The linear and the quadratic Born approximations of the inverse scattering
problem are analyzed in the case of multifrequency measurements. The attent
ion is focused on the determination of the maximum number of independent da
ta available to perform the inversion for a fixed frequency interval. This
number is obtained by performing the Fourier transform of the field scatter
ed by the object under test and calculating its bandwidth under both the ap
proximations, The results were that the quadratic model allows us to achiev
e a double number of independent data, changing the class of profiles that
can be reconstructed with respect to the linear model. In order to show the
validity of this conclusion, a numerical example of inversion under the tw
o different models is performed.