  Coronal magnetic fields are well known to be one of the crucial parameters
defining coronal physics and space weather. However, measuring the global
coronal magnetic fields remains challenging. The polarization properties of
coronal radio emissions are sensitive to coronal magnetic fields. While they
can prove to be useful probes of coronal and heliospheric magnetic fields,
their usage has been limited by technical and algorithmic challenges. We
present a robust algorithm for precise polarization calibration and imaging of
low-radio frequency solar observations and demonstrate it on data from the
Murchison Widefield Array, a Square Kilometer Array (SKA) precursor. This
algorithm is based on the Measurement Equation framework, which forms the basis
of all modern radio interferometric calibration and imaging. It delivers high
dynamic range and fidelity full Stokes solar radio images with instrumental
polarization leakages $<1\%$, on par with general astronomical radio imaging,
and represents the state-of-the-art. Opening up this rewarding, yet unexplored,
phase space will enable multiple novel science investigations and offer
considerable discovery potential. Examples include detection of low-level of
circularly polarization from thermal coronal emission to estimate large-scale
quiescent coronal fields; polarization of faint gyrosynchrotron emissions from
coronal mass ejections for robust estimation of plasma parameters; and
detection of the first-ever linear polarization at these frequencies. This
method has been developed with the SKA in mind and will enable a new era of
high fidelity spectro-polarimetric snapshot solar imaging at low-radio
frequencies.
