Generalised Holography Meets Coherent Diffractive Imaging

Coherent diffractive imaging (CDI) is an imaging technique that seeks to restore the exit-surface wave from intensity measurements, either in the far field diffraction plane or the Fresnel diffraction region. To date numerous strategies have been proposed to complete this restoration, the most successful being the original scheme proposed by Gerchberg and Saxton and its subsequent modifications [1]. These schemes all involve the iterative refinement of a trial wave function using a-priori known information about the sample in conjunction with the measured amplitude to constrain the proposed exit surface wave function phase. These approaches use the self interference of the exit surface wave to transform the reconstruction process into a nonsmooth, nonconvex nonlinear optimization problem and as such are plagued by uniqueness issues. Concurrent to developments in CDI have been developments to Fourier Holography [2]. In Fourier holography the measured interference between a reference wave and the unknown scattered wave is used to deduce the complex exit surface wave. Under special circumstances where the reference wave has a particular structure (i.e. a pinhole or uniformly redundant array in the object plane), the inversion from the diffraction measurement is direct and a unique solution is obtained.