© Victor Gustafsson

Magnetic fields play a fundamental role in shaping astrophysical environments, yet their structure and evolution remain difficult to probe. One of the most powerful tools for studying cosmic magnetism is Faraday rotation, which encodes information about the strength and topology of magnetic fields along the line of sight. However, recovering this information from interferometric polarization data is challenging due to the incomplete frequency sampling and limited bandwidth of radio observations.

In this talk, I will present two algorithms aimed at reconstructing the true Faraday dispersion from radio interferometric observations. The first integrates aperture synthesis and rotation measure (RM) synthesis into a single, self-consistent framework. This joint deconvolution enables deeper cleaning and more accurate reconstruction of polarized emission, while simultaneously correcting for direction-dependent effects that are common in modern radio interferometry.

The second approach explores the use of deep learning for RM synthesis deconvolution. This method, which operates on stacks of deconvolved two-dimensional polarized images, uses a less restrictive prior than conventional algorithms, enabling the recovery of extended and complex structures in Faraday depth space.

I will begin by outlining the theoretical foundations of both RM synthesis and aperture synthesis, highlighting their formal similarities as Fourier inversion problems. This perspective provides the motivation for treating them within a unified framework. I will then introduce the two algorithms designed to reconstruct the Faraday dispersion, and discuss their underlying assumptions and computational strategies. Finally, I will present results from applying these methods to both synthetic datasets and real observational data from the LOFAR and MeerKAT radio telescopes.