  We define the radiation fields of solutions to critical semilinear wave
equations in R^3 and use them to define the scattering operator. We also prove
a support theorem for the radiation fields with radial initial data. This
extends the well known support theorem for the Radon transform to this setting
and can also be interpreted as a Paley-Wiener theorem for the distorted
nonlinear Fourier transform of radial functions.
