Optical depth

The optical thickness (usually denoted τ ), and optical depth is a measure of how well a physical medium can electromagnetic waves happen. When passing through a layer of material (for example, the atmosphere) to the optical thickness τ = 1 is incident radiation density on the 1/e-fache from ( ≈ 37%). For the case τ »1 one speaks of optically thick if τ « 1, it is said optically thin.

The optical thickness of a material is different for different frequencies. It is calculated by integration of the absorption coefficient over the path that the radiation has to travel (light path ):

In a homogeneous medium is assumed to be the whole is simplified to a multiplication of the particle, and the light path cross section of the power in question.

Optical thickness of the atmosphere

The optical thickness of the atmosphere is a sunlight- independent measure of the transmissivity of the atmosphere.

The transmissivity at a given wavelength is calculated according to, wherein the intensity of solar radiation in the wavelength considered is on the ground, the exatmosphärische sunlight ( solar constant ). The transmissivity is, however, dependent on the position of the sun and therefore changes in atmospheric conditions also constant throughout the day.

Alternatively, the atmosphere can be regarded as a turbid medium under the law of Lambert -Beer. Then, the radiation can on the ground

Are shown. is in this case the atmospheric composition, ie, the distance through the atmosphere, as a multiple of the shortest possible distance on the zenith light. Usually, the atmospheric mass from the solar zenith angle is calculated. The optical thickness corresponds to the extinction coefficient in the Lambert- Beer law.

The optical thickness of the atmosphere is the sum of the thickness, the gas optical thickness and the aerosol optical thickness Rayleigh optical. The Rayleigh optical thickness contributes caused by Rayleigh scattering of air molecules absorbance bill that aerosol optical thickness by the Mie scattering by larger particles ( aerosols ). The gas - optical thickness is contributed by the absorption of atmospheric gases (particularly ozone, oxygen and water vapor), but only in the wavelength ranges of the absorption bands of the gases.

The total optical thickness can be measured with a photometer, the Rayleigh optical thickness is according to the formula

Be calculated. The optical thickness of the atmospheric gases (other than steam) is almost constant and can be taken from tables. From this, the aerosol optical thickness in the considered wavelength after

Be determined.