Inverse scattering from phaseless data in the freespace

In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method.