Figure 1. Schematics of the wide-angle scattering experiment.

In Born’s approximation, the far-field scattering intensity reads I(q)∝|∫ρ(r)e^iqrd³r|², where ρ(r) is the scattering density of the particle centered at r=0. After decomposing r into components parallel (r_||) and perpendicular (r_⊥) to the projection vector n_p=k_in+q/2, which is by definition perpendicular to q, the intensity can be recast as , representing the Fourier transform of the projected density ρ(r_⊥)=∫ρ(r)dr_|| on a plane with normal vector n_p. (a) For small scattering angles, the approximation n_p||k_in is valid, which inhibits access to any structural information along this direction. (b) The variation of n_p with q for large scattering angles provides access to the 3D properties of the particle. (c) In the experiment, single-shot diffraction patterns of silver particles intersecting the FEL photon beam are captured by the 2D detector.