  Twistor correspondences for R-invariant indefinite self-dual conformal
structures on R^4 are established explicitly. These correspondences are written
down by using a natural integral transform from functions on a two dimensional
cylinder to functions on the flat Lorentz space R^{1,2} which is related to the
wave equation and the Radon transform. A general method on the twistor
construction of indefinite self-dual 4-spaces and indefinite Einstein-Weyl
3-spaces are also summarized.
