The intensity I of a narrow beam of sunlight of a particular wavelength that reaches Earth's surface is given by
I = Ioe-(am)
where Io is the intensity of sunlight just above Earth's atmosphere, a is the total atmospheric optical thickness, and m is the relative air mass. m=1 when the sun is directly overhead and is otherwise approximately equal to sec(z), where z is the solar zenith angle.
The total atmospheric optical thickness can be divided into two parts -- one part due to the fact that molecules in the atmosphere scatter sunlight out of a direct beam from the sun (Rayleigh scattering) and another part due to scattering by aerosols. The Rayleigh scattering term aR is proportional to the ratio of atmospheric pressure at the observer's location to sealevel atmospheric pressure, p/po. Hence,
a = aa + aR(p/po)
If a sun photometer measures light intensity such that the voltage signal produced by the instrument is directly proportional to intensity, then
V = Vo(ro/r)2e-[aa + aR(p/po)]m
Solving for aa,
aa = [ln(Vo(ro/r)2) - ln(V) - aR(p/po)m]/m
Two quantities on the right side of this equation are constant because they are properties of your instrument. The voltage Vo, the extraterrestrial constant, is the voltage your sun photometer would see it were pointed at the sun just outside the earth's atmosphere when the earth is 1 astronomical unit (AU) from the sun. This calibration constant is determined for your instrument by the Science Team. The Rayleigh scattering term aR depends on the wavelength at which a particular sun photometer responds to sunlight. In the case of the GLOBE sun photometer, the value of aR is determined from the spectral response of the LED detectors and is equal to about 0.138 for the green channel and about 0.058 for the red channel.
The other quantities on the right side of the equation depend on the conditions under which you make a measurement. The voltage V is what you record when you point your GLOBE sun photometer at the sun, minus the dark voltage. (For various versions of the GLOBE sun photometer, the dark voltage has varied from less than 0.001V to 0.015 V.) The ratio ro/r is the ratio of 1AU to the actual distance from the earth to the sun, in units of AU, at the time you make a measurement; it is a function of the date on which a measurement is made and it is used to correct the constant Vo to the voltage your sun photometer would see at the time of a measurement. You can determine p/po either directly, with a barometer, or indirectly (to reasonable accuracy) by knowing the elevation of your observing site.
It is a simplification to say that total atmospheric optical thickness depends just on molecular (Rayleigh) scattering and aerosols. The simplification is useful because it conceptually separates the contributions of the "natural" (molecular) atmosphere from "contaminants" such as aerosols. Other contributors to the latter category include ozone, which absorbs sunlight in the wavelength range of the GLOBE sun photometer. Ozone absorption can be accounted for by direct measurements of total ozone in the atmosphere (not just tropospheric ozone, which is a GLOBE atmospheric protocol), by using ozone measurements made from satellites, or by using climatological averages of ozone concentrations for a particular location and season. Direct measurements of total ozone require very expensive equipment. Climatological averages are less accurate than satellite-based measurements. In very clean air, the errors due to ignoring absorption by ozone and other gases can be significant. However, it is possible to apply corrections "after the fact" if enough information is available from other sources.