  The strength of optomechanical interactions in a cavity optomechanical system
can be quantified by a vacuum coupling rate $\vcr$ analogous to cavity quantum
electrodynamics. This single figure of merit removes the ambiguity in the
frequently quoted coupling parameter defining the frequency shift for a given
mechanical displacement, and the effective mass of the mechanical mode. Here we
demonstrate and verify a straightforward experimental technique to derive the
vacuum optomechanical coupling rate. It only requires applying a known
frequency modulation of the employed electromagnetic probe field and knowledge
of the mechanical oscillator's occupation. The method is experimentally
verified for a micromechanical mode in a toroidal whispering-gallery-resonator
and a nanomechanical oscillator coupled to a toroidal cavity via its near
field.
