Imaging small polarizable scatterers with polarization data
This work addresses the challenge of imaging small scatterers with limited polarization data, providing a theoretical foundation for resolution and tensor component recovery, though it is an incremental extension of existing phase retrieval and migration techniques.
The authors develop an imaging method for small polarizable scatterers using polarization measurements, showing that Kirchhoff migration applied to preprocessed coherency matrix data yields images asymptotically identical to those from ideal data at high frequencies.
We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency matrix or Stokes parameters of the electric field at the array. We introduce a simple preprocessing of the coherency matrix data that partially recovers the ideal data where all the components of the electric field are known for different source dipole moments. We prove that the images obtained using an electromagnetic version of Kirchhoff migration applied to the partial data are, for high frequencies, asymptotically identical to the images obtained from ideal data. We analyze the image resolution and show that polarizability tensor components in an appropriate basis can be recovered from the Kirchhoff images, which are tensor fields. A time domain interpretation of this imaging problem is provided and numerical experiments are used to illustrate the theory.