Saturn's faint outermost ring, discovered in 2009 (ref. 1), is probably formed by particles ejected from the distant moon Phoebe(2,3). The ring was detected(1) between distances of 128 and 207 Saturn radii (R-S 5 60,330 kilometres) from the planet, with a full vertical extent of 40R(S), making it well over ten times larger than Saturn's hitherto largest known ring, the E ring. The total radial extent of the Phoebe ring could not, however, be determined at that time, nor could particle sizes be significantly constrained. Here we report infrared imaging of the entire ring, which extends from 100R(S) out to a surprisingly distant 270R(S). We model the orbital dynamics of ring particles launched from Phoebe, and construct theoretical power-law profiles of the particle size distribution. We find that very steep profiles fit the data best, and that elevated grain temperatures, arising because of the radiative inefficiency of the smallest grains, probably contribute to the steepness. By converting our constraint on particle sizes into a form that is independent of the uncertain size distribution, we determine that particles with radii greater than ten centimetres, whose orbits do not decay appreciably inward over 4.5 billion years, contribute at most about ten per cent to the cross-sectional area of the ring's dusty component.