  We consider the Helmholtz equation in the half space and suggest two methods
for determining the boundary impedance from knowledge of the far field pattern
of the time-harmonic incident wave. We introduce a potential for which the far
field patterns in specially selected directions represent its Fourier
coefficients. The boundary impedance is then calculated from the potential by
an explicit formula or from the WKB approximation. Numerical examples are given
to demonstrate efficiency of the approaches. We also discuss the validity of
the WKB approximation in determining the impedance of an obstacle.
