, such as in local thermal equilibrium. In practice, the mean opacity for Thomson electron scattering is: \kappa_{\rm es} = 0.20(1+X) ,\mathrm{cm^2 , g^{-1}} where X is the hydrogen mass fraction. For nonrelativistic thermal bremsstrahlung, or free-free transitions, assuming solar metallicity, it is: \kappa_{\rm ff}(\rho, T) = 0.64 \times 10^{23} (\rho[ {\rm g}~ {\rm, cm}^{-3}])(T[{\rm K}])^{-7/2} {\rm, cm}^2 {\rm, g}^{-1}. The Rosseland mean attenuation coefficient is: \frac{1}{\kappa} = \frac{\int_0^{\infty} (\kappa_{\nu, {\rm es}} + \kappa_{\nu, {\rm ff}})^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}.

References

References

1. Modest, Radiative Heat Transfer, {{ISBN. 978-0-12386944-9
2. Stuart L. Shapiro and [[Saul Teukolsky. Saul A. Teukolsky]], "Black Holes, White Dwarfs, and Neutron Stars" 1983, {{ISBN. 0-471-87317-9.
3. George B. Rybicki and [[Alan Lightman. 0-471-04815-1.