Ewald sphere, but in general we will use $\textbf{q}$ to be a general three-dimensional vector and $I(\textbf{q})$ is a three-dimensional function. The atomic scattering factor $f(q,t)$ depends upon the ionization state of the atom, which changes as a function of time. The ionic scattering factors can be calculated using Slater orbitals[@Slater1930] and we use $f_0(q)$ to denote the atomic scattering factor of the unionized atom. We assume that the probability of an ion having a particular ionization state at time $t$ is independent of where that atom is located in the sample. Although the ionization state as a function of time is different for each atom, statistically atoms of the same atomic species are assumed to be equivalent. We write $A(q)$ and $B(q)$ as a function of the magnitude of the scattering vector, $q$, because we assume the atomic scattering factors are spherically symmetric.

Consider an ensemble of 2D diffraction measurements, each with a unique damage scenario. For 3D imaging, the data needs to be assembled into a 3D intensity volume using an algorithm that accounts for the unknown molecular orientations. The desired solution of the algorithm is an average intensity, where each 2D measurement is correctly placed according to 