Strictly speaking, the badge is the finished article, as it were. However, at the heart of the badge is the film, which as far as I am aware, is a more or less conventional photographic emulsion which is sensitive to the energetic particles associated with radioactive decay. See for example
http://en.wikipedia.org/wiki/Ionizing_radiation under "monitoring".
Although the emulsions may be broadly similar, one type of radiological film cumulatively absorbs radioactive decay particles over time (the dosimeter), while the other, more familiar term, applies to the X-ray film used in hospitals.