## 1 Coherent Diffraction Imaging Using Synchrotron Light Source
With developing X-ray instrumentation and phase retrieval algorithms, coherent X-ray diffraction microscopy has been extended to nanoparticles [43; 44; 45; 46; 47; 48], mineral materials [49; 50], biological cells, bacteria and viruses [51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63]. Meanwhile, different CDI methods also developed quickly, such as Bragg-CDI [43; 44; 46; 48], Fresnel-CDI [64], Keyhole-CDI [65], Reflective-CDI [66] and Ptychography [67; 68]. These methods greatly increased the diversity and breadth of applications. Some technologies were incorporated from Cyro-EM, for example, Cryo-CDI [55; 56] and wet-CDI [60]. These borrowed technologies make high-resolution imaging without obvious radiation damage possible. In order to summarize the areas of attention for coherent X-ray diffraction microscopy, \(\sim\)200 published papers were analyzed. Fifty of them [24; 31; 32; 38; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78] were selected to generate the word cloud of Figure 1 which shows that reconstruction, diffraction, sample, resolution, structure and coherent are the most used terms during the last 18 years of synchrotron-based CDI papers. Besides, exposure, photons and radiation are also frequently used words. These suggest that published efforts have focused intensely on phase retrieval. It seems the reconstructed real space image was the main aspect of a publication a decade ago. Furthermore, the type of samples and the achieved resolution are also some of the most important parts of the selected papers. For biological specimen, radiation damage has also been a concern. From [PERSON]'s summarizing information [24], it can be found that one should be able to image a frozen-hydrated biological sample with CDI at a 10 nm resolution. To our knowledge, the currently published results showed that the best 3D image of biological samples'resolution is \(\sim\)30 nm [61], which is a little far away from the 10 nm resolution under the maximum radiation dose tolerance using a third-generation synchrotron light source. This lags behind the atomic resolution achieved by electron microscopy. For the similar samples, such as human chromosome, the resolution of 3D structures with CDI and Cryo-EM is \(\sim\)120 nm [57] and \(\sim\)50 nm [88], respectively. The advent of a fourth-generation source, diffraction-limit storage ring (DLSR), opens a promising pathway for CDI [90; 91; 92]. The low transverse emittance and beam divergence improve the coherent fraction of the X-ray beam, especially for hard X-rays. The direct result is that the coherent photon of DLSR will be higher than that of current synchrotron light source. The obtainable resolution for CDI scales directly with the spatial coherence (as long as damage can be avoided). At the moment, many facilities around the world intend to update or build DLSR facilities [93], such as ESRF Upgrade Phase II [94], Spring-8 [95], MAX-IV [96], Sirius [97], etc. Looking forward, the investment X-ray facilities are putting into DLSR operations will yield new science possibilities for CDI.