  We develop an enhanced technique for characterizing quantum optical processes
based on probing unknown quantum processes only with coherent states. Our
method substantially improves the original proposal [M. Lobino et al., Science
322, 563 (2008)], which uses a filtered Glauber-Sudarshan decomposition to
determine the effect of the process on an arbitrary state. We introduce a new
relation between the action of a general quantum process on coherent state
inputs and its action on an arbitrary quantum state. This relation eliminates
the need to invoke the Glauber-Sudarshan representation for states; hence it
dramatically simplifies the task of process identification and removes a
potential source of error. The new relation also enables straightforward
extensions of the method to multi-mode and non-trace-preserving processes. We
illustrate our formalism with several examples, in which we derive analytic
representations of several fundamental quantum optical processes in the Fock
basis. In particular, we introduce photon-number cutoff as a reasonable
physical resource limitation and address resource vs accuracy trade-off in
practical applications. We show that the accuracy of process estimation scales
inversely with the square root of photon-number cutoff.
