Beyond the lateral resolution limit by phase imaging

We present a theory stating how to overcome the classical Rayleigh-resolution limit. It is based upon a new resolution criterion in phase of coherent imaging process and its spatial resolution is thought to be only SNR limited. Recently, the experimental observation of systematically occurring phase singularities in coherent imaging of sub-Rayleigh distanced objects has been reported.¹ The phase resolution criterion relies on the unique occurrence of phase singularities. A priori, coherent imaging system's resolution can be extended to Abbe's limit.² However, by introducing a known phase difference, the lateral as well as the longitudinal resolution can be tremendously enlarged. The experimental setup is based on Digital Holographic Microscopy (DHM), an interferometric method providing access to the complex wave front. In off-axis transmission configuration, sub-wavelength nano-metric holes on a metallic film acts as the customized high-resolution test target. The nano-metric apertures are drilled with focused ion beam (FIB) and controlled by scanning electron microscopy (SEM). In this manner, Rayleighs classical two-point resolution condition can be rebuilt by interfering complex fields emanated from multiple single circular apertures on an opaque metallic film. By introducing different offset phases, enhanced resolution is demonstrated. Furthermore, the measurements can be exploited analytically or within the post processing of sampling a synthetic complex transfer function (CTF).