Optical thickness

This article deals with a measure of the optical transmittance of a medium; for a comparison between a distance in a medium and in a vacuum see optical path length .

The optical thickness , also called optical depth , is a dimensionless measure of how well a physical medium lets electromagnetic waves pass: ${\displaystyle \tau }$

• when passing through a layer of matter (e.g. the atmosphere ) with an optical thickness  = 1, the radiation density drops to 1 / e times (≈ 37%). ${\displaystyle \tau }$
• for the case  ≫ 1 one speaks of optically thick ${\displaystyle \tau }$
• for the case  ≪ 1 of optically thin . ${\displaystyle \tau }$

The optical thickness of a material is different for different frequencies . It is calculated by integrating the absorption coefficient over the path that the radiation has to cover ( light path ): ${\displaystyle f}$ ${\displaystyle a}$ ${\displaystyle d}$

${\displaystyle \tau (f)=\int _{0}^{d}a(x,f)\mathrm {d} x}$

In a medium assumed to be homogeneous , the whole thing is simplified to a multiplication:

${\displaystyle \tau =C_{i}\cdot \sigma \cdot d}$

With

• the particle density ${\displaystyle C_{i}}$
• the cross section for the energy in question . ${\displaystyle \sigma }$

Optical thickness of the atmosphere

determination

The optical thickness of the atmosphere is included in the transmissivity of the atmosphere as an extinction coefficient . This is calculated for a certain wavelength according to Lambert-Beer 's law: ${\displaystyle \tau }$ ${\displaystyle T}$

${\displaystyle T={\frac {I}{I_{0}}}=e^{-\tau \cdot m}}$

With

• the intensity of solar radiation in the observed wavelength on the ground ${\displaystyle I}$
• the exatmospheric solar radiation ( solar constant ) ${\displaystyle I_{0}}$
• the atmospheric mass , i.e. the distance through the atmosphere as a multiple of the shortest possible distance at zenith irradiation ( is the solar zenith angle ). ${\displaystyle m=1/\cos \Theta _{z}}$ ${\displaystyle \Theta _{z}}$

Due to the atmospheric mass, the transmissivity depends on the position of the sun , i. That is, it changes over the course of the day, even if the atmospheric conditions remain the same. In contrast, the optical thickness of the atmosphere does not depend on the position of the sun; it can be measured with a photometer .

Components

The optical thickness of the atmosphere is made up of:

${\displaystyle \tau =\tau _{\text{Gas}}+\tau _{R}+\tau _{A}}$

Describe it

• the gas-optical thickness the absorption in the atmospheric gases (especially ozone , oxygen and water vapor ), but only in the wavelength ranges of the absorption bands of the gases. The optical thickness of the atmospheric gases (except water vapor) is practically constant and can be found in tables. ${\displaystyle \tau _{\text{Gas}}}$ ${\displaystyle \lambda }$
• the Rayleigh optical thickness is the extinction caused by Rayleigh scattering of the air molecules ${\displaystyle \tau _{R}(\lambda )=0{,}008735\cdot \lambda ^{-4{,}085}}$
• the aerosol optical thickness the Mie scattering on larger particles ( aerosols ). It can be determined from the other (measured or looked up) components: ${\displaystyle \tau _{A}}$

${\displaystyle \Leftrightarrow \tau _{A}=\tau -\tau _{R}-\tau _{\text{Gas}}}$

For a more detailed breakdown see Lambert-Beer law, remote sensing (atmosphere) .

literature

• Harry Nussbaumer, Hans Martin Schmid: Astronomy . vdf Hochschulverlag AG, 2003, ISBN 3-7281-2910-0 , p. 84–90 ( limited preview in Google Book Search).

Web links

• Andreas Roesch: Microscale optical density of a cloud (PDF; 5.1 MB). ETH Zurich, lecture microclimatology WS 2005/06.
• Henning Budde tree: sun photometer measurements . Uni-Trier, May 13, 2008 - April 7, 2009, pp. 3–5.

Individual evidence

1. ↑ Detlev Möller: Air: chemistry, physics, biology, cleanliness, law . Walter de Gruyter, 2003, ISBN 978-3-11-016431-2 , p. 220 ( limited preview in Google Book search).
2. ^ ^{A b} Peter Kurzweil: The Vieweg formula lexicon: basic knowledge for engineers, natural scientists and medical professionals . Vieweg + Teubner, 2002, ISBN 3-528-03950-7 , pp. 275 .