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Atmosphere

Consider a source S_1 with intrinsic spectrum I_{0,1} and a source S_2 with intrinsic spectrum I_{0,2}. The fluxes measured on the atmosphere will be

S_1 = I_{0,1} R_{\nu} \exp^{-A_{\nu} am_1} S_2 = I_{0,2} R_{\nu} \exp^{-A_{\nu} am_2}

where R_{\nu} is the frequency-dependent response of the telescope, A_{\nu} the frequency-dependent atmospheric absorption and am_1, am_2 are the airmasses at which the two sources are observed.

Then

\frac{S_1}{S_2} = \frac{I_{0,1}}{I_{0,2}} \exp^{-A_{\nu} (am_1 - am_2)}

and thus

\log\left(\frac{S_1}{S_2}\right) = - \log\left(\frac{I_{0,1}}{I_{0,2}}\right) \cdot A_{\nu} (am_1 - am_2)

So, a logarithmic plot of the fluxes (divided by the intrinsic spectra) versus airmasses gives a straight line with a slope that corresponds to the atmospheric absorption. One can then interpolate the extinction at a certain airmass. This is done in Roy's Reduction Tools.