Better than a lens – A novel concept to break the SNR-limit, given by Fermat’s principle

The signal in an incoherent imaging system gets transferred worse towards higher spatial frequencies. Since the photon noise is distributed equally in Fourier space, the signal‐to‐noise ratio (SNR) decreases. Ina noisy situation this reduces the effective imaging resolution. We propose to improve on this, by splitting the pupil of an imaging system into two parts to simultaneously obtain sub-images via each of these sub-pupils. Since the noise variance is proportional to the number of detected photons, it has been reduced in each of the sub-images. Recombining them by weighted averaging in Fourier-space yields an enhancement in (Fourier-) SNR compared to conventional imaging, resulting in an increased effective resolution limit in real space. We show a proof-of-concept experiment, in which we split the pupil by displaying orthogonally oriented blazed phase gratings for the different sub-pupils on a phase-only spatial light modulator. Our experiments confirm the improvement in effective resolution.