Coherent diffractive imaging using short wavelength light sources

Techniques that recover images from diffraction data obtained using coherent short-wavelength light sources are currently under active development for applications in nanotechnology and structural biology. In this review, an outline of paraxial optics is provided in a form that is sufficiently general to incorporate the coherence properties and frequency structure of illumination sources used in diffractive imaging applications. The Fourier phase problem is formulated in the context of imaging algorithms that are designed to obtain uniquely-determined phase distributions from measurements of diffraction data. The properties of several iterative phase retrieval algorithms for both coherent and partially-coherent diffractive imaging applications are presented in a unified formalism, together with a brief discussion of a non-iterative technique. Approaches to diffractive imaging based on Fraunhofer and Fresnel diffraction configurations are compared. Applications are described utilising quasi-monochromatic third-generation synchrotron X-ray sources and polychromatic high-harmonic generation table-top soft X-ray sources. The review concludes with a consideration of proposed applications of diffractive imaging approaches to the determination of biomolecular structures from isolated molecules using fourth-generation X-ray free-electron laser sources.