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Scattering by large particles with Monte-Carlo integration

Reference: Monte-Carlo

This example demonstrates that for large particles (~$1000$ nm) the contribution to the scattered intensity from the form factor oscillates rapidly within one detector bin and analytical calculations (performed for the bin center) give completely a wrong intensity pattern. In this case Monte-Carlo integrations over detector bin should be used.

The simulation generates four plots using different sizes of the particles, (radius $=10$ nm, height $=20$ nm) or (radius $=1$ $\mu$m, height $=2$ $\mu$m), and different calculation methods: analytical calculations or Monte-Carlo integration. The other parameters are identical:

  • The sample is made of a monodisperse distribution of cylinders, deposited randomly on a substrate.
  • There is no interference between the scattered waves.
  • The wavelength is equal to 0.1 nm.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.

Real-space model

Intensity image
auto/Examples/scatter2d/LargeParticlesFormfactor.py