In order to determine the number of NO₂ molecules along the light path the Beer-Lambert Law is used. This states that the intensity of a light beam transmitted through a medium decreases exponentially as a function of the absorption coefficient of the medium. However, in our application the situation is more complicated:

• Many different absorbers are present in the Earth's atmosphere at the same time.
• Different types of scattering also contribute to the extinction observed.

Considering the effects of all J absorbers with absorption cross-sections σ_j and density ρ_j(s) as well as Rayleigh scattering and Mie scattering, the relation between the measured radiance I and unattenuated solar radiation I₀ can be written as

[1] —

where the integral is taken along the light path through the atmosphere. In this equation note that:

• The factor α accounts for the fact that scattered light is observed, and the overall intensity depends on the efficiency of the scattering.
• The measured intensity depends on wavelength as does the solar irradiance and the absorption cross-sections, but also on the solar zenith angle, Θ, since this determines the geometry.
• The densities of the absorbers and scatterers are a function of the position along the light path s, since they vary with altitude.
• σ_Ray and σ_Mie are the Rayleigh and Mie extinction cross-sections respectively.
• ρ_Ray and ρ_Mie are the densities of Rayleigh and Mie scatterers respectively.