  We report a technique for experimental characterization of an $M$-mode
quantum optical process, generalizing the single-mode coherent-state
quantum-process tomography method [M. Lobino et al., Science 322, 563 (2008);
A. Anis and A.I. Lvovsky, New J. Phys. 14, 105021 (2012)]. By measuring effect
of the process on multi-mode coherent states via balanced homodyne tomography,
we obtain the process tensor in the Fock basis. This rank-$4M$ tensor, which
predicts the effect of the process on an arbitrary density matrix, is
iteratively reconstructed directly from the experimental data via the
maximum-likelihood method. We demonstrate the capabilities of our method using
the example of a beam splitter, reconstructing its process tensor within the
subspace spanned by the first three Fock states. In spite of using purely
classical probe states, we recover quantum properties of this optical element,
in particular the Hong-Ou-Mandel effect.
