Iterative algorithm for interferometric retrieval of plasma density in case of considerably inhomogeneous objects

Interferometry is a widely used active diagnostic method for measurements of physical properties of plasmas. In case of axial symmetry of probed objects an Abel inversion can be used to retrieve plasma density profiles from phase shifts reconstructed from interferograms. This approach is based on the assumption of the diagnostic beam propagating along a straight line. However, it is well known that in case of inhomogeneous media the refraction process affects the diagnostic beam trajectory resulting in an inaccuracy of the retrieved density structure. In order to deal with this unfavourable effect a more sophisticated approach needs to be employed. In this paper a special iterative algorithm is proposed to deal with this issue. This algorithm turns the inversion procedure into series of iterations, where the appropriate distribution of plasma density is found by following the diagnostic beam actual trajectory during its propagation through the inhomogeneous medium. The assumption of axially symmetric plasma distribution still applies. The respective trajectories are calculated using the ray tracing method. This method also allows to use the paraxial wave equation. This iterative algorithm was tested on simulated data with different configurations of plasma density proving its functionality. Results from the simulated data analysis show that using this approach the effect of refraction can be fully compensated and plasma density is thus recovered accurately. Comparison with the results obtained only by the Abel inversion as such is provided for illustration.