Understanding Extinction corrections in Photometry


The Earth's atmosphere absorbs light from a star before it reaches our telescopes. The amount of light absorbed depends on the altitude of the star above the horizon. Observations of a star at different times of the night therefore will give different magnitudes. Extinction correction helps us adjust for how the atmosphere dims the starlight before it reaches our telescopes.


An important factor in correcting for extinction is the airmass through which the light of the star has to travel. At the zenith, the airmass is 1 and this increases to a value of 2 at a zenith distance of 60°. As the zenith distance of the star increases, the absorption increases.


The dominant source of extinction in the atmosphere is Rayleigh scattering by air molecules. This means that extinction is much higher in the blue than in the red. The extinction can also vary from night to night depending on the conditions in the atmosphere, e.g. dust blown over from the Sahara can increase the extinction for European observers by up to 1 magnitude, depending on their specific location.


No explicit extinction correction is required when performing differential photometry. This is because the target and comparison stars are always observed at the same airmass, and hence suffer the same extinction. 



Extinction Coefficients


Extinction coefficients quantify the dimming of starlight as it passes through the Earth's atmosphere. By applying these coefficients, we can correct our measurements to reflect the true brightness of the stars. Phoranso allows to enter the Extinction Coefficient for each of the UBVRI filters you are using. Given those coefficients are bound to your specific equipment, they are part of the Settings window. Most observers will enter them once.


  • First-Order Extinction Coefficient


The first-order extinction coefficient (often denoted as k’) deals with the atmospheric dimming that depends on the airmass. This coefficient is specified for each UBVRI photometric filter because the atmosphere affects different wavelengths of light differently (see Rayleigh scattering mentioned above). It is expressed as mag/airmass.


The first-order correction is ~0.25 mag/airmass, so in a small field of view, it won't amount to 0.01 mag, unless the observer is imaging at low altitudes. When working with large field sizes of several degrees, the first (and second) order extinction corrections become much higher. 


  • Second-Order Extinction Coefficient


For very accurate photometry, the wide bandpass of photometric filters has to be taken into account when correcting for extinction. Because extinction is so strongly colour dependent, a blue object actually loses more light to the atmosphere than a red one. This is true even within the relatively narrow wavelength range of the UBVRI filters. The solution is to introduce a colour-dependent secondary extinction coefficient, 


The second-order extinction coefficient (denoted as k”) takes into account the color of the star, expressed by the color index (B-V). Like the first-order coefficient, each filter (U, B, V, R, I) has its own second-order extinction coefficient to account for the color dependence.

Typically, the correction is ~0.03 mag per color index per airmass. In most cases, second-order extinction can be ignored. Exceptions for instance are when doing photometry on very red stars in a blue filter.