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.

Recently, the super-oscillation phenomenon has attracted attention because of its ability to super-resolve unlabelled objects in the far-field. Previous synthesis of super-oscillatory point-spread functions used the Chebyshev patterns where all sidelobes are equal. In this work, an approach is introduced to generate super-oscillatory Taylor-like point-spread functions that have tapered sidelobes. The proposed method is based on the Schelkunoff’s super-directive antenna theory. This approach enables the super-resolution, the first sidelobe level and the tapering rate of the sidelobes to be controlled. Finally, we present the design of several imaging experiments using a spatial light modulator as an advanced programmable grating to form the Taylor-like super-oscillatory point-spread functions and demonstrate their superiority over the Chebyshev ones in resolving the objects of two apertures and of a mask with the letter E.

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