Relative illumination is usually shown in a graph such as the one below
This effect can also be viewed in simulations. The first image below shows a simulated image through this eyepiece when ignoring the impact of relative illumination:
|Simulated image while ignoring the effect of relative illumination|
The second image shows the impact of relative illumination which can be seen at the edges
|Simulated image with relative illumination|
When we look at an optical design, we look to see that the relative illumination graph is monotonic, e.g. always decreasing. A non-monotonic curve (e.g. a sudden increase followed by a decrease) would manifest itself as a bright ring in the image, and this is usually not desired.