Exceeding the limits of algorithmic self-calibration in super-resolution imaging

Abstract: Fourier ptychographic microscopy is a computational imaging technique that provides quantitative phase information and high resolution over a large field-of-view. Although the technique presents numerous advantages over conventional microscopy, model mismatch due to unknown optical aberrations can significantly limit reconstruction quality. Many attempts to address this issue rely on embedding pupil recovery into the reconstruction algorithm. In this paper we demonstrate the limitations of a purely algorithmic approach and evaluate the merits of implementing a simple, dedicated calibration procedure. In simulations, we find that for a target sample reconstruction error, we can image without any aberration corrections up to a maximum aberration magnitude of $\lambda$/40. When we use algorithmic self-calibration, we can increase the aberration magnitude up to $\lambda$/10, and with our in situ speckle calibration technique, this working range is extended further to a maximum aberration magnitude of $\lambda$/3. Hence, one can trade-off complexity for accuracy by using a separate calibration process, which is particularly useful for larger aberrations.