# Full Width Half Maximum (FWHM)

The Full Width Half Maximum (FWHM) is a measure of the quality of an astronomical image based on how much the telescope and atmosphere have smeared a point source in an image over several pixels in the CCD.

When performing photometry, a value for the aperture has to be selected. This aperture is the size of the area containing the star that will be used to calculate the star's intensity. If this value is underestimated, measurements will not include all the light being collected by the telescope; if it is overestimated, it is possible that too much background light from nearby objects not related to the star might be included in the measurement. Some software packages calculate this value automatically, but it is usually better to calculate and fix this value in order to understand the limitations of your analysis. In an astronomical image, the photons collected from point sources such as stars will follow a distribution of a particular shape known as a Gaussian (see Figure 1). From this Gaussian, a value known as the Full Width Half Maximum can be calculated which gives us an optimum aperture size to select for our analysis. Figure 1: Full width half maximum. Credit: Michael Richmond, Rochester Institute of Technology

We can find this optimum aperture by choosing several values for the aperture radius (say between 5 and 40), and plotting a graph of radius against number of counts (see Figure 2). As we increase the aperture radius, we see that the count rate also increases. This is because more of the star is included within the aperture. Beyond a certain value however, the curve flattens showing that we have included the star and are merely adding in more of the background sky. The point at which this graph starts to flatten can be considered as an appropriate radius to use. It is worth noting though that there is not necessarily one unique correct answer here – rather, any aperture within a couple of pixels will probably be okay. In the example below, a value between and 11 and 15 would be appropriate. Figure 2: Calculating a suitable aperture. Credit: Sarah Roberts, Faulkes Telecope Project

Once chosen, it is important to stick to the same radius for all images of a particular dataset. For example, if you are performing photometry on the same star cluster in two different filters (e.g. B and V), then you should use the same radius for both images to ensure that you are comparing like with like. Equally, this should be the case if you intend performing photometry to create a lightcurve of a variable object over time.