Better than a lens -- Increasing the signal-to-noise ratio through pupil splitting

Experimental realization of the active convolved illumination imaging technique for enhanced signal-to-noise ratio

“…Since the shot noise variance is known from Eq. 5 (replacing I p,γ with N p,γ ) and we can assume the pixels are statistically independent, we can write [2][3][4] Var( Ñq,γ ) = Var…”

“…This is true, however typically (e.g., for incoherent light), the magnitude of the transfer function for an imaging system with an unobstructed pupil decreases with increasing spatial frequency [1]. It follows that the spectral SNR then also decreases with increasing spatial frequency, since the shot noise variance is constant in the spatial frequency domain [2][3][4]. Consequently, adding up more photons blindly does not lead to much increase for the SNR of high spatial frequencies.…”

“…The fundamental resolution limit to superresolving lenses is not determined by the diffraction limit, but rather by a shot noise limit, i.e. where the shot noise overcomes the transfer function in the spatial frequency domain [4,[42][43][44]. How to tackle this problem ideally has been an open question for decades [43][44][45][46][47][48].…”

“…Popular techniques to improve image resolution or SNR are structured illumination microscopy (SIM) [3,[49][50][51][52][53], stimulated emission depletion (STED) microscopy [49,54,55], stochastic optical reconstruction microscopy/photoactivated localization microscopy (STORM/PALM) [49,56,57], and computational methods [43][44][45][46][47][48][58][59][60] including machine learning [42,61,62]. An interesting method for far-field imaging with a constant "photon budget" (i.e., a constant number of photons in the object plane), based on a split-pupil-optimization, has recently been put forward to break the SNR limit imposed by Fermat's principle [4]. However, ACI operates down at the physical layer and enhances data acquisition, thus expected to benefit both conventional and novel approaches.…”

“…The previous works on the foundations of ACI [2,32,37,[39][40][41], along with further inspiration from other research in far-field imaging [3,4], led us to construct the current work, which presents the first experimental realization of ACI. Following the implementation sketched in Fig.…”