Far-Field Linear Optical Superresolution via Heterodyne Detection in a Higher-Order Local Oscillator Mode

Abstract

Rayleigh criterion has been the unbreakable rule for direct imaging. In the past few decades, new imaging techniques emerged to circumvent Rayleigh limit by changing the imaging conditions. By analysing the optical field in image plane with quantum optics, one can find quantum Fisher information for estimating the distance between two light sources remains constant, which means one can always estimate this distance with finite error. This discovery makes Rayleigh criterion irrelevant to quantum optimal measurements. Inspired by the theoretical analysis, we propose an experimental implementation to achieve sub-Rayleigh resolution. Using optical heterodyne detection with a local oscillator in TEM01, we can measure the single slit position within 0.0015 and 0.012 of Rayleigh limit for coherent and incoherent light. We can also measure the distance between two slits emitting incoherent light within 0.019 of Rayleigh limit. By engaging more Hermite-Gaussian modes, we can reconstruct the full image.