Using a high-resolution infrared spectrometer (FTIR) with the sun as radiation source it is possible to obtain:

This information is obtained via molecular absorption features within the terrestrial solar infrared spectrum, the so-called finger prints:

Solar absorption spectra are measured using a Fourier-Transform Infrared Spectrometer (FTIR):

A high-resolution FTIR can spectrally resolve individual vibrationâ€“rotation lines of the absorption bands:

The vertical column density of an atmospheric trace species (unit: molecules/cm^{2}) can then be derived from the absorption depth and the area of a single measured vibration-rotation line.

In addition, the shape of the absorption line of an atmospheric trace species contains information on the altitude profile of its concentration (e.g., volume mixing ratio as a function of altitude). The reason for this is the (linear) pressure broadening of the lines, which implies an altitude dependency of the line width:

Unfortunately, only the calculation of a spectral line shape (vector y) into a vertical concentration profile (vector x) is straight forward possible (forward calculation y = F(x)). The inverse problem x = I(y) is physically ill posed. In this situation one possible way to the solution is via the Bayesian approach:

The retrieved concentration profile x_{ret} is a weighted mean from information from the actual spectral measurement and the a priori information (or regularization) used in the inversion process. The relative contribution of spectral and a priori information depends on various factors (e.g. solar zenith angel and noise of the spectral measurement). Therefore, the retrieved profile has to be characterized via a so-called averaging kernel matrix A. It provides a linear relation between the true profile at the moment of observation x_{true}, the retrieved profile x_{ret} and the a priori profile x_{a}:

The colored functions are the rows of A which are called averaging kernels characterizing the retrieval at a certain altitude. Their vertical half-width is a measure for the achieved altitude resolution, their area is a measure for the sensitivity at the nominal altitude of the kernel.