  In solar physics, it is a big challenge to measure the magnetic fields
directly from observations in the upper solar atmosphere, including the
chromosphere and corona. Radio observations are regarded as the most feasible
approach to diagnose the magnetic field in solar chromosphere and corona.
However, because of the complexity and diversity of the emission mechanisms,
the previous studies have only presented the implicit diagnostic functions of
the magnetic field for specific mechanism from solar radio observations. This
work collected and sorted out all methods for diagnosing coronal magnetic field
from solar radio observations, which are expressed as a set of explicit
diagnostic functions. In particular, this work supplemented some important
diagnostic methods missed in other reviews. This set of diagnostic functions
can completely cover all regions of the solar chromosphere and corona,
including the quiet region, active region and flaring source regions. At the
same time, it also includes incoherent radiation such as bremsstrahlung
emission of thermal plasma above the quiet region, cyclotron and
gyro-synchrotron emissions of magnetized hot plasma and mildly relativistic
nonthermal electrons above the active regions, as well as coherently plasma
emission around flaring source regions. Using this set of diagnostic functions
and the related broadband spectral solar radio imaging observations, we can
derive the magnetic fields of almost all regions in the solar atmosphere,which
may help us to make full use of the spectral imaging observations of the new
generation solar radio telescopes (such as MUSER, EVOSA and the future FASR,
etc.) to study the solar activities, and provide a reliable basis for the
prediction of disastrous space weather events.
