Coherent Diffraction Imaging

For centuries, lens-based microscopy, such as light, phase-contrast, fluorescence, confocal and electron microscopy, has played an important role in the evolution of modern science and technology. In 1999, a novel form of microscopy, known as coherent diffraction imaging (CDI) or lensless imaging, was developed and transformed our traditional view of microscopy, in which the diffraction pattern of a noncrystalline object or a nanocrystal was first measured and then directly phased to obtain an image (1). The well-known phase problem is solved by combining the oversampling method with iterative algorithms. The origin of the oversampling concept can be traced back to the Shannon sampling theorem (2). When the diffraction pattern of a finite object is sampled at a frequency sufficiently finer than the Nyquist interval, the phase information is in principle encoded in the diffraction intensities (3) and can be directly retrieved by an iterative algorithm (4). Over the past decade, various CDI methods, such as plane wave CDI, Bragg CDI and ptychographic CDI, have been implemented using synchrotron radiation, X-ray free electron lasers (XFELs), high harmonic generation, optical lasers, and electrons (517).