# 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
or graphically as

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.