Precise Localization of Multiple Noncooperative Objects in a Disordered Cavity by Wave Front Shaping

Complicated multipath trajectories of waves in disordered cavities cause object localization to be very challenging with traditional ray-tracing approaches. Yet it is known that information about the object position is encoded in the Green’s function. After a calibration step, traditional time-reversal approaches retrieve a source’s location from a broadband impulse response measurement. Here, we show that a nonemitting object’s scattering contribution to a reverberant medium suffices to localize the object. We demonstrate our finding in the microwave domain. Then, we further simplify the scheme by replacing the temporal degrees of freedom (d.o.f.) of the broadband measurement with spatial d.o.f. obtained from wave front shaping. A simple electronically reconfigurable reflectarray inside the cavity dynamically modulates parts of the cavity boundaries, thereby providing spatial d.o.f. The demonstrated ability to localize multiple noncooperative objects with a single-frequency scheme may have important applications for sensors in smart homes.

Figure 1

Experimental setup. See the main text for a description.

Figure 2

Uniqueness of dictionary entries using 391 temporal (left) or 500 spatial (right) d.o.f. (a),(b) Magnitude and complex representation of three sample dictionary entries $s_i$; the crosses indicate $⟨s_i⟩$. (c),(d) Average similarity between dictionary entries evaluated in two different ways; cf. main text. Sample similarity matrices $C^{\prime }$ are shown for the indicated cases.

Figure 3

Average localization success rate using frequency diversity as a function of the number of temporal d.o.f. $N_t=\mathrm{\Delta }f/\mathrm{\Delta }{f}_{\mathrm{corr}}$ used [see Eq. (2)].

Figure 4

Average localization success rate using wave front shaping. (a)–(c) Dependence of the success rate on the working frequency for scenarios of known $p$. (d)–(f) Average over the 16 best working frequencies as a function of the number of random SMM configurations $N_s$ used.