Differential optical absorption spectroscopy

In atmospheric chemistry, differential optical absorption spectroscopy (DOAS) is used to measure concentrations of trace gases.

When combined with basic optical spectrometers such as prisms or diffraction gratings and automated, ground-based observation platforms, it presents a cheap and powerful means for the measurement of trace gas species such as ozone and nitrogen dioxide.

The subscript i denotes different species, assuming that the medium is composed of multiple substances.

The first is to pull the absorption cross section out of the integral by assuming that it does not change significantly with the path—i.e.

Rather, what is done is to take the ratio of two measurements with different paths through the atmosphere and so determine the difference in optical depth between the two columns (Alternative a solar atlas can be employed, but this introduces another important error source to the fitting process, the instrument function itself.

If the reference spectrum itself is also recorded with the same setup, these effects will eventually cancel out): A significant component of a measured spectrum is often given by scattering and continuum components that have a smooth variation with respect to wavelength.

Removing the continuum components and adding in the wavelength dependence produces a matrix equation with which to do the inversion: What this means is that before performing the inversion, the continuum components from both the optical depth and from the species cross sections must be removed.

Obviously, this will not produce an exact equality between the measured optical depths and those calculated with the differential cross-sections but the difference is usually small.

Alternatively a common method which is applied to remove broad-band structures from the optical density are binomial high-pass filters.

Also, unless the path difference between the two measurements can be strictly determined and has some physical meaning (such as the distance of telescope and retro-reflector for a longpath-DOAS system), the retrieved quantities,

Measurements are taken at two different times of day: once with the sun high in the sky, and once with it near the horizon.

In both cases the light is scattered into the instrument before passing through the troposphere but takes different paths through the stratosphere as shown in the figure.

To deal with this, we introduce a quantity called the airmass factor which gives the ratio between the vertical column density (the observation is performed looking straight up, with the sun at full zenith) and the slant column density (same observation angle, sun at some other angle): where amfi is the airmass factor of species i,

Note that with this method, the column along the common path will be subtracted from our measurements and cannot be recovered.