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

Abstract

Incoherent imaging via an unmodified full pupil seemingly yields the maximum achievable signal-to-noise ratio (SNR) with respect to a fixed photon budget. Such photon-limited SNR is critical in many imaging scenarios, for example, in the case of fluorescence microscopy. In this work, we propose a general method that achieves a better SNR for transmitting high spatial frequency information through an optical imaging system, without the need to capture more photons. This is achieved by splitting the pupil of an incoherent imaging system such that two sub-images are simultaneously acquired and computationally recombined. We compared the theoretical performance of split pupil imaging to the non-split scenario and implement the splitting using a tilted elliptical mirror covering ≈50% of the pupil, placed at the back-focal-plane (BFP) of a fluorescence widefield microscope. Additionally, the proposed system exhibits an extended-depth-of-field (EDoF), utilized further to assign some of the measured (in-focus) signal to different axial planes of the reconstructed sample, through thick slice deconvolution. Our proposed method can be modified to tailor SNR enhancements to specific metrology tasks or to exploit other properties (e.g., spectral or polarization information) for SNR enhancement with impact on future imaging schemes.

Incoherent Active Convolved Illumination Enhances the Signal-to-Noise Ratio for Shot Noise: Experimental Evidence

“…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,[35][36][37]. How to tackle this problem ideally has been an open question for decades [36][37][38][39][40].…”

“…Popular techniques to improve image resolution or SNR are structured illumination microscopy (SIM) [3,[41][42][43][44], stimulated emission depletion (STED) microscopy [41,45,46], stochastic optical reconstruction microscopy/photoactivated localization microscopy (STORM/PALM) [41,47,48], and computational methods [36-40, 49, 50] including machine learning [35,51]. An interesting method for farfield imaging with a constant 'photon budget' (i.e., a con-stant 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 it is expected to benefit both conventional and novel approaches.…”

“…The auxiliary pattern is typically found by characterizing the spectral distribution of noise obtained from the reference imaging system in Fig. 1(a) [2], as the noise poses the fundamental limit to accessible spatial information [4,35,36]. The auxiliary and object patterns can also be implemented as an inherently single entity (i.e., from a single undivided source) in the object plane as shown in Fig.…”

“…The previous works on the foundations of ACI [2,27,[31][32][33][34], along with further inspiration from other research on noisy far-field imaging [3,4], led us to construct the current work, which presents the first experimental evidence for the theory of ACI. Following the implementation sketched in Fig.…”