We present a theory to extend the classical Abbe resolution limit by introducing a spatially varying phase into the illumination beam of a phase imaging system. It allows measuring lateral and axial distance differences between point sources to a higher accuracy than intensity imaging alone. Various proposals for experimental realization are debated. Concretely, the phase of point scatterers' interference is experimentally visualized by high numerical aperture (NA = 0.93) digital holographic microscopy combined with angular scanning. Proof-of-principle measurements are presented by using sub-wavelength nanometric holes on an opaque metallic film. In this manner, Rayleighs classical two-point resolution condition can be rebuilt. With different illumination phases, enhanced bandpass information content is demonstrated, and its spatial resolution is theoretically shown to be potentially signal-to-noise ratio limited.
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.<sup>1</sup> 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.<sup>2</sup> 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).