  The quantized electromagnetic field inside and outside an absorbing high-$Q$
cavity is studied, with special emphasis on the absorption losses in the
coupling mirror and their influence on the outgoing field. Generalized operator
input-output relations are derived, which are used to calculate the Wigner
function of the outgoing field. To illustrate the theory, the preparation of
the outgoing field in a Schr\"{o}dinger cat-like state is discussed.
