We report a methodology to determine the quality factor (Q) of wavy dark matter detectors equipped with multilayered resonators, including Fabry-Pérot interferometers and the so-called dielectric haloscope. An anechoic chamber enables the observation of the resonance frequency and its amplitude for an unlimited series of layers for the first time, which is conveniently filtered. The frequency-normalized power enhancement measured in a Dark Photons and Axionlike Particles Interferometer (DALI) prototype is a few hundred per layer over a sweep bandwidth of a few dozen of megahertz. In light of this result, this scaled-down prototype is sensitive to axions saturating the local dark matter density with a coupling to photons between gaγγ≳10-12 and gaγγ≳few×10-14 GeV-1 at frequencies of several dozens of gigahertz once cooled down to the different working temperatures of the experiment and immersed in magnetic fields ranging from about 1 to 10 T; while the sensitivity of the full-scale DALI is projected at gaγγ≳few×10-15 GeV-1 over the entire 25–250 μeV range since Q≳104 is expected.