Summary: An inverse scattering problem of estimating the surface impedance for an inhomogeneous half-space is investigated. By virtue of the fact that the far field representation contains the spectral function of the scattered field, complex values of the function are estimated from a set of absolute values of the far field. An approximate function for the spectral function is reconstructed from the estimated complex values by the least-squares sense. The surface impedance is estimated through calculating the field on the surface of the half-space expressed by the inverse Fourier transform. Numerical examples are given and the accuracy of the estimation is discussed.