  We establish the angle-resolved thermal emission spectroscopy (ARTES) as a
new platform to characterize the intrinsic eigenmode properties of
non-Hermitian systems. This method can directly map the dispersion of
meta-crystals within the light cone with a high angular resolution. To
illustrate its usefulness, we demonstrate the existence of bound states in the
continuum (BICs) and non-Hermitian Fermi arcs in a planar corrugated
meta-crystal by measuring its angle-resolved thermal emission spectra. We show
that change in the thickness of the meta-crystal can induce a band inversion
between a BIC and a radiative state, and a pair of exceptional points emerge
when the band inversion occurs. With this approach, the band mapping of
non-Hermitian photonic systems can become a relatively straightforward task.
