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Differential Airmass

Radu Corlan     January 10, 2005

The difference in airmass between two points in a frame depends on the angular separation between them, the airmass of the frame and the relative orientation of the two points. The difference will be greatest when the two point lie on top of each other (i.e. they have the same azimuth); this is the worst case for differential airmass. This worst-case difference is plotted for various separations below:

differential airmass vs airmass

Using this graph, it is easy to determine if and when differential extinction can be neglected. For a given separation and airmass, find the differential airmass value from the graph and multiply it with the extinction coefficient. The resulting value is an upper bound to the magnitude of the differential extinction term. For the purpose of determining it, it is not necessary to use a precise extinction coefficient value; a typical value is enough (like 0.3-0.4 for the V band). If we want to make sure the differential extinction terms are below 0.003 for instance, it is reasonable to place a limit of 0.01 for the differential airmass.

The above graph was generated with gnuplot, using this command file.