# Point Spread Function size: Full Width Half Maximum (FWHM) vs Sigma

I having been studying some astronomy papers related to galaxy observations and I realized that every time they want to express the size of the Point Spread Function (PSF) of a system which can be approximated by Gaussian they use the Full Width Half Maximum (FWHM) and not the sigma. Is there a reason behind that?

Thank you.

-

## 1 Answer

FWHM is the indicator of the width of a Gaussian that is easiest to measure, and is least error prone in terms of actual physical measurement (due to the slope of a Gaussian being the highest near half maximum - not exactly sure about this, but it does seem like that's the case - so error in y contributes least in the measurement of width, relatively. If this is not clear, look at a noisy Gaussian - something like this: http://www.astronomie-amateur.fr/Documents_Supernovae/Mesure_Vexp_gauss.PNG - and you'll know what I mean. It seems most sensible to estimate width using FWHM). And it has a simple correlation to the sigma with a factor of 2.35 if the distribution is actually Gaussian (which is often the assumption for PSFs - correct me if I'm wrong). Measuring actual standard deviation of data with errors is much more complicated than just simply measuring FWHM, and often it is enough to know the FWHM estimate. Hope this is the answer you were looking for.

-