A unified phase retrieval algorithm for both far-flield and near-field diffractive imaging

X-ray coherent diffractive imaging is attracting interest within the x-ray community because it promises wavelength-limited resolution for imaging nonperiodic objects. It is well known that a wave diffracted or scattered by an object can be described simply by the Fourier transform of the object's electron density distribution. However, this result is general only in the so-called far-field regime, where most practical work is done. In the near-field regime, evaluations of wave field amplitudes become more complicated, and Fresnel diffraction and imaging effects have to be taken into account. In this paper, we present an algorithm that can be used to reconstruct an object from a near-field diffraction pattern. The algorithm uses the concept of a 'phase-chirped' distorted object, where a Fresnel-zone construction is embedded on an original object. This algorithm can eliminate the twin image ambiguity in phase retrieval and will therefore improve the convergence of retrieval. Our algorithm is a unified algorithm, consistent with those used in far-field experiments. Our algorithm extends the applicability of Fourier-based iterative phasing algorithms that are already established for far-field diffraction into the near-field holographic regime where phase retrieval has traditionally been difficult.