During the last years we have seen the birth of free-electron lasers, a new type of light source ten billion times brighter than syncrotrons and able to produce pulses only a few femtoseconds long. One of the main motivations for building these multi-million dollar machines was the prospect of imaging biological samples such as proteins and viruses in 3D without the need for crystallization or staining. This thesis contains some of the first biological results from free-electron lasers. These results include 2D images, both of whole cells and of the giant mimivirus and also con- tains a 3D density map of the mimivirus assembled from diffraction patterns from many virus particles. These are important proof-of-concept experiments but they also mark the point where free-electron lasers start to produce biologically relevant results. The most noteworthy of these results is the unexpectedly non-uniform density distribution of the internals of the mimivirus. We also present Hawk, the only open-source software toolkit for analysing single particle diffraction data. The Uppsala-developed program suite supports a wide range fo algorithms and takes advantage of Graphics Processing Units which makes it very computationally efficient. Last, the problem introduced by structural variability in samples is discussed. This includes a description of the problem and how it can be overcome, and also how it could be turned into an advantage that allows us to image samples in all of their conformational states.

Coherent diffractive imaging (CDI) has become a very popular technique over the past two decades. CDI is a "lensless" imaging method which replaces the objective lens of a conventional microscope by a computational image reconstruction procedure. Its increase in popularity came together with the development of X-ray free-electron lasers (XFELs) which produce extremely bright and coherent X-rays. By facilitating these unique properties, CDI enables structure determination of non-crystalline samples at nanometre resolution and has many applications in structural biology, material science and X-ray optics among others. This work focuses on two specific CDI techniques, flash X-ray diffractive imaging (FXI) on biological samples and X-ray ptychography. While the first FXI demonstrations using soft X-rays have been quite promising, they also revealed remaining technical challenges. FXI becomes even more demanding when approaching shorter wavelengths to allow subnanometre resolution imaging. We described one of the first FXI experiments using hard X-rays and characterized the most critical components of such an experiment, namely the properties of X-ray focus, sample delivery and detectors. Based on our findings, we discussed experimental and computational strategies for FXI to overcome its current difficulties and reach its full potential. We deposited the data in the Coherent X-ray Database (CXIDB) and made our data analysis code available in a public repository. We developed algorithms targeted towards the needs of FXI experiments and implemented a software package which enables the analysis of diffraction data in real time. X-ray ptychography has developed into a very useful tool for quantitative imaging of complex materials and has found applications in many areas. However, it involves a computational reconstruction step which can be slow. Therefore, we developed a fast GPU-based ptychographic solver and combined it with a framework for real-time data processing which already starts the ptychographic reconstruction process while data is still being collected. This provides immediate feedback to the user and allows high-throughput ptychographic imaging. Finally, we have used ptychographic imaging as a method to study the wavefront of a focused XFEL beam under typical FXI conditions.  We are convinced that this work on developing strategies and algorithms for FXI and ptychography is a valuable contribution to the development of coherent diffractive imaging.

The newly emerging technology of X-ray free-electron lasers (XFELs) has the potential to revolutionise molecular imaging. XFELs generate very intense X-ray pulses and predictions suggest that they may be used for structure determination to atomic resolution even for single molecules. XFELs produce femtosecond pulses that outrun processes of radiation damage and permit the study of structures at room temperature and of structural dynamics. While the first demonstrations of flash X-ray diffractive imaging (FXI) on biological particles were encouraging, they also revealed technical challenges. In this work we demonstrated how some of these challenges can be overcome. We exemplified, with heterogeneous cell organelles, how tens of thousands of FXI diffraction patterns can be collected, sorted, and analysed in an automatic data processing pipeline. We improved  image resolution and reduced problems with missing data. We validated, described, and deposited the experimental data in the Coherent X-ray Imaging Data Bank. We demonstrated that aerosol injection can be used to collect FXI data at high hit ratios and with low background. We reduced problems with non-volatile sample contaminants by decreasing aerosol droplet sizes from ~1000 nm to ~150 nm. We achieved this by adapting an electrospray aerosoliser to the Uppsala sample injector. Mie scattering imaging was used as a diagnostic tool to measure positions, sizes, and velocities of individual injected particles. XFEL experiments generate large amounts of data at high rates. Preparation, execution, and data analysis of these experiments benefits from specialised software. In this work we present new open-source software tools that facilitates prediction, online-monitoring, display, and pre-processing of XFEL diffraction data. We hope that this work is a valuable contribution in the quest of transitioning FXI from its first experimental demonstration into a technique that fulfills its potentials.