  Radiation from a narrow circular ring shows a characteristic double-horn
profile dominated by photons having energy around the maximum or minimum of the
allowed range, i.e. near the extremal values of the energy shift. The energy
span of a spectral line is a function of the ring radius, black hole spin, and
observer's view angle. We describe a useful approach to calculate the extremal
energy shifts in the regime of strong gravity. Then we consider an accretion
disk consisting of a number of separate nested annuli in the equatorial plane
of Kerr black hole, above the innermost stable circular orbit (ISCO). We
suggest that the radial structure of the disk emission could be reconstructed
using the extremal energy shifts of the individual rings deduced from the broad
wings of a relativistic spectral line.
