The aims of the Centre depend on understanding the interaction of the field with the molecules, and on being able to interpret the diffracted data when it is acquired. This program will provide this capability.

Algorithms: The first aim of the program will be to continue our development of the algorithmic approaches to coherent diffractive imaging and to optimise the methods. In particular, we have obtained results that indicate that the use of phase-curved beams leads to a much more reliable image reconstruction and more rapid convergence . This aim will be completed by the end of year 1 and will feed into the Experimental X-ray Program concerned with imaging nanostructures. We note also that the development of computational algorithms is rather removed from the experimental implementation of the methods and so the Theory and Modelling program will at all times take responsibility for ensuring that the recovery methods are robust with respect to the experimental realities of the program. Conventional diffraction depends for its success on the amplification of the diffracted signal due to the structural periodicity of the sample, and for the structure to have sufficient long-range periodicity for the assumptions of conventional crystallography to apply. Small crystals may be formed but not diffract sufficiently strongly to give a clear periodic diffraction pattern and thus the recovery of the structure by conventional inversion techniques is precluded. The development of approaches to extract structural information from these systems is another major aim of this program, which is to say that we will seek to develop ab-initio phase determination from Small Angle X-ray Scattering (SAXS) data. The recent work on non-crystallographic diffraction lays a sound basis for this aim. The Experimental Methods Program will deliver non-crystalline but orientated samples and the Biological Sciences Program will deliver two-dimensional crystalline samples. Both of these will be very weakly diffracting and algorithms for combining multiple noisy data sets will be required. This will be done by drawing on methods developed in the electron diffraction community.

Coherence Physics: The whole Centre is based on a deep understanding of what can be achieved with coherent optics, including an understanding of such exotic phenomena as x-ray phase discontinuities. This work, which currently exists as part of Nugent Federation Fellowship program, will continue as a fundamental physical underpinning of the work. The overall aim is to ask how much information can realistically be extracted from a coherent or partially coherent wavefield. In the context of much of the thinking in the field of diffraction, partial coherence is considered a disadvantage, with the emphasis on source development being towards the development of ever more coherent sources. However it is well-established that wide-field microscopy is best performed using partially coherent light, a reflection of the fact that the information capacity of partially coherent fields can be far greater that that of coherent fields. This raises the issue of whether there are benefits in a partially coherent field for diffraction physics. The analysis will no doubt have an added complexity, but the information yielded may be greater.

Molecular Modelling: The response of a sample to the electric field of a beam generated by a third-generation synchrotron source is routinely modelled as a "weak perturbation" to the underlying electronic structure. For a biomolecular sample, this involves an electronic description that is essentially nonrelativistic in character and that is decoupled in lowest order from the description of the incident radiation field. The use of X-FEL radiation will require, in contrast, a greatly increased understanding of the fundamental physical interactions between radiation and matter if it is to be used as a tool in biomolecular imaging. The peak electric field strength of an intense X-ray laser source is estimated to be 10¹³-10¹⁴Vm^-1, which is more than sufficient to overwhelm the Coulomb field of the nuclei of first-row elements. This profoundly modifies the electronic structure of the sample, invalidating the weak field approximation inherent in conventional X-ray diffraction studies, and necessitating a coupled description of the matter and radiation. The acceleration of the electrons by the oscillating electromagnetic field of an X-ray laser pulse is sufficiently large that a relativistic dynamical treatment is required, and the large-amplitude excursions caused by the field oscillations invalidates the use of the dipole approximation to describe the matter-radiation interaction, so that retardation corrections must be included. While the theory describing the time-dependent evolution of the coupled matter-radiation system is well-developed for one-electron systems , the consistent inclusion of relativistic, many-body and retardation effects presents a significant theoretical and computational challenge to attempts to model complex systems. As an example, studies of exposure of material samples to intense VUV laser radiation have yielded some surprising results. Perhaps the most counterintuitive of these is that the rate of photionization may decrease from a peak value as the intensity is increased, indicating intensity stabilization of the system. The response of the system and any stabilization depends critically on features such as the oscillation frequency and the shape of the pulse. In the context of X-ray imaging studies these are open questions that can be answered only by detailed modelling of the matter-radiation dynamics.