  We investigate the effect of decoherence on Fano resonances in wave
transmission through resonant scattering structures. We show that the Fano
asymmetry parameter q follows, as a function of the strength of decoherence,
trajectories in the complex plane that reveal detailed information on the
underlying decoherence process. Dissipation and unitary dephasing give rise to
manifestly different trajectories. Our predictions are successfully tested
against microwave experiments using metal cavities with different absorption
coefficients and against previously published data on transport through quantum
dots. These results open up new possibilities for studying the effect of
decoherence in a wide array of physical systems where Fano resonances are
present.
