Figure 2
Mosaic rotational model used for (a) image simulation and (b) data analysis. To create each simulated image, the crystal volume is broken into 25 separately rotated mosaic domains of equal volume, each of which diffracts independently, with the final diffraction representing a sum over all contributions [equation (6) ]. Each of the 25 domains has a slightly perturbed orientation with respect to the randomly chosen reference orientation of the crystal as a whole [equation (5) ]. (a) illustrates the ensemble of these perturbations, plotting the action of the 25 rotation matrices UD on x^, y^ and z^ unit vectors attached to the reference crystal, with displacements expressed in degrees, while (b) represents the 200 domains used for data analysis. A critical assumption is that the crystal contains a smooth continuum of domain orientations, thus satisfying the Bragg diffraction condition over a range of incident energies. If the number of domains were small (ND ≪ 25) or the distribution of perturbations non-Gaussian, then it would be difficult to find mutual scaling factors for the diffraction from different energy channels of the SASE pulse. For simplicity, the same ensemble of 25 perturbations UD was used for all image simulations; however, this did not prevent the simulated data from being successfully analyzed under the assumption of a smooth distribution. |