to recover the initial position **R** of each atom in the sample. For simplicity, we will give equations for the case of a single atomic species, noting that the generalization to multiple atomic species is similar to that found in Ref. [@Quiney2011]. The intensity of a single measurement of a single molecule can be written $$I(\textbf{q}) = r_e^2 P(\textbf{q}) d\Omega I_0 \left[ \sum_{i=1}^N A_{i}(q) + 2 \sum_{i=1}^N \sum_{j=1}^{i-1} B_{ij}(\textbf{q}) \right] \;,
\label{eq:I}$$ where $\textbf{q}$ is the scattering vector with magnitude $q$, $d\Omega$ is the solid-angle term, $r_e$ is the classical electron radius, $N$ is the number of atoms and $P(\textbf{q})$ is a polarization term that will be ignored in this discussion. To simplify mathematical notation, we assume the incident intensity takes a uniform value $I_0$ for the duration of the pulse. We have defined $$A_{i}(q) = \int_0^T |f_i(q,t)|^2  dt \;
\label{eq:Ai}$$ and $$\begin{aligned}
B_{ij}(\textbf{q}) &=  \int_0^T f_i(q,t) f_j(q,t) \cos[ 2 \pi \textbf{q} \cdot (\textbf{R}_i - \textbf{R}_j + \bm{\epsilon}_i(t) - \bm{\epsilon}_j(t))] dt \;,
\label{eq:Bij}\end{aligned}$$ where $\bm{\epsilon}_i(t)$ is the displacement of the $i^{th}$ atom from its initial position and $T$ is the duration of the pulse. For a single two-dimensional measurement, it is understood that $\textbf{q}$ is sampled at points on the 