An inverse scattering problem of estimating the reflection coefficient and the surface impedance from two sets of absolute values of the near field with periodic change is investigated. The problem is formulated in terms of a nonlinear simultaneous equations which is derived from the relation between the two sets of absolute values and the field defined by a finite summation of the modal functions by applying the Fourier analysis. The reflection coefficient is estimated by solving the equations by Newton's method through the successive algorithm with the increment of the number of truncation in the summation one after another. Numerical examples are given and the accuracy of the estimation is discussed.