Review of partially coherent diffraction imaging

Coherent diffraction imaging (CDI), a type of lensless imaging method, relies on the use of light source with high-degree coherence to compute highly resolved complex-valued objects. The coherence of light source consists of temporal coherence and spatial coherence. In practice, it is difficult to obtain a fully coherent source. Spatial decoherence can be generated in the following three scenarios: no synchronization mechanism for the whole radiation source, a finite (non-zero) point spread function of the detector, and the sample variation within exposure time. Partial temporal coherence means that the beam is not quasi-monochromatic, behaving as the energy spread of the illumination. The consequence of reduced degree of temporal and/or spatial coherence in CDI is the decrease of visibility in the measured diffraction intensity. A fundamental assumption of CDI is the full temporal and spatial coherence, and even a relatively small deviation from full coherence can prevent the phase retrieval algorithm from converging accurately. It is necessary to break the barrier of limited coherence by improving the experimental setups directly or optimizing the phase retrieval algorithms to mitigate decoherence. Based on the Wolf's model of coherence-mode of light and the framework of CDI using partially coherent light proposed by Nugent et al., various methods have been proposed to solve the problems induced by low coherence. Those methods generally experience a similar development process, that is, from the requirement for measuring the spatial (coherent length or complex coherent factor) or temporal (spectrum distribution) coherence properties to without the need for such priori knowledge. Here in this work, the principles of partial coherent CDI, and the major progress of CDI with partial spatial- and temporal-coherent light are reviewed.