Quantitative Diffraction Tomography for Weak Scatterers Based on Aliasing Modification of the Multifrequency Spatial Spectrum

Abstract

Diffraction tomography (DT) is a linear approach to solving electromagnetic inverse scattering problems. Based on the weak scattering assumptions (such as Born or Rytov approximations), the spatial spectrum of the contrast at one certain frequency is a linear mapping of the scattered field data. As is well known, using more frequencies means better performance of noise suppression. However, the spatial spectra are aliased in cases of multi-frequency data. In addition, the permittivity and the conductivity are coupled in the aliased multi-frequency spatial spectrum. In this paper, a quantitative DT for weak scatterers is proposed by firstly doing a coordinate transformation, then decoupling the permittivity and the conductivity, and finally modifying the aliased multi-frequency spatial spectrum. In doing so, the modified spatial spectra of the permittivity and conductivity are formulated respectively, leading to a quantitative diffraction tomography for weak scatterers based on aliasing modification of the multi-frequency spectrum. Inversion results with synthetic and experimental data demonstrate that the proposed method outperforms the conventional DT approach in terms of quantitative inversion accuracy for weak scatterers of multi-frequency data while maintaining the anti-noise performance.