Nanostructures imaging via numerical solution of a 3-D inverse scattering problem without the phase information

Inverse scattering problems without the phase information arise in imaging of nanostructures, whose sizes are hundreds of nanometers, as well as in imaging of biological cells. The governing equation is the 3-D generalized Helmholtz equation with the unknown coefficient, which represents the spatially distributed dielectric constant. It is assumed in the classical inverse scattering problem that both the modulus and the phase of the complex valued scattered wave field are measured outside of a scatterer. Unlike this, it is assumed here that only the modulus of the complex valued scattered wave field is measured on a certain interval of frequencies. The phase is not measured. In this paper a substantially modified reconstruction procedure of [25] is developed and numerically implemented. Ranges of parameters, which are realistic for imaging of nanostructures, are used in numerical examples. Note that numerical studies were not carried out in [25].