FWHM explained
The technical term Full-Width Half-Maximum, or FWHM, is used to describe
a measurement of the width of an object in a picture, when that object
does not have sharp edges.
A simple box can be described just by its width, and a rectangle by its
width and height. However, the image of a star in an astronomical
picture has a profile which is closer to a Gaussian curve, given
mathematically by
![[exp(-x^2/sigma^2)]](gaussmath.gif)
or graphically as ![[gauss curve]](gausscurve.gif)
In order to compare different profiles, we can use the Gaussian
parameter in the denominator of the mathematical expression, usually
represented by the Greek letter sigma (
).
This does not really describe the extent of the profile, but we cannot
use the "total width" of the profile, because it extends forever,
albeit at a very low level after a distance of a few times sigma.
An alternative, which better reflects the approximate size of the
star's image as seen by the eye, is the width across the profile
when it drops to half of its peak, or maximum, value (shown in the graph
above). This is the full width of the image at half maximum value,
or full-width half-maximum, or FWHM. It is a simple and
well-defined number which can be used to compare the quality of images
obtained under different observing conditions.
In the usual sort of astronomical image, the FWHM is measured for a
selection of stars in the frame and the "seeing" or image quality is
reported as the mean value.