### Beam divergence

By default, the incident beam is perfectly monochromatic and collimated. Here we show how to set finite distributions of wavelengths and of incident angles.

• The wavelength follows a log-normal distribution around the mean value of $1$ $\unicode{x212B}$ with a scale parameter equal to $0.1$.
• Both incident angles follow a Gaussian distribution around the average values $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$, respectively and $\sigma_{\alpha_i} = \sigma_{\phi_i} = 0.1^{\circ}$.

The DWBA simulation is shown for a standard sample model:

• The sample is composed of monodisperse cylinders deposited on a substrate.
• The cylinders are dilute and distributed at random, hence there is no interference between scattered waves.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66  """ Cylinder form factor in DWBA with beam divergence """ import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with uncorrelated cylinders on a substrate. """ # defining materials m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0) m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8) m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8) # collection of particles cylinder_ff = ba.FormFactorCylinder(5*nm, 5*nm) cylinder = ba.Particle(m_particle, cylinder_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder, 1.0) # assembling the sample air_layer = ba.Layer(m_ambience) air_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_substrate) multi_layer = ba.MultiLayer() multi_layer.addLayer(air_layer) multi_layer.addLayer(substrate_layer) return multi_layer def get_simulation(): """ Returns a GISAXS simulation with beam (+ divergence) and detector defined. """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(100, 0.0*deg, 2.0*deg, 100, 0.0*deg, 2.0*deg) simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg) wavelength_distr = ba.DistributionLogNormal(1.0*angstrom, 0.1) alpha_distr = ba.DistributionGaussian(0.2*deg, 0.1*deg) phi_distr = ba.DistributionGaussian(0.0*deg, 0.1*deg) simulation.addParameterDistribution("*/Beam/Wavelength", wavelength_distr, 5) simulation.addParameterDistribution("*/Beam/InclinationAngle", alpha_distr, 5) simulation.addParameterDistribution("*/Beam/AzimuthalAngle", phi_distr, 5) return simulation def run_simulation(): """ Runs simulation and returns intensity map. """ simulation = get_simulation() simulation.setSample(get_sample()) print(simulation.treeToString()) print(simulation.parametersToString()) simulation.runSimulation() return simulation.result() if __name__ == '__main__': result = run_simulation() ba.plot_simulation_result(result) 
BeamDivergence.py