  We describe a practical procedure for extracting the spatial structure and
the growth rates of slow eigenmodes of a spatially extended system, using a
unique experimental capability both to impose and to perturb desired initial
states. The procedure is used to construct experimentally the spectrum of
linear modes near the secondary instability boundary in Rayleigh-B\'{e}nard
convection. This technique suggests an approach to experimental
characterization of more complex dynamical states such as periodic orbits or
spatiotemporal chaos.
