  We use the inside-outside duality approach proposed by Kirsch-Lechleiter to
identify transmission eigenvalues associated with artificial backgrounds. We
prove that for well chosen artificial backgrounds, in particular for the ones
with zero index of refraction at the inclusion location, one obtains a
necessary and sufficient condition characterizing transmission eigenvalues via
the spectrum of the modified far field operator. We also complement the
existing literature with a convergence result for the invisible generalized
incident field associated with the transmission eigenvalues.
  This work is based on several of the pioneering works of our dearest
colleague and friend Armin Lechleiter and is dedicated to his memory.
