  We introduce the Optimal Fingerprinting Process which is aimed at accurately
identifying the parameters which characterize the dynamics of a physical
system. A database is first built from the time evolution of an ensemble of
dynamical systems driven by a specific field, which is designed by optimal
control theory to maximize the efficiency of the recognition process. Curve
fitting is then applied to enhance the precision of the identification. As an
illustrative example, we consider the estimation of the relaxation parameters
of a spin- 1/2 particle. The experimental results are in good accordance with
the theoretical computations. We show on this example a physical limit of the
estimation process.
