[1] —

At this point, all the ρ_j(s) are unknowns, and the measurement does not contain enough information to retrieve vertical profiles of all absorbers. The slant column density, SC_j, is therefore introduced, which is defined as the total number of molecules of a species per unit area integrated along the light path:

[2] —

The slant column density is often abbreviated to slant column although that is not strictly the correct nomenclature.

If we now assume that the absorption and scattering cross-sections σ_j do not depend on s i.e. on where the molecule is located, then the sum over the individual terms and the integral along the light path can be exchanged and equation [1] be expressed in slant column densities:

[3] —

This assumption is valid as long as the absorption cross-sections have no pressure and temperature dependence. While the pressure dependence can in most cases be neglected, many absorption cross-sections including that of NO₂ have significant temperature dependence. This can be corrected but will not be described here.