Fig. 1. The schematic representation of the imaging set-up, for the object formed by (a) an array of small particles/lines and (b) a (binary) mask. D labels the position of a (coherent) detector, L is the size of the object (and equivalently the imaging aperture), and R is the distance from the object to the detector; in the far field R≫L.

Fig. 2. Super-resolution object reconstruction for a binary mask, from its coherently detected diffraction pattern in the far field. The inset shows the schematics of the object profile. The main panel plots the error probability in the recovered profile, as a function of the effective SNR. The data shown were obtained for 10,000 different realizations. The boundary separating the light-red and light-green background corresponds to the value of the SNR corresponding to Δ sufficient to resolve the λ/16 spacing (see the inset). The red arrow indicates the minimum value of SNR when the numerical reconstruction produces no errors.

Fig. 3. Super-resolution imaging of a subwavelength object, based on structured illumination with Bessel beams. (a) The “incident” Bessel beam of the order m=12 (shown in gray scale) focused at the center of the subwavelength object (red). (b) The Bessel beam profiles in the object plane, for different orders m=0 (red), 1 (orange), 2 (magenta), 3 (blue), 4 (cyan), and 5 (green). For a small distance from the center, the Bessel function of order m behaves as xm, so illumination with the Bessel beams of different orders effectively “projects” the target on the set {xm} for different values of m. As the latter form a complete basis set, this procedure allows high-resolution reconstruction of the original object profile, without any use of super-oscillations or subwavelength focusing. (c) The subwavelength object profile and its reconstruction with Bessel beam illumination. The object corresponds to the red line in (c). The reconstructed profiles are shown for the effective SNRs of 106 [blue line in (c)] and 104 [green line in (c)].