  Non-Hermitian physics has found a fertile ground in optics. Recently, the
study of mode degeneracies, i.e. exceptional points, has led to the discovery
of intriguing and counterintuitive phenomena. Degeneracies are typically
modeled through the coupled mode theory to determine the behaviour of
eigenstates and eigenvalues. However, the complex nature of the eigenvalues
makes hard their direct characterization from the response spectrum. Here, we
demonstrate that a coherent interferometric excitation allows estimating both
the real and imaginary parts of the eigenvalues. We studied the clockwise and
counter-clockwise modes in an optical microresonators both in the case of
Hermitian and non-Hermitian intermodal coupling. We show the conditions by
which a resonant doublet, due to the dissipative coupling of
counter-propagating modes caused by surface roughness backscattering, merges to
a single Lorentzian. This permits to estimate the optimal quality factor of the
microresonator in the absence of modal coupling caused by backscattering.
Furthermore, we demonstrate that a taiji microresonator working at an
exceptional point shows a degeneracy splitting only in one propagation
direction and not in the other. This follows from the strongly non-Hermitian
intermodal coupling caused by the inner S-shaped waveguide.
