  The 3-d inverse scattering problem of the reconstruction of the unknown
dielectric permittivity in the generalized Helmholtz equation is considered.
The main difference with the conventional inverse scattering problems is that
only the modulus of the scattering wave field is measured. The phase is not
measured. The initializing wave field is the incident plane wave. On the other
hand, in the previous recent works of the authors about the "phaseless topic"
the case of the point source was considered [20,21,22]. Two reconstruction
procedures are developed for a linearized case. However, the linearization is
not the Born approximation. This means that, unlike the Born approximation, our
linearization does not break down when the frequency tends to the infinity.
Applications are in imaging of nanostructures and biological cells.
