X-Ray Cross-Correlation Analysis of Disordered Ensembles of Particles: Potentials and Limitations

Figure 5

(a)–(f) Statistical convergence of the amplitudes |⟨𝐶^𝑛_𝑞1,𝑞2⟩_𝑀| and phases arg[⟨𝐶^𝑛_𝑞1,𝑞2⟩_𝑀] at 𝑞₁=0.25nm⁻¹, 𝑞₂=0.09nm⁻¹, 𝑛=4,8,14, and 16, calculated as a function of the number of diffraction patterns 𝑀 used in the averaging. (g)–(i) The phases arg[⟨𝐶^𝑛1,𝑛2_{𝑞1,𝑞2,𝑞3}⟩_𝑀] at 𝑞₁=0.23nm⁻¹, 𝑞₂=0.24nm⁻¹, and 𝑞₃=0.25nm⁻¹, calculated for three different combinations of 𝑛₁ and 𝑛₂ as a function of 𝑀. Simulations were performed (a), (d), (g) without noise, (b), (e), (h) for the incident photon fluence 4⋅10¹⁰photons/𝜇m², and (c), (f), (i) for the photon fluence 4⋅10¹¹photons/𝜇m², and the scattered intensity is expressed in photon counts. In (b), (e), (h), and (c), (f), (i) Poisson noise was included.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)