## 2 Coherent Diffraction Imaging with X-ray Lasers
The final imaging resolution was estimated to be 62 nm, where the phase retrieval transfer function (PRTF) drops to a value of 1/e. After this successful demonstration of the principle, pump-probe methodologies were applied to XFEL-CDI. Figure 2b,c [128; 120] show time-resolved imaging of transforming materials under a visible light stimulus at FLASH and LCLS, respectively. Dynamic changes in man-made structures (Figure 2b) and nanoparticles (Figure 2c) were observed. Such measurements represent examples of the truly unique power of XFELs to study dynamic systems. Other methods can also be combined with XFEL-CDI to yield further information. Figure 2d [126] shows the functional imaging of multiple nanoparticles. Time-of-flight mass spectrometry was used simultaneously with imaging, which allowed the morphology and chemical content to be captured at the same time by a single shot. Other methods such as fluorescence and emission spectroscopies can also be applied to reveal specific chemical information and correlate it to the structure revealed by imaging. Three-dimensional imaging is typically not only desired but also necessary to fully understand a system being studied. However, focused XFEL pulses are too intense and destroy the sample typically in one pulse, limiting the information available to two-dimensions in one pulse. Without attenuation, the ultra-intense pulses will destroy almost all particles interacting with the X-ray laser [143]. Three-dimensional images typically cannot be obtained by rotating samples using an X-ray FEL which makes computed tomography (CT) and transmission X-ray microscopy (TXM) regularly performed at synchrotron light sources not particularly suitable for XFELs. Three-dimensional information is obtained using an XFEL by using re-producible particles delivered to the X-ray laser pulses one at a time. In this manner, thousands to hundreds of thousands of diffraction patterns with random orientations are recorded by large pixel array detectors. Using methods such as diffusion maps or threshold methods, valid hits and single-particle hits can be selected and their relative orientation can be determined. After phase retrieval, high-resolution real-space images can be obtained. Worthy of noted, [PERSON] and colleagues developed a single-shot 3D imaging method for high-symmetry objects and demonstrated the idea on gold nanoparticles with X-ray lasers [131]. Figure 2e shows a 3D image of a nanoparticle from SACLA. By using the symmetry of gold nanoparticles, 48 diffraction patterns were generated. The 3D image was obtained after the finding of common arcs and phase retrieval. The final resolution was determined to be \(\sim\)5.5 nm. Compared to non-bioparticles, the coherent scattering cross-section of bioparticles is typically much smaller as they are composed of low atomic number elements primarily carbon, oxygen, nitrogen and hydrogen. In other words, the scattering signal of bioparticles is less than other particles when the particle size and photon parameters are the same. For example, the coherent scattering cross-section of gold (19.32 g/cm\({}^{3}\)) and DNA (C\({}_{10}\)H\({}_{11}\)N\({}_{4}\)O\({}_{6}\)P, 1.70 g/cm\({}^{3}\)) are 6.5 cm\({}^{2}\)/g and 0.4 cm\({}^{2}\)/g under 7 keV. However, the scattering ability of gold is over 100 times stronger than that of DNA. The weak scattering and low signal-to-noise-ratio (SNR) make high-resolution imaging of biological samples more challenging. Figure 3a [135] shows the first coherent diffraction imaging of biological samples at LCLS. High-quality diffraction data were obtained with a single X-ray laser pulse from a mimivirus. The reconstructed exit wavefront (image) shows a full-period resolution of 32 nm. Single cell, virus or bacteria imaging is of potential great importance to disease detection and drug design. It enables the  
Figure 2: Coherent diffraction imaging of materials with or without pump-probe using X-ray free-electron lasers. (**a**) The first demonstration of coherent diffraction imaging with X-ray lasers at FLASH in 2006.