Remote sensing of NO2
2.2.2.1.1 Beer-Lambert Law: basics

The Beer-Lambert Law describes the relationship between the amount of light that passes through an absorbing substance, the concentration of the substance and the distance the light travels through the substance.

The basic form of the Beer-Lambert Law is

where

λ is the wavelength of the light [m];
Aλ is the absorbance at wavelength λ [dimensionless];
σλ is the absorption coefficient for the absorbing substance at wavelength λ, which in the case of a gas is expressed as the absorption cross-section [m2];
L is the optical path length, that is the distance that the light travels through the absorbing substance [m];
C is the concentration of the absorbing substance in the light path, which in the case of a gas is expressed as a density [kg·m-3].

Since the absorbance can be expressed as

where

I0λ is the monochromatic radiance of the incident light at wavelength λ [W·m-2·m-1·sr-1]
I1λ is the monochromatic radiance after passing through the material at wavelength λ [W·m-2·m-1·sr-1]

the Beer-Lambert Law can also be expressed as

or

Thus if the optical path length L and the light intensities before and after absorption are known, the concentration C of the absorbing substance can be calculated.

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