Noniterative Exact Solution to the Phase Problem in Optical Imaging Implemented with Scanning Probe Microscopy

Abstract

An object is characterized by its amplitude and phase. However, when acquiring optical data about such an object, using a recording medium such as a camera, phase information is lost. Crystallography experienced a breakthrough in phase retrieval for large molecular entities by Max Perutz's introduction of "heavy atoms" using the method of isomorphous replacement. The availability of scanning probe microscopy and its full integration with optical microscopy allows us to apply these X-ray concepts to implement "heavy atom" restoration of phase in optical phase retrieval. In analogy to the heavy atom method, we acquire Fourier intensities in place of an X-ray diffraction pattern, and in place of the heavy atom, we utilize a nanometrically translatable point source of light based on the propagating field of a cantilevered near-field scanning optical microscopic (NSOM) probe controlled by an atomic force microscope (AFM). This integration of NSOM/AFM technology with far-field imaging achieves robust phase retrieval independent of external parameters, leading to 3D optical imaging. The methodology has super-resolution potential, and thus, heavy atom restoration of phase with super-resolution (HARPS) shows the potential of transparently integrated scanning probe microscopy with optical and other imaging modalities such as electron or ion optical imaging.