Abstract The resolution of an imaging system has long been constrained by the Abbe-Rayleigh diffraction limit. While significant progress has been made in developing superresolution techniques, many approaches rely on near-field scanning, fluorescence labeling, and are hindered by trade-offs among resolution, field-of-view, and energy efficiency. Here, we introduce a conceptually new approach that enables far-field, label-free superresolution imaging while avoiding the image-plane sidebands inherent to real-space superoscillatory imaging systems. By exploiting a 3D-patterned metalens with a topology-optimized response in both real- and k (wavevector)-space, we disrupt the spatially shift-invariance assumption in classical imaging systems, significantly expanding the effective lens aperture through a mechanism we term k -space superoscillation. This achieves resolution beyond the Rayleigh criterion. Prototype experiments at microwave frequencies demonstrate a twofold resolution enhancement over the diffraction limit without computational post-processing. This work opens avenues for applications ranging from biology, astronomy, and materials science.
Zhang et al. (2026) studied this question.