Super Interferometric Range Resolution

We probe the fundamental underpinnings of range resolution in coherent remote sensing. We use a novel class of self-referential interference functions to show that we can greatly improve upon currently accepted bounds for range resolution. We consider the range resolution problem from the perspective of single-parameter estimation of amplitude versus the traditional temporally resolved paradigm. We define two figures of merit: (i) the minimum resolvable distance between two depths and (ii) for temporally subresolved peaks, the depth resolution between the objects. We experimentally demonstrate that our system can resolve two depths greater than $100\times$ the inverse bandwidth and measure the distance between two objects to approximately $20\mathrm{\mu }\mathrm{m}$ (35 000 times smaller than the Rayleigh-resolved limit) for temporally subresolved objects using frequencies less than 120 MHz radio waves.

Figure 1

Free-space (a) and guided-wave (b) and (c) ranging experimental schematics. Using parameter estimation techniques on interference-class waveforms, we estimate the distance between two scattering depths from a target which would otherwise be temporally subresolved.

Figure 2

Pulses and fast Fourier transforms. Panel (a) shows the functions used in the Letter. Panel (b) shows their Fourier transforms. Panel (c) shows the interfered waveforms from the coherent interference of two equal-amplitude pulses.

Figure 3

The signal $S$ is plotted against bandwidth of the triangle function with (interference) and without (no interference) a delay cable.

Figure 4

Signal $S$ vs time shift. The signal $S$ from Eq. (7) is computed and measured as a function of the relative shift of two $g(t)$ functions.