Sub-wavelength passive single-shot computational super-oscillatory imaging

Abstract

Super-oscillatory (SO) imaging presents a passive solution to the sub-diffraction imaging challenge. The point spread functions (PSFs) of SO systems are band-limited and locally oscillate faster than their highest Fourier frequency. Because of this property, SO imaging systems are not bound by the Nyquist limit, allowing them to acquire details finer than the diffraction limit. In this work, we present a comprehensive theoretical analysis of passive incoherent SO imaging, leading to two key results. First, we show that the SO property of an imaging system is preserved when the system is combined with a general system of lenses. This opens the door for integrating SO imaging into existing microscopes and telescopes. Second, we show that incoherent SO imaging cannot resolve feature sizes below λ / 2 because of the inability to achieve incoherence at finer scales. This establishes the operational limits of the approach. We demonstrate our theory experimentally with a compound SO system that achieves sub-wavelength resolutions using high-NA lenses and Fourier spectrum modulation.