Figure 5.

(a–d) Comparison of the ‘diagonal’ (solid line) and ‘off-diagonal’ terms (dashed line) in the intensity correlations (first and second terms after the last equality sign in (6.1)). These lines suggest although the ‘off-diagonal’ terms tend to dominate the measurable angular correlation functions, they tend to be of a relatively simple form (in this case, a constant as a function of angle Δρ, a fact that will probably allow their isolation, and hence removal. The remaining ‘diagonal’ terms contain the structural information of a single particle, as illustrated in (e–h). (e–h) Comparison of J(q, q’, Δϕ) curves obtained from a single particle per snapshot, and from five randomly oriented particles per snapshot (appropriately divided by 5). These calculations were performed for the small protein chignolin (PDB entry 1 UAO), but illustrate the general point that the sum of the diagonal terms in J (i.e. the intensity correlations from scattering by the same particles) are essentially independent of the number of such particles per snapshot (to within a factor of N, the number of particles per snapshot, even if the particles are randomly oriented). The radii q and q’ of the resolution rings are chosen randomly from our range (up to a maximum value q_max = 2π/5 Å⁻¹, or 5 Å resolution) to demonstrate that the result is essentially independent of the precise values of q and q’. (Online version in colour.)